{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T10:38:02Z","timestamp":1742380682904,"version":"3.32.0"},"reference-count":93,"publisher":"Elsevier","isbn-type":[{"type":"print","value":"9780444862174"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1982]]},"DOI":"10.1016\/s0169-7161(82)02006-9","type":"book-chapter","created":{"date-parts":[[2005,4,18]],"date-time":"2005-04-18T19:58:53Z","timestamp":1113854333000},"page":"61-100","source":"Crossref","is-referenced-by-count":13,"title":["3 Large sample approximations and asymptotic expansions of classification statistics"],"prefix":"10.1016","author":[{"given":"Minoru","family":"Siotani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0169-7161(82)02006-9_bib1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1093\/biomet\/59.1.19","article-title":"Separate sample logistic discrimination","volume":"59","author":"Anderson","year":"1972","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib2","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/BF02313425","article-title":"Classification by multivariate analysis","volume":"16","author":"Anderson","year":"1951","journal-title":"Psychometrika"},{"year":"1958","series-title":"An Introduction to Multivariate Statistical Analysis","author":"Anderson","key":"10.1016\/S0169-7161(82)02006-9_bib3"},{"key":"10.1016\/S0169-7161(82)02006-9_bib4","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1214\/aos\/1176342518","article-title":"An asymptotic expansion of the distribution of the studentized classification statistic","volume":"1","author":"Anderson","year":"1973","journal-title":"Ann. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib5","series-title":"Discriminant Analysis and Applications","first-page":"17","article-title":"Asymptotic evaluation of the probabilities of misclassification by linear discriminant functions","author":"Anderson","year":"1973"},{"key":"10.1016\/S0169-7161(82)02006-9_bib6","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1214\/aoms\/1177704568","article-title":"Classification into two multivariate normal distributions with different covariance matrices","volume":"33","author":"Anderson","year":"1962","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib7","series-title":"Studies in Item Analysis and Prediction","first-page":"169","article-title":"On classification based on response to N dichotomous items","author":"Bahadur","year":"1961"},{"key":"10.1016\/S0169-7161(82)02006-9_bib8","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1093\/biomet\/52.3-4.653","article-title":"Bounds in a minimax classification procedure","volume":"52","author":"Banerjee","year":"1965","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib9","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1093\/biomet\/50.1-2.17","article-title":"Discrimination in the case of zero mean differences","volume":"50","author":"Bartlett","year":"1963","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib10","series-title":"Studies in Item Analysis and Prediction","first-page":"285","article-title":"A representation of Hotelling's T2 and Anderson's classification statistic W in terms of simple statistics","author":"Bowker","year":"1961"},{"key":"10.1016\/S0169-7161(82)02006-9_bib11","series-title":"Studies in Item Analysis and Prediction","first-page":"293","article-title":"An asymptotic expansion for the distribution function of the W-classification statistic","author":"Bowker","year":"1961"},{"key":"10.1016\/S0169-7161(82)02006-9_bib12","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1080\/01621459.1974.10482949","article-title":"Classification based on dichotomous and continuous variables","volume":"69","author":"Chang","year":"1974","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02006-9_bib13","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1093\/biomet\/47.1-2.185","article-title":"Geometry and linear discrimination","volume":"47","author":"Clunies-Ross","year":"1960","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib14","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF02868561","article-title":"Comparison of two methods of handling covariates in discriminatory analysis","volume":"16","author":"Cochran","year":"1964","journal-title":"Ann. Inst. Statist. Math."},{"key":"10.1016\/S0169-7161(82)02006-9_bib15","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1214\/aoms\/1177730242","article-title":"Discriminant functions with covariance","volume":"19","author":"Cochran","year":"1946","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib16","doi-asserted-by":"crossref","first-page":"10","DOI":"10.2307\/2527493","article-title":"Some classification problems with multivariate qualitative data","volume":"17","author":"Cochran","year":"1961","journal-title":"Biometrics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib17","first-page":"215","article-title":"The hyperplane in pattern recognition","volume":"5","author":"Cooper","year":"1962","journal-title":"Cybernetica"},{"key":"10.1016\/S0169-7161(82)02006-9_bib18","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/S0019-9958(62)90641-1","article-title":"The hypersphere in pattern recognition","volume":"5","author":"Cooper","year":"1962","journal-title":"Information and Control"},{"key":"10.1016\/S0169-7161(82)02006-9_bib19","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1093\/biomet\/50.3-4.439","article-title":"Statistical classification with quadratic forms","volume":"50","author":"Cooper","year":"1963","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib20","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1109\/TIT.1965.1053760","article-title":"Quadratic discriminant functions in pattern recognition","volume":"11","author":"Cooper","year":"1965","journal-title":"IEEE Trans. Inform. Theory"},{"key":"10.1016\/S0169-7161(82)02006-9_bib21","series-title":"Research Papers in Statistics: Festschrift for J. Neyman","first-page":"55","article-title":"Some procedures associated with the logistic qualitative response curve","author":"Cox","year":"1966"},{"key":"10.1016\/S0169-7161(82)02006-9_bib22","doi-asserted-by":"crossref","first-page":"113","DOI":"10.2307\/2346482","article-title":"The analysis of multivariate binary data","volume":"21","author":"Cox","year":"1972","journal-title":"Appl. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib23","doi-asserted-by":"crossref","first-page":"1174","DOI":"10.1214\/aoms\/1177699990","article-title":"Optimum classification rules for classification into two multivariate normal populations","volume":"36","author":"Das Gupta","year":"1965","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib24","series-title":"Discriminant Analysis and Applications","first-page":"77","article-title":"Theories and methods in classification: A review","author":"Das Gupta","year":"1973"},{"key":"10.1016\/S0169-7161(82)02006-9_bib25","doi-asserted-by":"crossref","first-page":"313","DOI":"10.2307\/2528164","article-title":"A general maximum likelihood discriminant","volume":"23","author":"Day","year":"1967","journal-title":"Biometrics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib26","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1080\/01621459.1978.10481574","article-title":"On the performance of some multinomial classification rules","volume":"73","author":"Dillon","year":"1978","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02006-9_bib27","series-title":"Studies in Item Analysis and Prediction","first-page":"276","article-title":"An expansion principle for distribution functions with applications to Student's statistic and the one-dimensional classification statistic","author":"Elfving","year":"1961"},{"key":"10.1016\/S0169-7161(82)02006-9_bib28","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1111\/j.1469-1809.1936.tb02137.x","article-title":"The use of multiple measurements in taxonomic problems","volume":"7","author":"Fisher","year":"1936","journal-title":"Ann. Eugenics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib29","first-page":"658","article-title":"On the expected error in the probability of misclassification","volume":"53","author":"Friedman","year":"1965"},{"key":"10.1016\/S0169-7161(82)02006-9_bib30","series-title":"Essays in Probability and Statistics","first-page":"305","article-title":"The ML classification statistic in covariate discriminant analysis and its asymptotic expansions","author":"Fujikoshi","year":"1976"},{"key":"10.1016\/S0169-7161(82)02006-9_bib31","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1080\/01621459.1968.10480936","article-title":"On discrimination using qualitative variables","volume":"63","author":"Gilbert","year":"1968","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02006-9_bib32","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1080\/01621459.1972.10481213","article-title":"Sample-based classification procedures derived from density estimators","volume":"67","author":"Glick","year":"1972","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02006-9_bib33","doi-asserted-by":"crossref","first-page":"241","DOI":"10.2307\/2529389","article-title":"Sample-based multinomial classification","volume":"29","author":"Glick","year":"1973","journal-title":"Biometrics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib34","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1207\/s15327906mbr1102_3","article-title":"An approximate test for comparative discriminatory power","volume":"11","author":"Goldstein","year":"1976","journal-title":"Multiv. Behav. Res."},{"key":"10.1016\/S0169-7161(82)02006-9_bib35","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1207\/s15327906mbr1203_5","article-title":"A two-group classification procedure for multivariate dichotomous responses","volume":"12","author":"Goldstein","year":"1977","journal-title":"Multiv. Behav. Res."},{"key":"10.1016\/S0169-7161(82)02006-9_bib36","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1080\/01621459.1975.10480302","article-title":"Selection of variates for the two-group multinomial classification problem","volume":"70","author":"Goldstein","year":"1975","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02006-9_bib37","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1093\/biomet\/55.3.586","article-title":"A note on discrimination in the case of unequal covariance matrices","volume":"55","author":"Han","year":"1968","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib38","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1214\/aoms\/1177697602","article-title":"Distribution of discriminant function when covariance matrices are proportional","volume":"40","author":"Han","year":"1969","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib39","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/BF02506327","article-title":"Distribution of discriminant function in circular models","volume":"22","author":"Han","year":"1970","journal-title":"Ann. Inst. Statist. Math."},{"key":"10.1016\/S0169-7161(82)02006-9_bib40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1966.tb00614.x","article-title":"Allocation rules and their error rates","volume":"28","author":"Hills","year":"1966","journal-title":"J. Roy. Statist. Soc. Ser. B"},{"key":"10.1016\/S0169-7161(82)02006-9_bib41","doi-asserted-by":"crossref","first-page":"237","DOI":"10.2307\/2985920","article-title":"Discrimination and allocation with discrete data","volume":"16","author":"Hills","year":"1967","journal-title":"Appl. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib42","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1214\/aoms\/1177698251","article-title":"Generalized asymptotic expansions of Cornish-Fisher type","volume":"39","author":"Hill","year":"1968","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib43_1","first-page":"301","article-title":"On some classification problems, I, II","volume":"22","author":"John","year":"1960","journal-title":"Sankhy\u0101"},{"key":"10.1016\/S0169-7161(82)02006-9_bib43_2","first-page":"309","article-title":"On some classification problems, I, II","volume":"22","author":"John","year":"1960","journal-title":"Sankhy\u0101"},{"key":"10.1016\/S0169-7161(82)02006-9_bib44","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF02868645","article-title":"On classification by the statistics R and Z","volume":"14","author":"John","year":"1963","journal-title":"Ann. Inst. Statist. Math."},{"key":"10.1016\/S0169-7161(82)02006-9_bib45","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1093\/biomet\/36.1-2.149","article-title":"Systems of frequency curves gerated by methods of translation","volume":"36","author":"Johnson","year":"1949","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib46","first-page":"7","article-title":"The asymptotic cut-off point and comparison of error probabilities in covariate discriminant analysis","volume":"9","author":"Kanazawa","year":"1979","journal-title":"J. Japan Statist. Soc."},{"key":"10.1016\/S0169-7161(82)02006-9_bib47","first-page":"81","article-title":"The distribution of the Studentized classification statistics W* in covariate discriminant analysis","volume":"7","author":"Kanazawa","year":"1977","journal-title":"J. Japan Statist. Soc."},{"year":"1979","series-title":"Comparison of the three procedures in covariate discriminant analysis","author":"Kanazawa","key":"10.1016\/S0169-7161(82)02006-9_bib48"},{"key":"10.1016\/S0169-7161(82)02006-9_bib49","doi-asserted-by":"crossref","first-page":"925","DOI":"10.2307\/2283885","article-title":"The estimation of probability densities and cumulatives by Fourier series methods","volume":"63","author":"Kronmal","year":"1968","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02006-9_bib50","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1080\/01621459.1975.10480303","article-title":"Discrimination and classification using both binary and continuous variables","volume":"70","author":"Krzanowski","year":"1975","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02006-9_bib51","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1080\/01621459.1976.10480957","article-title":"Canonical representation of the location model for discrimination or classification","volume":"71","author":"Krzanowski","year":"1976","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02006-9_bib52","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1080\/00401706.1977.10489527","article-title":"The performance of Fisher's linear discriminant function under non-optimal conditions","volume":"19","author":"Krazanowski","year":"1977","journal-title":"Technometrics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib53","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1214\/aoms\/1177729487","article-title":"An application of information theory to multivariate analysis, I","volume":"23","author":"Kullback","year":"1952","journal-title":"Ann. Math. Statist."},{"year":"1959","series-title":"Information Theory and Statistics","author":"Kullback","key":"10.1016\/S0169-7161(82)02006-9_bib54"},{"key":"10.1016\/S0169-7161(82)02006-9_bib55","first-page":"96","article-title":"The classificatory problem viewed as a two-decision problem","volume":"13","author":"Kudo","year":"1959","journal-title":"Mem. Fac. Sci. Kyushu Univ. Ser. A."},{"key":"10.1016\/S0169-7161(82)02006-9_bib56","first-page":"63","article-title":"The classificatory problem viewed as a two-decision problem, II","volume":"14","author":"Kudo","year":"1960","journal-title":"Mem. Fac. Sci. Kyushu Univ. Ser. A"},{"key":"10.1016\/S0169-7161(82)02006-9_bib57","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1080\/03610927308827006","article-title":"Robustness of the linear and quadratic discriminant functions to certain types of non-normality","volume":"1","author":"Lachenbruch","year":"1973","journal-title":"Comm. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib58","doi-asserted-by":"crossref","first-page":"657","DOI":"10.2307\/1266637","article-title":"Discriminant analysis when the initial samples are misclassified","volume":"8","author":"Lachenbruch","year":"1966","journal-title":"Technometrics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib59","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00401706.1968.10490530","article-title":"Estimation of error rates in discriminant analysis","volume":"10","author":"Lachenbruch","year":"1968","journal-title":"Technometrics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib60","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1007\/BF02613873","article-title":"Zur Wahl von Variablen in der Trennanalyse","volume":"4","author":"Linhart","year":"1961","journal-title":"Metrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib61","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/BF02863571","article-title":"Decision rule, based on the distance, for the classification problem","volume":"8","author":"Matusita","year":"1956","journal-title":"Ann. Inst. Statist. Math."},{"key":"10.1016\/S0169-7161(82)02006-9_bib62","first-page":"299","article-title":"Classification based on distance in multivariate Gaussian cases","volume":"1","author":"Matusita","year":"1967"},{"key":"10.1016\/S0169-7161(82)02006-9_bib63","doi-asserted-by":"crossref","first-page":"203","DOI":"10.2307\/2528968","article-title":"Probability models, estimation and classification for multivariate dichotomous populations","volume":"28","author":"Martin","year":"1972","journal-title":"Biometrics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib64","series-title":"Dissertation submitted in partial fulfillment of Ph. D. requirements","article-title":"Comparison of the W* and Z* procedures in covariate discriminant analysis","author":"McGee","year":"1976"},{"key":"10.1016\/S0169-7161(82)02006-9_bib65","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1080\/00401706.1972.10488926","article-title":"Asymptotic results for discriminant analysis when the initial samples are misclassified","volume":"14","author":"McLachlan","year":"1972","journal-title":"Technometrics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib66","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1111\/j.1467-842X.1973.tb00201.x","article-title":"An asymptotic expansion of the expectation of the estimated error rate in discriminant analysis","volume":"15","author":"McLachlan","year":"1973","journal-title":"Austral. J. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib67","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1093\/biomet\/61.1.131","article-title":"The asymptotic distributions of the conditional error rate and risk in discriminant analysis","volume":"61","author":"McLachlan","year":"1974","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib68","doi-asserted-by":"crossref","first-page":"239","DOI":"10.2307\/2529646","article-title":"An asymptotic unbiased technique for estimating the error rates in discriminant analysis","volume":"30","author":"McLachlan","year":"1974","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib69","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1080\/00401706.1974.10489183","article-title":"Estimation of the errors of misclassification on the criterion of asymptotic mean square error","volume":"16","author":"McLachlan","year":"1974","journal-title":"Technometrics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib70","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1080\/00401706.1974.10489239","article-title":"The relationship in terms of asymptotic mean square error between the seperate problems of estimating each of the three types of error rate of the linear discriminant function","volume":"16","author":"McLachlan","year":"1974","journal-title":"Technometrics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib71","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1093\/biomet\/63.2.239","article-title":"The bias of the apparent error rate in discriminant analysis","volume":"63","author":"McLachlan","year":"1976","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib72","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1080\/03610927708827515","article-title":"Constrained sample discrimination with the Studentized classification statistic W","volume":"6","author":"McLachlan","year":"1977","journal-title":"Comm. Statist. A \u2014 Theory Methods"},{"key":"10.1016\/S0169-7161(82)02006-9_bib73","series-title":"Ph. D. Dissertation","article-title":"Z statistic in discriminant analysis","author":"Memon","year":"1968"},{"key":"10.1016\/S0169-7161(82)02006-9_bib74","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1214\/aoms\/1177696794","article-title":"The classification statistic W* in covariate discriminant analysis","volume":"41","author":"Memon","year":"1970","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib75","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/0047-259X(71)90004-2","article-title":"Asymptotic expansion of the distribution of the Z statistic in discriminant analysis","volume":"1","author":"Memon","year":"1971","journal-title":"J. Multivariate Anal."},{"key":"10.1016\/S0169-7161(82)02006-9_bib76","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1080\/01621459.1973.10482440","article-title":"Evaluation of five discrimination procedures for binary variables","volume":"68","author":"Moore","year":"1973","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02006-9_bib77","first-page":"1","article-title":"Discrimination for variance matrices","volume":"13","author":"Okamoto","year":"1961","journal-title":"Osaka Math. J."},{"key":"10.1016\/S0169-7161(82)02006-9_bib78","doi-asserted-by":"crossref","first-page":"1286","DOI":"10.1214\/aoms\/1177703864","article-title":"An asymptotic expansion for the distribution of the linear discriminant function","volume":"34","author":"Okamoto","year":"1963","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib79","doi-asserted-by":"crossref","first-page":"1358","DOI":"10.1214\/aoms\/1177698265","article-title":"Correction to \u201cAn asymptotic expansion for the distribution of the linear discriminant function\u201d","volume":"39","author":"Okamoto","year":"1968","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib80","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1214\/aoms\/1177705052","article-title":"Multivariate correlation models with mixed discrete and continuous variables","volume":"32","author":"Olkin","year":"1961","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib81","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1080\/01621459.1976.10480356","article-title":"Some classification procedures for multivariate binary data using orthogonal functions","volume":"71","author":"Ott","year":"1976","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/S0169-7161(82)02006-9_bib82","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1214\/aoms\/1177728653","article-title":"A general theory of discrimination when the information about alternative population distributions is based on samples","volume":"25","author":"Rao","year":"1954","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib83","first-page":"202","article-title":"The non-central x2 and F distributions and their applications","volume":"36","author":"Patnaik","year":"1949","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib84","first-page":"19","article-title":"Asymptotic approximations to the conditional distributions of the classification statistic Z and its Studentized form Z*","volume":"11","author":"Siotani","year":"1980","journal-title":"Tamkang. J. Math."},{"article-title":"Further expansion formulae for error rates and comparison of the W- and Z-procedures in discriminant analysis","year":"1975","author":"Siotani","key":"10.1016\/S0169-7161(82)02006-9_bib85"},{"key":"10.1016\/S0169-7161(82)02006-9_bib86","series-title":"Multivariate Analysis IV","first-page":"523","article-title":"Asymptotic expansions for error rates and comparison of the W-procedure and the Z-procedure in discriminant analysis","author":"Siotani","year":"1977"},{"key":"10.1016\/S0169-7161(82)02006-9_bib87","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1111\/j.1469-1809.1946.tb02368.x","article-title":"Some examples of discrimination","volume":"13","author":"Smith","year":"1947","journal-title":"Ann. Eugenics"},{"key":"10.1016\/S0169-7161(82)02006-9_bib88","series-title":"Studies in Item Analysis and Prediction","first-page":"177","article-title":"Classification procedures based on dichotomous response vectors","author":"Solomon","year":"1961"},{"key":"10.1016\/S0169-7161(82)02006-9_bib89","series-title":"Studies in Item Analysis and Prediction","first-page":"252","article-title":"Computation of an empirical sampling distribution for the W-classification statistic","author":"Teichroew","year":"1961"},{"key":"10.1016\/S0169-7161(82)02006-9_bib90","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1214\/aoms\/1177731280","article-title":"On a statistical problem arising in the classification of an individual into one of two groups","volume":"15","author":"Wald","year":"1944","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0169-7161(82)02006-9_bib91","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1093\/biomet\/42.1-2.151","article-title":"The autocorrelation function and the spectral density function","volume":"42","author":"Wise","year":"1955","journal-title":"Biometrika"},{"key":"10.1016\/S0169-7161(82)02006-9_bib92","first-page":"107","article-title":"The efficiency of a linear discriminant function for arbitrary distributions","volume":"6","author":"Zhezhel, Yu.","year":"1968","journal-title":"Engrg. Cybernetics"}],"container-title":["Handbook of Statistics","Classification Pattern Recognition and Reduction of Dimensionality"],"original-title":[],"language":"en","deposited":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T19:31:44Z","timestamp":1735673504000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0169716182020069"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982]]},"ISBN":["9780444862174"],"references-count":93,"URL":"https:\/\/doi.org\/10.1016\/s0169-7161(82)02006-9","relation":{},"ISSN":["0169-7161"],"issn-type":[{"type":"print","value":"0169-7161"}],"subject":[],"published":{"date-parts":[[1982]]}}}