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Anal."],"published-print":{"date-parts":[[2023,2,28]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we analyze a method for approximating the distribution function and density of a random variable that depends in a nontrivial way on a possibly high number of independent random variables, each with support on the whole real line. Starting with the integral formulations of the distribution and density, the method involves smoothing the original integrand by preintegration with respect to one suitably chosen variable, and then applying a suitable quasi\u2013Monte Carlo method to compute the integral of the resulting smoother function. Interpolation is then used to reconstruct the distribution or density on an interval. The preintegration technique is a special case of conditional sampling, a method that has previously been applied to a wide range of problems in statistics and computational finance. In particular, the pointwise approximation studied in this work is a specific case of the conditional density estimator previously considered by L\u2019Ecuyer, Puchhammer, and Ben Abdellah INFORMS J. Comput., 34 (2022), pp. 1729\u20131748]. Our theory provides a rigorous regularity analysis of the preintegrated function, which is then used to show that the errors of the pointwise and interpolated estimators can both achieve nearly first-order convergence. Numerical results support the theory.<\/jats:p>","DOI":"10.1137\/21m146658x","type":"journal-article","created":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T14:38:16Z","timestamp":1677076696000},"page":"135-166","source":"Crossref","is-referenced-by-count":4,"title":["Analysis of Preintegration Followed by Quasi\u2013Monte Carlo Integration for Distribution Functions and Densities"],"prefix":"10.1137","volume":"61","author":[{"given":"Alexander D.","family":"Gilbert","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, UNSW Sydney, Sydney NSW 2052, Australia."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Frances Y.","family":"Kuo","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, UNSW Sydney, Sydney NSW 2052, Australia."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ian H.","family":"Sloan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, UNSW Sydney, Sydney NSW 2052, Australia."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,2,23]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/110855909"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-41095-6_9"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S1748499517000252"},{"key":"ref4","first-page":"1","author":"Bayer C.","year":"2022","journal-title":"Quant. 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Y. Kuo , Lattice Rule Generating Vectors, https:\/\/web.maths.unsw.edu.au\/\u223cfkuo\/lattice\/index.html."},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jco.2009.07.005"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.46.9.1214.12231"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.2021.1135"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jco.2014.02.004"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970081"},{"key":"ref26","doi-asserted-by":"crossref","unstructured":"Y. Peng , \nM. Fu , \nJ. Hu , \nP. L\u2019Ecuyer , and \nB. Tuffin , Variance Reduction for Generalized Likelihood Ratio Method by Conditional Monte Carlo and Randomized Quasi-Monte Carlo, hal-03196379, 2021.","DOI":"10.1016\/j.jmse.2022.02.002"},{"key":"ref27","volume-title":"Approximation Theory and Practice","author":"Trefethen L. 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