{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T03:13:49Z","timestamp":1770693229356,"version":"3.49.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,5,26]],"date-time":"2025-05-26T00:00:00Z","timestamp":1748217600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,5,26]],"date-time":"2025-05-26T00:00:00Z","timestamp":1748217600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>In this paper, the problem of robust estimation and validation of location-scale families is revisited. The proposed methods exploit the joint asymptotic normality of sample quantiles (of <jats:italic>i.i.d.<\/jats:italic> random variables) to construct the ordinary and generalized least squares estimators of location and scale parameters. These <jats:italic>quantile least squares<\/jats:italic> (QLS) estimators are easy to compute because they have explicit expressions, their robustness is achieved by excluding extreme quantiles from the least-squares estimation, and efficiency is boosted by using as many non-extreme quantiles as practically relevant. The influence functions of the QLS estimators are specified and plotted for several location-scale families. They closely resemble the shapes of some well-known influence functions yet those shapes emerge automatically (i.e., do not need to be specified). The joint asymptotic normality of the proposed estimators is established and their finite-sample properties are explored using simulations. Also, computational costs of these estimators, as well as those of MLE, are evaluated for sample sizes <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$n = 10^6, 10^7, 10^8, 10^9$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:msup>\n                      <mml:mn>10<\/mml:mn>\n                      <mml:mn>6<\/mml:mn>\n                    <\/mml:msup>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:msup>\n                      <mml:mn>10<\/mml:mn>\n                      <mml:mn>7<\/mml:mn>\n                    <\/mml:msup>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:msup>\n                      <mml:mn>10<\/mml:mn>\n                      <mml:mn>8<\/mml:mn>\n                    <\/mml:msup>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:msup>\n                      <mml:mn>10<\/mml:mn>\n                      <mml:mn>9<\/mml:mn>\n                    <\/mml:msup>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. For model validation, two goodness-of-fit tests are constructed and their performance is studied using simulations and real data. In particular, for the daily stock returns of Google over the years 2020-2023, both tests strongly support the logistic distribution assumption and reject other bell-shaped competitors.<\/jats:p>","DOI":"10.1007\/s11222-025-10626-6","type":"journal-article","created":{"date-parts":[[2025,5,26]],"date-time":"2025-05-26T10:53:12Z","timestamp":1748256792000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quantile least squares: a flexible approach for robust estimation and validation of location-scale families"],"prefix":"10.1007","volume":"35","author":[{"given":"Mohammed","family":"Adjieteh","sequence":"first","affiliation":[]},{"given":"Vytaras","family":"Brazauskas","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,26]]},"reference":[{"issue":"2","key":"10626_CR1","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/0378-3758(89)90115-8","volume":"22","author":"MM Ali","year":"1989","unstructured":"Ali, M.M., Umbach, D.: A Shapiro-Wilk type goodness-of-fit test using a few order statistics. 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