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Hössjer, OlaKarlsson, Måns
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Number of Authors: 22023 (English)In: Open Mathematics, ISSN 2391-5455, Vol. 21, no 1, article id 20220597Article, review/survey (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2023. Vol. 21, no 1, article id 20220597
##### Keywords [en]

bird phenology, coefficient of determination, L-functionals, L-statistics, order numbers, orthogonal series expansion, quantile function, quantile regression
##### National Category

Probability Theory and Statistics
##### Identifiers

URN: urn:nbn:se:su:diva-203755DOI: 10.1515/math-2022-0597ISI: 001053084400001Scopus ID: 2-s2.0-85170428452OAI: oai:DiVA.org:su-203755DiVA, id: diva2:1653221
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##### In thesis

In this article, we survey and unify a large class or L -functionals of the conditional distribution of the response variable in regression models. This includes robust measures of location, scale, skewness, and heavytailedness of the response, conditionally on covariates. We generalize the concepts of L -moments (G. Sillito, *Derivation of approximants to the inverse distribution function of a continuous univariate population from the order statistics of a sample*, Biometrika 56 (1969), no. 3, 641–650.), L -skewness, and L -kurtosis (J. R. M. Hosking, *L-moments: analysis and estimation of distributions using linear combinations or order statistics*, J. R. Stat. Soc. Ser. B Stat. Methodol. 52 (1990), no. 1, 105–124.) and introduce order numbers for a large class of L -functionals through orthogonal series expansions of quantile functions. In particular, we motivate why location, scale, skewness, and heavytailedness have order numbers 1, 2, (3,2), and (4,2), respectively, and describe how a family of L -functionals, with different order numbers, is constructed from Legendre, Hermite, Laguerre, or other types of polynomials. Our framework is applied to models where the relationship between quantiles of the response and the covariates follows a transformed linear model, with a link function that determines the appropriate class of L -functionals. In this setting, the distribution of the response is treated parametrically or nonparametrically, and the response variable is either censored/truncated or not. We also provide a framework for asymptotic theory of estimates of L -functionals and illustrate our approach by analyzing the arrival time distribution of migrating birds. In this context, a novel version of the coefficient of determination is introduced, which makes use of the abovementioned orthogonal series expansion.

1. Statistical Methods for Taxon Classification and Bird Migration Phenology$(function(){PrimeFaces.cw("OverlayPanel","overlay1653368",{id:"formSmash:j_idt1554:0:j_idt1559",widgetVar:"overlay1653368",target:"formSmash:j_idt1554:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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