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Semiparametric additive models under symmetric distributions

Content Provider	Springer Nature Link
Author	Ibacache Pulgar, Germán Paula, Gilberto A. Cysneiros, Francisco José A.
Copyright Year	2012
Abstract	In this paper we discuss estimation and diagnostic procedures in semiparametric additive models with symmetric errors in order to permit distributions with heavier and lighter tails than the normal ones, such as Student-t, Pearson VII, power exponential, logistics I and II, and contaminated normal, among others. Such models belong to the general class of statistical models GAMLSS proposed by Rigby and Stasinopoulos (Appl. Stat. 54:507–554, 2005). A back-fitting algorithm to attain the maximum penalized likelihood estimates (MPLEs) by using natural cubic smoothing splines is presented. In particular, the score functions and Fisher information matrices for the parameters of interest are expressed in a similar notation of that used in parametric symmetric models. Sufficient conditions on the existence of the MPLEs are presented as well as some inferential results and discussions on degrees of freedom and smoothing parameter estimation. Diagnostic quantities such as leverage, standardized residual and normal curvatures of local influence under two perturbation schemes are derived. A real data set previously analyzed under normal linear models is reanalyzed under semiparametric additive models with symmetric errors.
Starting Page	103
Ending Page	121
Page Count	19
File Format	PDF
ISSN	11330686
Journal	Test
Volume Number	22
Issue Number	1
e-ISSN	18638260
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-10-03
Publisher Institution	Spanish Society of Statistics and Operations Research
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Back-fitting algorithm Cubic smoothing splines Non-parametric models Robust estimates Student-t models Data analysis Nonparametric regression Diagnostics Statistics Statistical Theory and Methods Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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