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Estimating the Conditional Error Distribution in Non‐parametric Regression
Author(s) -
KIWITT SEBASTIAN,
NEUMEYER NATALIE
Publication year - 2012
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2011.00763.x
Subject(s) - mathematics , kernel regression , conditional probability distribution , empirical distribution function , covariate , statistics , parametric statistics , kernel (algebra) , asymptotic distribution , empirical likelihood , nonparametric regression , weak convergence , conditional expectation , kernel density estimation , kernel smoother , regression analysis , econometrics , regression , kernel method , computer science , artificial intelligence , computer security , combinatorics , estimator , radial basis function kernel , support vector machine , asset (computer security)
. We consider a general non‐parametric regression model, where the distribution of the error, given the covariate, is modelled by a conditional distribution function. For the estimation, a kernel approach as well as the (kernel based) empirical likelihood method are discussed. The latter method allows for incorporation of additional information on the error distribution into the estimation. We show weak convergence of the corresponding empirical processes to Gaussian processes and compare both approaches in asymptotic theory and by means of a simulation study.