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Efficient Statistical Inference Procedures for Partially Nonlinear Models and their Applications
Author(s) -
Li Runze,
Nie Lei
Publication year - 2008
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2007.00937.x
Subject(s) - inference , statistical inference , computer science , nonlinear system , machine learning , econometrics , artificial intelligence , mathematics , statistics , physics , quantum mechanics
Summary Motivated by an analysis of a real data set in ecology, we consider a class of partially nonlinear models where both a nonparametric component and a parametric component are present. We develop two new estimation procedures to estimate the parameters in the parametric component. Consistency and asymptotic normality of the resulting estimators are established. We further propose an estimation procedure and a generalized F ‐test procedure for the nonparametric component in the partially nonlinear models. Asymptotic properties of the newly proposed estimation procedure and the test statistic are derived. Finite sample performance of the proposed inference procedures are assessed by Monte Carlo simulation studies. An application in ecology is used to illustrate the proposed methods.