Goodness-of-Fit Tests for Parametric Regression Models

• Published in: Journal of the American Statistical Association Vol. 96; no. 454; pp. 640 - 652
• Main Authors: Fan, Jianqing, Huang, Li-Shan
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.06.2001; American Statistical Association; Taylor & Francis Ltd
• Subjects: Adaptive Neyman test; Contiguous alternatives; Data analysis; Estimators; Exact sciences and technology; Fourier transformations; General topics; Goodness of fit; Linear inference, regression; Linear models; Linear regression; Mathematics; Model testing; Nonparametric inference; Null hypothesis; Parametric models; Partial linear model; Power; Probability and statistics; Regression analysis; Sciences and techniques of general use; Statistical analysis; Statistical models; Statistical variance; Statistics; Theory and Methods; Threshing; Wavelet thresholding; F test; Neyman Pearson detection; Generalized linear model; Threshold detection; Bias; Non parametric estimation; Regression residual; Adaptive method; Linear model; Hypothesis test; Statistical test; Neyman test; Distribution function; Test method; Linear estimation; Test power; Test statistic; Linear regression; Goodness of fit test; Order statistic; Statistical estimation; Statistical method; Statistical regression; Wavelets; Regression model; Wavelet thresholding; Graphic method; Biased estimation
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214501753168316

Several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives. These tests formally check if the bias vector of residuals from parametric fits is negligible by using the adaptive Neyman test and other methods. The testing procedures formalize the traditional model diagnostic tools based on residual plots. We examine the rates of contiguous alternatives that can be detected consistently by the adaptive Neyman test. Applications of the procedures to the partially linear models are thoroughly discussed. Our simulation studies show that the new testing procedures are indeed powerful and omnibus. The power of the proposed tests is comparable to the F-test statistic even in the situations where the F test is known to be suitable and can be far more powerful than the F-test statistic in other situations. An application to testing linear models versus additive models is also discussed.