Validation of linear regression models

• 成果类型: Article
• 署名作者: Dette, H; Munk, A
• 署名单位: Ruhr University Bochum
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 778-800
• 关键词: GOODNESS-OF-FIT; Nonparametric Regression; nonlinear-regression; diagnostics; bioavailability; EQUIVALENCE; EQUALITY; variance; CURVES; tests

摘要

A new test is proposed in order to verify that a regression function, say g, has a prescribed (Linear) parametric form. This procedure is based on the large sample behavior of an empirical L-2-distance between g and the subspace U spanned by the regression functions to be verified. The asymptotic distribution of the test statistic is shown to be normal with parameters depending only on the variance of the observations and the L-2-distance between the regression function g and the model space U. Based on this result, a test is proposed for the hypothesis that g is not in a preassigned L-2-neighborhood of U, which allows the verification of the model U at a controlled type I error rate. The suggested procedure is very easy to apply because of its asymptotic normal law and the simple form of the test statistic. In particular, it does not require nonparametric estimators of the regression function and hence, the test does not depend on the subjective choice of smoothing parameters.