Efficient estimation and inferences for varying-coefficient models. (English) Zbl 0999.62052

Cai, Zongwu; Fan, Jianqing; Li, Runze

J. Am. Stat. Assoc. 95, No. 451, 888-902 (2000).

Summary: This article deals with statistical inferences based on the varying-coefficient models proposed by T. Hastie and R. Tibshirani [J. R. Stat. Soc., Ser. B 55, No. 4, 757-796 (1993; Zbl 0796.62060)]. Local polynomial regression techniques are used to estimate coefficient functions, and the asymptotic normality of the resuling estimators is established. The standard error formulas for estimated coefficients are derived and are empirically tested. A goodness-of-fit test technique, based on a nonparametric maximum likelihood ratio type of test, is also proposed to detect whether certain coefficient functions in a varying-coefficient model are constant or whether any covariates are statistically significant in the model. The null distribution of the test is estimated by a conditional bootstrap method.
Our estimation techniques involve solving hundreds of local likelihood equations. To reduce the computational burden, a one-step Newton-Raphson estimator is proposed and implemented. The resulting one-step procedure is shown to save computational cost on an order of tens with no deterioration in performance, both asymptotically and empirically. Both simulated and real data examples are used to illustrate our proposed methodology.

MSC:

62J12	Generalized linear models (logistic models)
62G10	Nonparametric hypothesis testing
65C60	Computational problems in statistics (MSC2010)

Keywords:

asymptotic normality; bootstrap; goodness-of-fit; local polynomial fitting; one-step procedure

Citations:

Zbl 0796.62060

Software:

KernSmooth