Semiparametric inference with kernel likelihood

We study a class of semiparametric likelihood models in which parameters are incorporated explicitly, with the unknown likelihood specified nonparametrically by the kernel estimator. The maximum likelihood estimator (MLE) under this semiparametric model is used for inference of the parameters. The method is a generalisation of the semiparametric regression model we proposed recently. Such semiparametric models are robust, and MLEs under these likelihoods are shown to be consistent, asymptotic normal with rate √n and possess Wilks property.

[1]  A. Yuan,et al.  Semiparametric Regression with Kernel Error Model , 2006 .

[2]  P. Hall,et al.  On the estimation of entropy , 1993 .

[3]  W. J. Hall,et al.  Information and Asymptotic Efficiency in Parametric-Nonparametric Models , 1983 .

[4]  C. J. Stone,et al.  Adaptive Maximum Likelihood Estimators of a Location Parameter , 1975 .

[5]  H. Joe.  Estimation of entropy and other functionals of a multivariate density , 1989 .

[6]  S. Cosslett.  Efficient Semiparametric Estimation of Censored and Truncated Regressions via a Smoothed Self‐Consistency Equation , 2004 .

[7]  Art B. Owen,et al.  Empirical Likelihood for Linear Models , 1991 .

[8]  Jianqing Fan,et al.  Generalized likelihood ratio statistics and Wilks phenomenon , 2001 .

[9]  L. Devroye.  The Equivalence of Weak, Strong and Complete Convergence in $L_1$ for Kernel Density Estimates , 1983 .

[10]  Thomas M. Stoker,et al.  Semiparametric Estimation of Index Coefficients , 1989 .

[11]  R. Beran.  An Efficient and Robust Adaptive Estimator of Location , 1978 .

[12]  Constance Van Eeden,et al.  Efficiency-Robust Estimation of Location , 1970 .

[13]  R. Spady,et al.  AN EFFICIENT SEMIPARAMETRIC ESTIMATOR FOR BINARY RESPONSE MODELS , 1993 .

[14]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

[15]  Jianqing Fan,et al.  Robust Non-parametric Function Estimation , 1994 .

[16]  Chunrong Ai,et al.  A Semiparametric Maximum Likelihood Estimator , 1997 .

[17]  R. Carroll,et al.  Locally Efficient Estimators for Semiparametric Models With Measurement Error , 2006 .

[18]  P. Bickel.  Efficient and Adaptive Estimation for Semiparametric Models , 1993 .

[19]  Young K. Truong,et al.  ROBUST NONPARAMETRIC FUNCTION ESTIMATION , 1994 .

[20]  Ing Rj Ser.  Approximation Theorems of Mathematical Statistics , 1980 .

[21]  W. Newey,et al.  Semiparametric Efficiency Bounds , 1990 .

[22]  P. Hall.  On powerful distributional tests based on sample spacings , 1986 .

[23]  S. S. Wilks.  The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses , 1938 .

[24]  R. Berk,et al.  Limiting Behavior of Posterior Distributions when the Model is Incorrect , 1966 .

[25]  P. J. Huber.  The behavior of maximum likelihood estimates under nonstandard conditions , 1967 .

[26]  J. Pfanzagl.  On the measurability and consistency of minimum contrast estimates , 1969 .

[27]  Jianqing Fan,et al.  Censored Regression - Local Linear-approximations and Their Applications , 1994 .

[28]  Jon A. Wellner,et al.  Semiparametric models: progress and problems , 1985 .