Supplementary Materials to Semiparametric Analysis of Heterogeneous Data Using Varying-Scale Generalized Linear Models
نویسندگان
چکیده
The supplementary materials are a full Appendix of the paper. It includes two parts: Appendix A contains an additional theorem on asymptotic expansions of λ θ (z) and λ (1) θ (z), two related corollaries, and their proofs. Appendix B contains proofs of the three theorems in the paper. In Appendix A.1, we provide an additional theorem on asymptotic expansions of the local maximum likelihood estimator λ θ (z), as well as its derivative with respect to θ θ, λ (1) θ (z). The asymptotic expansions of w θ (z) and w (1) θ (z), and their uniform bounds are provided in Corollaries A1 and A2, respectively. Proofs of this theorem and the two corollaries are outlined in Appendix A.2. A.1 Asymptotic Expansions of λ θ , λ (1) θ And w θ , w (1) θ. The following theorem holds under some mild conditions. Theorem A. Let K(t) be a symmetric kernel function. Suppose b = O(n −ξ), 1/6 < ξ < 1/4 and H is invertible. For any given β β ∈ B n (r), δ δ ∈ ˜ B n (˜ r) and z 0 , we have the following asymptotic expansions: J(λ θ − λ) = {H −1 + o(1)} 1 n n j=1 J −1 z j,0 {y j − µ(w (0) j η (0) j + ˜ η (0) j)}η (0) j τ (w (0) j η (0) j + ˜ η (0) j)K b (z j − z 0) + b 2 2 w (2) (z 0)f z (z 0)γ(z 0) υ 2 0 + 1 0 w (0) (z 0)f z (z 0){γ γ 1 (z 0)} T (β β − β β 0) + 1 0 f z (z 0){˜γ γ 1 (z 0)} T (δ δ − δ δ 0) + o p (1 √ n) and J λ (1) θ = {H −1 + o(1)} − 1 n n j=1 J −1 z j,0 w (0) j x T j v j
منابع مشابه
Semiparametric Analysis of Heterogeneous Data Using Varying-Scale Generalized Linear Models.
This article describes a class of heteroscedastic generalized linear regression models in which a subset of the regression parameters are rescaled nonparametrically, and develops efficient semiparametric inferences for the parametric components of the models. Such models provide a means to adapt for heterogeneity in the data due to varying exposures, varying levels of aggregation, and so on. Th...
متن کاملGeneralized varying coefficient partially linear measurement errors models
We study generalized varying coefficient partially linearmodels when some linear covariates are error prone, but their ancillary variables are available. We first calibrate the error-prone covariates, then develop a quasi-likelihood-based estimation procedure. To select significant variables in the parametric part, we develop a penalized quasi-likelihood variable selection procedure, and the re...
متن کاملWeb-based Supplementary materials for: “Semiparametric Analysis of Linear Transformation Models with Covariate Measurement Errors”
متن کامل
Generalized Ridge Regression Estimator in Semiparametric Regression Models
In the context of ridge regression, the estimation of ridge (shrinkage) parameter plays an important role in analyzing data. Many efforts have been put to develop skills and methods of computing shrinkage estimators for different full-parametric ridge regression approaches, using eigenvalues. However, the estimation of shrinkage parameter is neglected for semiparametric regression models. The m...
متن کاملVarying Index Coefficient Models
It has been a long history of using interactions in regression analysis to investigate alterations in covariate-effects on response variables. In this article, we aim to address two kinds of new challenges arising from the inclusion of such high-order effects in the regression model for complex data. The first kind concerns a situation where interaction effects of individual covariates are weak...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008