Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model

This paper studies the estimation of a varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model [Fan and Huang, Manuscript, University of North Carolina, Chapel Hill, USA, 2002]. We focus on the case where some covariates are measured with additive errors. The usual profile least squares and local polynomial estimations lead to biased estimators of the parametric and nonparametric components, respectively, when measurement errors are ignored. By correcting the attenuation we propose a modified profile least squares estimator for the parametric component and a local polynomial estimator for the nonparametric component. We show that the former is consistent, asymptotically normal and achieves the rate in the law of the iterated logarithm, and the latter achieves the optimal strong convergence rate of the usual nonparametric regression. In addition, a consistent estimator is also developed for the error variance. These results can be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators

Statistical inference of partially linear regression models with heteroscedastic errors

The authors study a heteroscedastic partially linear regression model and develop an inferential procedure for it. This includes a test of heteroscedasticity, a two-step estimator of the heteroscedastic variance function, semiparametric generalized least-squares estimators of the parametric and nonparametric components of the model, and a bootstrap goodness of fit test to see whether the nonparametric component can be parametrized

Tests of Transformation in Nonlinear Regression

This paper presents three versions of the Lagrange multiplier (LM) tests of transformation in nonlinear regression: (i) LM test based on expected information, (ii) LM test based on Hessian, and (iii) the LM test based on gradient. All three tests can be easily implemented through a nonlinear least squares procedure. Simulation results show that, in terms of finite sample performance, the LM test based on expected information is the best, followed by the LM test based on Hessian and then the LM test based on gradient. The LM test based on gradient can perform rather poorly. An example is given for illustration

Case deletion diagnostics in multilevel models

AbstractThis paper studies case deletion diagnostics for multilevel models. Using subset deletion, diagnostic measures for identifying influential units at any level are developed for both fixed and random parameters. Two approximate update formulae are derived. The first formula uses one-step approximation, while the second formula also includes the impact of estimating the random parameter. Two examples are used to illustrate the methodology developed

Geometric Ergodicity of Nonlinear Autoregressive Models With Changing Conditional Variances

The authors give easy-to-check su#cient conditions for the geometric ergodicity and the finiteness of the moments of a random process x t = #(x t-1,...,x t-p)+# t #(x t-1,...,x t-q) in which # : IR p # IR, # : IR q # IR and (# t ) is a sequence of independent and identically distributed random variables. They deduce strong mixing properties for this class of nonlinear autoregressive models with changing conditional variances which includes, among others, the ARCH(p), the AR(p)-ARCH(p), and the double-threshold autoregressive models. R ESUM E Les auteurs enoncent des conditions faciles averifier qui garantissent l'ergodicitegeometrique et la finitude des moments d'un processus aleatoire x t = #(x t-1,...,x t-p)+ # t #(x t-1 ,...,x t-q)d efini a partir de fonctions # : IR p # IR, # : IR q # IR et d'une suite (# t )d'aleas independants de meme loi. Ils en deduisent des proprietes de melangeance forte pour cette classe de modeles autoregressifs non lineaires a variances condi..