Parametric and semiparametric hypotheses in the linear model
نویسندگان
چکیده
The independent additive errors linear model consists of a structure for the mean and a separate structure for the error distribution. The error structure may be parametric or it may be semiparametric. Under alternative values of the mean structure, the best fitting additive errors model has an error distribution which can be represented as the convolution of the actual error distribution and the marginal distribution of a misspecification term. The model misspecification term results from the covariates’ distribution. Conditions are developed to distinguish when the semiparametric model yields sharper inference than the parametric model and vice-versa. The main conditions concern the actual error distribution and the covariates’ distribution. The theoretical results explain a paradoxical finding in semiparametric Bayesian modelling, where the posterior distribution under a semiparametric model is found to be more concentrated than is the posterior distribution under a corresponding parametric model. The paradox is illustrated on a set of allometric data.
منابع مشابه
Model Selection for Semiparametric Bayesian Models with Application to Overdispersion
In analyzing complicated data, we are often unwilling or not confident to impose a parametric model for the data-generating structure. One important example is data analysis for proportional or count data with overdispersion. The obvious advantage of assuming full parametric models is that one can resort to likelihood analyses, for instance, to use AIC or BIC to choose the most appropriate regr...
متن کاملRidge Stochastic Restricted Estimators in Semiparametric Linear Measurement Error Models
In this article we consider the stochastic restricted ridge estimation in semipara-metric linear models when the covariates are measured with additive errors. The development of penalized corrected likelihood method in such model is the basis for derivation of ridge estimates. The asymptotic normality of the resulting estimates are established. Also, necessary and sufficient condition...
متن کاملGeneralized 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 کاملTesting Generalized Linear and Semiparametric Models Against Smooth Alternatives
We propose goodness of t tests for testing generalized linear models and semiparametric regression models against smooth alternatives The focus is on models having both continuous and factorial covariates As smooth extension of a parametric or semiparametric model we use generalized varying coe cient models as proposed by Hastie Tibshirani A likelihood ratio statistic is used for testing and as...
متن کاملSemiparametric Single Index versus Fixed Link Function Modelling
Discrete choice models are frequently used in statistical and econometric practice. Standard models such as logit models are based on exact knowledge of the form of the link and linear index function. Semiparametric models avoid possible mis-speciication but often introduce a computational burden. It is therefore interesting to decide between approaches. Here we propose a test of semiparametric...
متن کامل