The problem of estimation of the nite dimensional parameter in a partial linear model is considered. We derive upper and lower bounds for the second minimax order risk and show that the second order minimax estimator is a penalized maximum likelihood estimator. It is well known that the performance of the estimator is depending on the choice of a smoothing parameter. We propose a practically fe...

In linear models with hierarchical interaction structures product type designs are shown to be D{optimal simultaneously for the whole parameter vector and for testing against any hierarchical submodel. Moreover, product type designs are also q {optimal for the highest order interactions.

ALEXANDER AUE0, LAJOS HORVÁTH1, MARIE HUŠKOVÁ2 AND PIOTR KOKOSZKA3 0Department of Mathematical Sciences, Clemson University, O-324 Martin Hall, Clemson, SC 29634, USA E-mail: [email protected] 1Department of Mathematics, University of Utah, 155 South 1440 East, Salt Lake City, UT 84112–0090, USA E-mails: [email protected] and [email protected] 2Department of Statistics, Charles University...

Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the virtues of the ellipse and her higher-dimensional cousins for both these purposes in a variety of contexts, including linear models, multivariate linear models ...

This is an expanded version of Wooldridge (2003), which provided an overview of cluster-sample methods in linear models. Here I include additional details for linear models and provide, as much as possible, a parallel treatment for nonlinear models, including a summary of strategies for dealing with data sets having a small number of clusters.

Several new tests are proposed for examining the adequacy of a family of parametric models against large nonparametric alternatives. These tests formally check if the bias vector of residuals from parametric Ž ts is negligible by using the adaptive Neyman test and other methods. The testing procedures formalize the traditional model diagnostic tools based on residual plots. We examine the rates...

Hierarchical linear models with a block circular covariance structure are considered. Sufficient conditions for obtaining explicit and unique estimators for the variance-covariance components are derived. Different restricted models are discussed and maximum likelihood estimators are presented.

We introduce a new class of functional generalized linear models, where the response is a scalar and some of the covariates are functional. We assume that the response depends on multiple covariates, a finite number of latent features in the functional predictor, and interaction between the two. To achieve parsimony, the interaction between the multiple covariates and the functional predictor i...

Some physically relevant non-linear models with solitons, which have target space S 2 , are known to have submodels with infinitly many conservation laws defined by the eikonal equation. Here we calculate all the symmetries of these models and their submodels by the prolongation method. We find that for some models, like the Baby Skyrme model, the submodels have additional symmetries, whereas f...