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.

Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describ...

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...

Various linear models may be specified when attempting to estimate an apparent linear trend in real data sets, based on assumptions about the possibly unknown mechanism for generating the data. However, in many cases the best-fit line obtained from implementation of the specified model does not agree at all with the apparent trend in a scatterplot of the data, based on the evident geometric str...

introduction: in spite of improving the water productivity due to development in water infrastructure systems, population increasing causing the water withdrawal is triple in the last fifty years. in this situation competition on water consumption especially in the agricultural sector which is the biggest consumer in the world and also in iran is a severe problem. water allocation has been asse...