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For multivariate nonlinear regression and multivariate generalized linear regression models, with repeated measurements and possible missing values, we derive the asymptotic normality of a general estimating equations estimator of the regression matrix. We also provide consistent estimators of the covariance matrix of the response vectors. In our setting both the response variable and the covariates may be multivariate. Furthermore, the regression parameters are allowed to be dependent on a finite number of time units or some other categorical variable. For example, one may test whether or not the parameter vectors are equal across the different time units. Missing values are permitted, though certainly are not necessary, in order for the asymptotic theory to hold. Herein, any missingness is allowed to depend upon the values of the covariates but not on the response variable. No distributional assumptions are made on the data.

In this article we develop a new test procedure for testing a linear hypothesis in a fixed effects linear model with heteroscedastic errors. This test is based on the ordinary least squares estimator (OLSE) of the regression parameter and uses the variance estimator of OLSE that accounts for heteroscedasticity. The null distribution of this statistics is approximated by a multiple of central F distribution. Simulation studies suggest that the new critical region performs well both in terms of size and power.

This article addresses the problem of constructing confidence intervals for ordered population means of k independent normal populations using jackknife and bootstrap methodologies. The goal is to achieve the nominal coverage probability with width of the interval no bigger than that of the standard confidence interval centered at the unrestricted maximum likelihood estimator (UMLE). Confidence intervals considered in this article are based on the point estimator introduced in Hwang and Peddada (1994). The methodology described in this article is applicable to a reasonably broad class of order restrictions. It is seen that the bootstrap procedures such as the percentile method, the BC method and the BCa method fail rather badly, while the confidence intervals based on weighted jackknife performs very well. Simulation studies suggest that the new procedure is robust even if the data are obtained from heavy tailed distributions such as t distribution with very small degrees of freedom.

This article deals with the confidence interval estimation of θ 1 , when the parameters θ 1 , θ 2 ,…, θ k of k populations are subject to some non-linear constraints. We shall consider two types of restrictions (a) θ belongs to a k -dimensional ball and (b) k =2 and θ 1 ⩽ φ ( θ 2 ), where φ(·) satisfies some conditions. In terms of coverage probability of the confidence intervals, it is seen in case of (a) that it does not always pay to use the additional information available on the parameter. This phenomena is also observed when the mean squared error criterion is considered.

Following the comments of Schenker (1985), Efron (1987) introduced the BCa methodology to construct confidence intervals. In this article we demonstrate that the BCa confidence intervals can degenerate with a very high probability if a ⩾ 0.4. On the other hand, if a is small it is not necessary that the BCa intervals perform better in the sense of the size of the confidence interval and/or the coverage probability. This is illustrated by considering the estimation of confidence intervals for the variance components in a two way analysis of variance model.