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Abstract: Necessary and sufficient conditions are derived for the equalities of the best linear unbiased estimators (BLUEs) of parametric functions under a general linear model and its restricted and stochastically restricted models to hold. [Copyright &y& Elsevier]

Abstract: Omelka [Omelka, M., 2007. Second-order linearity of Wilcoxon rank statistics. Ann. Inst. Statist. Math. 59, 385–402] proposed an alternative way of constructing a confidence interval based on -estimators for single parameters in linear models. We will compare this confidence interval with a traditional (Wald type) confidence interval theoretically as well as by means of a Monte Carlo experiment. As a by-product we will show the asymptotic normality of the estimator of proposed in [Koul, H.L., Sievers, G.L., McKean, J., 1987. An estimator of the scale parameter for the rank analysis of linear models under general score functions. Scand. J. Statist. 14, 131–141] under somewhat different assumptions from those in [Thewarepperuma, P.S., 1987. On estimation of some density functionals under regression and one sample models. Ph.D. Thesis. Michigan State University, Department of Statistics and Probability]. [Copyright &y& Elsevier]

Abstract: The method of least squares provides the most widely used algorithm for fitting a linear model. A variety of nonparametric procedures have been developed that are designed to be robust against model violations and resistant against aberrant points. One such method introduced by Theil [1950. A rank-invariant method of linear and polynomial regression analysis. I, II, III. Proc. Ned. Akad. Wet. 53, 386–392, 521–525, 1397–1412] is based on pairwise estimates. There are many examples in which the data are nonlinear, and in particular, where a quadratic fit may be more appropriate. We here propose a nonparametric method for fitting a quadratic regression. [Copyright &y& Elsevier]

Abstract: Reproductive dispersion linear models (RDLMs) include generalized linear model [Nelder and Wedderburn (1972). Generalized linear models. J. Roy. Statist. Soc. Ser. A 135, 370–384] as a special case. Some mild regularity conditions analogous to those given by Fahrmeir and Kaufmann [1985. Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. Ann. Statist. 13, 342–368] are proposed. On the basis of the proposed mild conditions, the existence, weak consistency, strong consistency, and asymptotic normality of the maximum likelihood estimate (MLE) are provided in RDLMs. The asymptotic results of Fahrmeir and Kaufmann [1985. Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. Ann. Statist. 13, 342–368] are generalized to RDLMs. [Copyright &y& Elsevier]

Abstract: An alternative criterion is presented for a linear function of the unknown parameters, in a linear model, to be estimable. If there is a linear relationship between members of a subset of the columns of the design matrix , then the parameters associated with all the columns in that subset are not estimable. Also any part of their linear relationship is non-estimable. [Copyright &y& Elsevier]