Superiority comparisons between mixed regression estimators

This paper gives necessary and sufficient conditions for a mixed regression estimator to be superior to another mixed estimator. The comparisons are based on the mean square error matrices of the estimators. Both estimators are allowed to be biased.     

The estimation of derivatives of a nonparametric regression function when the data are correlated

A kernel estimator of a derivative of arbitrary order of a nonparametric average population curve is considered for a correlated-errors model with balanced replicate measurements at each design point. Asymptotic expansions of the mean squared error are derived for two classes of correlation functions in the model. Consistency, choice of smoothing parameter, and rates of convergence are examined for the important special cases of estimating the first and second derivatives.     

Half-sample variance estimation

This paper studies an alternative to the jackknife variance estimator, the half-sample variance estimator. Both theoretical and Monte Carlo comparisons between the half-sample variance estimator and the jackknife variance estimator indicate that the former is better in some situations.     

Considerations for optimal nonparametric regression under a generalizederror structure

Nonparametric smoothing, such as kernel or spline estimation, has been examined extensively under the assumption of uncorrelated errors. This paper addresses the effects of potential correlation on consistency and other asymptotic properties in a repeated-measures model, using directly optimized linear smoothers of the replicate means. Unrestricted optimal weights, with respect to squared error loss, are used to confirm a lack of consistency for all linear estimators in an autocorrelated errors model. The results indicate kernel methods that work well for an uncorrelated errors model may not have the ability to perform satisfactorily when correlation is introduced, due to an asymmetry in the optimal weights, which disappears for an uncorrelated errors model. These would include data-driven bandwidth selection methods, adjustments of the bandwidth to accommodate correlation, higher-order kernels, and related bias reduction techniques. The analytic results suggest alternative approaches, not considered here in detail, which have shown merit.     

Maximal inequalities for partial sums of independent random vectors with multi dimensional time parameters

We obtain upper and lower bounds on the distribution of the partial sums constructed from a multi-dimensional array of independent random vectors. These bounds include, among others, generalizations of some of the well known classical inequalities such as the converse Kolmogorov and the Skorokhod-Ottaviani maximal inequalities.     

Estimation of the smaller and larger of two exponential location parameters

Assume independent random samples are drawn from two populations which are exponentially distributed with unknown location parameters and a common known scale parameter. We want to estimate the maximum and the minimum of the unknowo location paremeters. In this paper several estimators are proposed which are better than the natural estimations in terms of absolute bias and /or meaqn squared error.     

MSE-matrix superiority of the mixed over the least squares estimator in the presence of outliers

In his recent paper, Ali (1991) has shown that the mixed regression estimator, when data contain mean-shift or variance inflation outliers, is uniformly superior to the ordinary least squares estimator in terms of scalar-valued mean square error. However, when using the matrix-valued mean square error criterion, this dominance fails to hold in general. The subsequent investigation gives a complete characterization of the situation where the mixed estimator is superior to the LS-estimator when the comparison is made with respect to this stronger MSE-property. Vice versa, the LS-estimator never dominates the mixed estimator relative to this criterion.     

An alternative approach to variable selection for prediction

A procedure for selecting a subset of predictor variables in regression analysis is suggested. The procedure is so designed that it leads to the selection of a subset of variables having an adequate degree of informativeness with a directly specified confidence coefficient. Some examples are considered to illustrate the application of the procedure.     

On the almost unbiased generalized liu estimator and unbiased estimation of the bias and mse

In this paper, we derive the almost unbiased generalized Liu estimator and examine an exact unbiased estimator of the bias and mean squared error of the feasible generalized Liu estimator . We compare the almost unbiased generalized Liu estimator (AUGLE) with the generalized Liu estimator (GLE) and with the ordinary least squares estimator (OLSE).     

Assessment of modeling longitudinal binary data based on graphical methods

Longitudinal categorical data are commonly applied in a variety of fields and are frequently analyzed by generalized estimating equation (GEE) method. Prior to making further inference based on the GEE model, the assessment of model fit is crucial. Graphical techniques have long been in widespread use for assessing the model adequacy. We develop alternative graphical approaches utilizing plots of marginal model-checking condition and local mean deviance to assess the GEE model with logit link for longitudinal binary responses. The applications of the proposed procedures are illustrated through two longitudinal binary datasets.