We discuss optimal design problems for a popular method of series estimation in regression problems. Commonly used design criteria are based on the generalized variance of the estimates of the coefficients in a truncated series expansion and do not take possible bias into account. We present a...

Two robust estimators of a matrix-valued location parameter are introduced and discussed. Each is the average of the members of a subsample–typically of covariance or cross-spectrum matrices–with the subsample chosen to minimize a function of its average. In one case this function is the...

Equality and proportionality of the ordinary least-squares estimator (OLSE), the weighted least-squares estimator (WLSE), and the best linear unbiased estimator (BLUE) for X[beta] in the general linear (Gauss-Markov) model are investigated through the matrix rank method.

We study and compare methods of covariance matrix estimation, and some diagnostic procedures, to accompany generalized ("Bounded Influence") M-estimation of regression in the linear model. The methods derive from one-step approximations to the delete-one estimates of the regression parameters....

We obtain designs which are optimally robust against possibly misspecified regression models, assuming that the parameters are to be estimated by one of several types of M-estimation. Such designs minimize the maximum mean squared error of the predicted values, with the maximum taken over a...

For the approximately linear model , with i.i.d. errors [epsilon]i and fixed carriers z(xi), we establish the asymptotic normality of a generalized M-estimator of regression/scale. The estimator minimizes a weighted Huber-Dutter loss function. The function fn(x) contributes a bias term to the...

We construct minimax robust designs for estimating wavelet regression models. Such models arise from approximating an unknown nonparametric response by a wavelet expansion. The designs are robust against errors in such an approximation, and against heteroscedasticity. We aim for exact, rather...

Experimentation in scientific or medical studies is often carried out in order to model the 'success' probability of a binary random variable. Experimental designs for the testing of lack of fit and for estimation, for data with binary responses depending upon covariates which can be controlled...