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...

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...

We study the construction of experimental designs, the purpose of which is to aid in the discrimination between two possibly non-linear regression models, each of which might be only approximately specified. A rough description of our approach is that we impose neighbourhood structures on each...

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...