Spline estimation of generalized additive models is considered here. Cross-validation is used as a criterion of model estimation. Some computationally simpler approximations to cross-validation are given.

Optimal interpolation designs are given for estimation of the value of a linear functional of an unknown polynomial mean. For example, optimal designs are given for estimation of the average value of a multivariate polynomial over a sphere of radius a r when observations are available only in...

Given data, uj,yj,j=1,...,n, with uj an input sequence to a system while output is yj, an approximation to the structure of the system generating yj is to be obtained by regressing yj on uj-i,yj-ii=1,...,pn, where pn increases with n. In this paper the rate of convergence of the coefficient...

In a general multiparameter setup, this paper proves an optimality property of Rao's test, in terms of maximization of "average" third-order power under contiguous alternatives, within a very wide class of tests that includes the likelihood ratio and Wald's tests. The use of a new kind of...

The Brunn-Minkowski inequality asserts a concavity feature of the volume functional under convex addition of sets. Among its applications has been Anderson's treatment of multivariate densities. Here we present a generalization which interprets the inequality in terms of random sets. This...

In this note we settle a question posed by Kasahara, Maejima, and Vervaat. We show that the [alpha]-stable Lévy motion is the only (1/[alpha])-self-similar [alpha]-stable process with stationary increments if 0 [alpha] 1. We also introduce new classes of (1/[alpha])-self-similar...

The predictive ratio is considered as a measure of spread for the predictive distribution. It is shown that, in the exponential families, ordering according to the predictive ratio is equivalent to ordering according to the posterior covariance matrix of the parameters. This result generalizes...

We establish certain general characterization results on elliptically symmetric distributions and exchangeable random variables. These results yield, in particular, the results given earlier by Maxwell, Bartlett, Kingman, Ali, Smith, Arnold and Lynch, and several others.

Application of exact Bahadur efficiencies in testing theory or exact inaccuracy rates in estimation theory needs evaluation of large deviation probabilities. Because of the complexity of the expressions, frequently a local limit of the nonlocal measure is considered. Local limits of large...

The paper extends the results of Khatri to complex elliptical variates. Asymptotic confidence bounds on location parameters for the linear growth curve for the complex variates, the asymptotic distribution of the canonical correlations for the two sets of complex variates, and the asymptotic...