The construction of confidence regions for parameter vectors is a difficult problem in the nonparametric setting, particularly when the sample size is not large. We focus on bootstrap ellipsoidal confidence regions. The bootstrap has shown promise in solving this problem, but empirical evidence...

In a variety of statistical problems one needs to solve an equation in order to get an estimator. We consider the large sample properties of such estimators generated from samples that are not necessarily identically distributed. Very general assumptions that lead to the existence, strong...

Let (X1, Y1), (X2, Y2), ..., be d+1 dimensional random vectors which are distributed as (X, Y). Let [theta](x) be the conditional median, that is, [theta](x)=inf{y: P(Y[less-than-or-equals, slant]y | X=x)[greater-or-equal, slanted]1/2}. We consider the problem of...

For a distribution [mu] on the unit interval we define the associated perpetuity [Psi]([mu]) as the distribution of 1+X1+X1X2+X1X2X3+..., where (Xn)n[set membership, variant] is a sequence of independent random variables with distribution [mu]. Such quantities arise in insurance mathematics and...

We report a matrix expression for the covariance matrix of MLEs of factor loadings in factor analysis. We then derive the analytical formula for covariance matrix of the covariance estimators of MLEs of factor loadings by obtaining the matrix of partial derivatives, which maps the differential...

The varying-coefficient model is an attractive alternative to the additive and other models. One important method in estimating the coefficient functions in this model is the local polynomial fitting approach. In this approach, the choice of bandwidth is crucial. If the unknown curve is spatial...

Consider the partial linear models of the formY=X[tau][beta]+g(T)+e, where thep-variate explanatoryXis erroneously measured, and bothTand the responseYare measured exactly. LetXbe the surrogate variable forXwith measurement error. Let the primary data set be that containing independent...

This paper studies a semi-linear errors-in-variables model of the formYi=x'i[beta]+g(Ti)+ei,Xi=xi+ui(1[less-than-or-equals, slant]i[less-than-or-equals, slant]n). The estimators of parameters[beta],[sigma]2and of the smooth functiongare derived by using the nearest neighbor-generalized least...

Consider the linear models of the form Y=X[tau][beta]+[var epsilon] with the response Y censored randomly on the right and X measured erroneously. Without specifying any error models, in this paper, a semiparametric method is applied to the estimation of the parametric vector [beta] with the...

It is well known that a bivariate distribution belongs to the domain of attraction of an extreme value distribution G if and only if the marginals belong to the domain of attraction of the univariate marginal extreme value distributions and the dependence function converges to the stable tail...