Consider the d-dimensional unit cube [0,1]d and portion it into n regions, A1,..., An. Select and fix a point in each one of these regions so we have x1,..., xn. Consider observable variables Yi, i = 1,..., n, satisfying the multivariate regression model Yi = g(xi) + [var epsilon]i, where g is...

This paper develops a semiparametric method for estimating the nonrandom part V(.) of a random utility function U(v, omega) - V(v) + e(omega) from data on discrete choice behavior. Here v and omega are, respectively, vectors of observable and unobservable attributes of an alternative, and...

I review issues related with the presence or absence of Gibbsianness in measures describing random fields in lattices. After a brief exposition of the definition and properties of Gibbs measures, I discuss the phenomenon of non-Gibbsianness, its examples, characterization, the proposed...

The problem of prediction is revisited with a view towards going beyond the typical nonparametric setting and reaching a fully model-free environment for predictive inference, i.e., point predictors and predictive intervals. A basic principle of model-free prediction is laid out based on the...

This article considers estimation of regression function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$f$$</EquationSource> </InlineEquation> in the fixed design model <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$Y(x_i)=f(x_i)+ \epsilon (x_i), i=1,\ldots ,n$$</EquationSource> </InlineEquation>, by use of the Gasser and Müller kernel estimator. The point set <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\{ x_i\}_{i=1}^{n}\subset [0,1]$$</EquationSource> </InlineEquation> constitutes the sampling design points, and <InlineEquation ID="IEq4"> <EquationSource...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

Consider a compound Poisson process which is discretely observed with sampling interval <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\Delta $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="normal">Δ</mi> </math> </EquationSource> </InlineEquation> until exactly <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>n</mi> </math> </EquationSource> </InlineEquation> nonzero increments are obtained. The jump density and the intensity of the Poisson process are unknown. In this paper, we build and study parametric estimators...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

The bootstrap method is based on resampling of the original randomsample drawn from a population with an unknown distribution. In the article it was shown that because of the progress in computer technology resampling is actually unnecessary if the sample size is not too large. It is possible to...