Models are studied where the response Y and covariates X, T are assumed to fulfill E(Y|X; T) = G{XT β + α + m1(T1) + … + md(Td)}. Here G is a known (link) function, β is an unknown parameter, and m1, …, md are unknown functions. In particular, we consider additive binary response models...

A procedure for testing the signicance of a subset of explanatory variables in a nonparametric regression is proposed. Our test statistic uses the kernel method. Under the null hypothesis of no effect of the variables under test, we show that our test statistic has a nhp2/2 standard normal...

The aim of this paper is to provide an alternative way of specification and estimation of a labor supply model. The proposed estimation procedure can be included in the so called predicted wage methods and its main interest is twofold. First, under standard assumptions in studies of labor...

Multivariate versions of the law of large numbers and the central limit theorem for martingales are given in a generality that is often necessary when studying statistical inference for stochastic process models. To illustrate the usefulness of the results, we consider estimation for a...

We consider density pointwise estimation and look for best attainable asymptotic rates of convergence. The problem is adaptive, which means that the regularity parameter, β, describing the class of densities, varies in a set B. We shall consider, successively, two classes of densities, issued...

We consider chi-squared type tests for testing the hypothesis H 0 that a density f of observations X1,..., Xn lies in a parametric class of densities F. We consider a version of chi-squared type test using kernel estimates for the density. The main result is, following Liero, Läuter and Konakov...

We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the...

For the problems of nonparametric estimation of nonincreasing and symmetric unimodal density functions with bounded supports we determine the projections of estimates onto the convex families of possible parent densities with respect to the weighted integrated squared error. We also describe the...

We consider two tests for testing the hypothesis that a density lies in a parametric class of densities and compare them by means of simulation. Both considered tests are based on the integrated squared distance of the kernel density estimator from its hypothetical expectation. However,...