Let be a convex mapping and a Hilbert space. In this paper we prove the following refinement of Jensen's inequality: for every A,B such that and B[subset of]A. Expectations of Hilbert-space-valued random elements are defined by means of the Pettis integrals. Our result generalizes a result of...

The canonical correlation (CANCOR) method for dimension reduction in a regression setting is based on the classical estimates of the first and second moments of the data, and therefore sensitive to outliers. In this paper, we study a weighted canonical correlation (WCANCOR) method, which...

Consider the semiparametric regression model yi=xi[beta]+g(ti)+Vi,1=i=n, where [beta] is an unknown parameter of interest, (xi,ti) are nonrandom design points, yi are the response variables, g([dot operator]) is an unknown function defined on the closed interval [0,1], and the correlated errors...

We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple and composite hypotheses, extending the maximum likelihood...

In this paper, we investigate the model checking problem for a partial linear model while some responses are missing at random. By imputation and marginal inverse probability weighted methods, two completed data sets are constructed. Based on the two completed data sets, we build two empirical...

Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for...

The asymptotic distribution for the local linear estimator in nonparametric regression models is established under a general parametric error covariance with dependent and heterogeneously distributed regressors. A two-step estimation procedure that incorporates the parametric information in the...

Necessary and sufficient conditions are derived for the BLUE in a general multiple-partitioned linear model to be the sum of the BLUEs under the k small models , ..., . Some consequences and further research topics are also given.

Linear dependence coefficients are defined for random fields of continuous-index, which are modified from those already defined for random fields indexed by an integer lattice. When a selection of these linear dependence conditions are satisfied, the random field will have a continuous spectral...