Let Y be a random vector taking its values in a measurable space and let z be a vector-valued function defined on that space. We consider gamma minimax estimation of the unknown expected value p of the random vector z(Y). We assume a weighted squared error loss function.

Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in regression models,...

Gaussian process modeling is one of the most popular approaches for building a metamodel in the case of expensive numerical simulators. Frequently, the code outputs correspond to physical quantities with a behavior which is known a priori: Chemical concentrations lie between 0 and 1, the output is increasing with respect to some parameter, etc. Several approaches have been proposed to deal with such information. In this paper, we introduce a new framework for incorporating constraints in Gaussian...

Gaussian semiparametric or local Whittle estimation of the memory parameter in standard long memory processes was proposed by Robinson [18]. This technique shows several advantages over the popular log- periodogram regression introduced by Geweke and Porter–Hudak [7]. In particular under milder assumptions than those needed in the log periodogram regression it is asymptotically more efficient. We analyse the asymptotic behaviour of the Gaussian semiparametric estimate of the memory parameter in...

We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.

The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of copulas and stable mixing variables, extending approaches in Tawn [14], Joe and Hu [6] and Fougères et al. [3]. The...

We consider two continuous time processes; the first one is valued in a semi-metric space, while the second one is real-valued. In some sense, we extend the results of F. Ferraty and P. Vieu in ``Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination'' (2004), by establishing the convergence, with rates, of the generalized regression function when a real-valued continuous time response is considered. As corollaries, we deduce the...

We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis $H_0$: “$f=f_0$” against the composite alternative $H_a$: “$f\ne f_0$” under the assumption that the true regression function $f$ is decreasing. The test statistic is based on the ${𝕃}_1$-distance between the isotonic estimator of $f$ and the function $f_0$, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under $H_0$. We study the asymptotic...

We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis H0: “ƒ = ƒ0” against the composite alternative Ha: “ƒ ≠ ƒ0” under the assumption that the true regression function f is decreasing. The test statistic is based on the ${𝕃}_1$-distance between the isotonic estimator of f and the function f0, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under H0....

The skew-Laplace distribution is frequently used to fit the logarithm of particle sizes and it is also used in Economics, Engineering, Finance and Biology. We show the Anderson-Darling and Cramér-von Mises goodness of fit tests for this distribution.

The aim of the paper is to present a test of goodness of fit with weigths in the classes based on weighted $\left(h,\phi \right)$-divergences. This family of divergences generalizes in some sense the previous weighted divergences studied by Frank et al [frank] and Kapur [kapur]. The weighted $\left(h,\phi \right)$-divergence between an empirical distribution and a fixed distribution is here investigated for large simple random samples, and the asymptotic distributions are shown to be either normal or equal to the distribution of a linear...

Chi-squared goodness-of-fit test for the family of logistic distributions id proposed. Different methods of estimation of the unknown parameters θ of the family are compared. The problem of homogeneity is considered.

Using characterization conditions of continuous distributions in terms of moments of order statistics given in [12], [23], [6] and [7] we present new goodness-of-fit techniques.

We construct goodness-of-fit tests for continuous distributions using their characterizations in terms of moments of order statistics and moments of record values. Our approach is based on characterizations presented in [2]-[4], [5], [9].

In this paper a new family of statistics based on $K_{\phi }$-divergence for testing goodness-of-fit under composite null hypotheses are considered. The asymptotic distribution of this test is obtained when the unspecified parameters are estimated by maximum likelihood as well as minimum $K_{\phi }$-divergence.

Starting from characterizations of continuous distributions in terms of the expected values of two functions of record values we construct a family of goodness-of-fit tests calculated from U-statistics.

Test procedures are constructed for testing the goodness-of-fit in parametric regression models. The test statistic is in the form of an L2 distance between the empirical characteristic function of the residuals in a parametric regression fit and the corresponding empirical characteristic function of the residuals in a non-parametric regression fit. The asymptotic null distribution as well as the behavior of the test statistic under contiguous alternatives is investigated. Theoretical results are...

In a recent paper Fay and Philippe [ESAIM: PS 6 (2002) 239–258] proposed a goodness-of-fit test for long-range dependent processes which uses the logarithmic contrast as information measure. These authors established asymptotic normality under the null hypothesis and local alternatives. In the present note we extend these results and show that the corresponding test statistic is also normally distributed under fixed alternatives.