Some limit properties of an approximate least squares estimator in a nonlinear regression model with correlated nonzero mean errors.
Some methods of constructing kernels in statistical learning
This paper is a collection of numerous methods and results concerning a design of kernel functions. It gives a short overview of methods of building kernels in metric spaces, especially and . However we also present a new theory. Introducing kernels was motivated by searching for non-linear patterns by using linear functions in a feature space created using a non-linear feature map.
Some monotonicity and limit results for the regularised incomplete gamma function
Letting P(u,x) denote the regularised incomplete gamma function, it is shown that for each α ≥ 0, P(x,x+α) decreases as x increases on the positive real semi-axis, and P(x,x+α) converges to 1/2 as x tends to infinity. The statistical significance of these results is explored.
Some New Random Effect Models for Correlated Binary Responses
Exchangeable copulas are used to model an extra-binomial variation in Bernoulli experiments with a variable number of trials. Maximum likelihood inference procedures for the intra-cluster correlation are constructed for several copula families. The selection of a particular model is carried out using the Akaike information criterion (AIC). Profile likelihood confidence intervals for the intra-cluster correlation are constructed and their performance are assessed in a simulation experiment. The sensitivity...
Some properties of beta functions and the distribution for the product of independent beta random variables.
Products of independent beta random variables appear in a large number of problems in multivariate statistical analysis. In this paper we show how a convenient factorial expansion of gamma ratios can be suitably used in deriving the exact density for a product of independent beta random variables. Possible applications of this result for obtaining the exact densities of the likelihood ratio criteria for testing hypotheses in the multinormal case are also pointed out. For the sake of illustration,...
Some properties of the best linear unbiased estimators in multivariate growth curve models.
Some remarks on comparison of predictors in seemingly unrelated linear mixed models
In this paper, we consider a comparison problem of predictors in the context of linear mixed models. In particular, we assume a set of different seemingly unrelated linear mixed models (SULMMs) allowing correlations among random vectors across the models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of joint unknown vectors under SULMMs and their combined model. We use the matrix rank and inertia...
Some remarks on the control of false discovery rate under dependence
We investigate controlling false discovery rate (FDR) under dependence. Our main result is a generalization of the results obtained by Genovese and Wasserman (2004) and Farcomeni (2007).
Some remarks to multivariate regression model
Some remarks to problems of point and interval estimation, testing and problems of outliers are presented in the case of multivariate regression model.
Some results envolving the concepts of moment generating function and affinity between distribution functions. Extension for r k-dimensional normal distribution functions.
We present a function ρ (F1, F2, t) which contains Matusita's affinity and expresses the affinity between moment generating functions. An interesting results is expressed through decomposition of this affinity ρ (F1, F2, t) when the functions considered are k-dimensional normal distributions. The same decomposition remains true for other families of distribution functions. Generalizations of these results are also presented.
Some statistical aspects of the estimation of parameters of a linear conform transformation
Sparsity in penalized empirical risk minimization
Let (X, Y) be a random couple in S×T with unknown distribution P. Let (X1, Y1), …, (Xn, Yn) be i.i.d. copies of (X, Y), Pn being their empirical distribution. Let h1, …, hN:S↦[−1, 1] be a dictionary consisting of N functions. For λ∈ℝN, denote fλ:=∑j=1Nλjhj. Let ℓ:T×ℝ↦ℝ be a given loss function, which is convex with respect to the second variable. Denote (ℓ•f)(x, y):=ℓ(y; f(x)). We study the following penalized empirical risk minimization problem which is an empirical version of the problem (hereɛ≥0...
Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction
We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory...
Spatial scan statistics adjusted for multiple clusters.
Special structures of mixed linear models with nuisance parameters
Spiked Dirichlet process priors for Gaussian process models.
Stabilité de l'analyse en composantes principales par rapport à une perturbation des données
Stabilité du pouvoir discriminant des facteurs par rapport à des perturbations des données en analyse linéaire discriminante
Stabilité d'un opérateur de classification
Stabilité d'un opérateur de classification