Edgeworth expansions for a sample sum from a finite set of independent random variables.
Effective WLLN, SLLN and CLT in statistical models
Weak laws of large numbers (WLLN), strong laws of large numbers (SLLN), and central limit theorems (CLT) in statistical models differ from those in probability theory in that they should hold uniformly in the family of distributions specified by the model. If a limit law states that for every ε > 0 there exists N such that for all n > N the inequalities |ξₙ| < ε are satisfied and N = N(ε) is explicitly given then we call the law effective. It is trivial to obtain an effective statistical...
Eigenvalues of the Laguerre process as non-colliding squared Bessel processes.
Eine simultane Charakterisierung der geometrischen Verteilung und logistischen Verteilung.
Einige Bemerkungen zur Theorie der Maximum Probability Schätzer.
Empirical analysis of current status data for additive hazards model with auxiliary covariates
In practice, it often occurs that some covariates of interest are not measured because of various reasons, but there may exist some auxiliary information available. In this case, an issue of interest is how to make use of the available auxiliary information for statistical analysis. This paper discusses statistical inference problems in the context of current status data arising from an additive hazards model with auxiliary covariates. An empirical log-likelihood ratio statistic for the regression...
Erratum: Second-order approximation of the entropy in nonlinear least-squares estimation
Errors estimation and the asymptotic distribution of probabilistic estimates.
Erwartungswerte, Varianzen und Kovarianzen mehrerer Maxima der Abstände unabhängiger rechteckverteilter Zufallsvariabler.
Estabilización de la varianza de una distribución hipergeométrica.
En este trabajo se determina una transformación tipo arco seno para una distribución hipergeométrica H(N,D = pN,n) de forma que estabilice la varianza de la misma en función de la fracción p de objetos de un cierto tipo. Como caso particular de las expresiones obtenidas se deducen las dadas por F. J. Anscombe (1948) para la distribución binomial B(n,p). Al final del trabajo se efectúa una investigación numérica de los resultados obtenidos y se dan algunas aplicaciones para realizar inferencias sobre...
Estimación no paramétrica de curvas notables para datos dependientes.
Sea {Xt: t ∈ Z} una serie de tiempo estacionaria, con valores en Rp, verificando la condición de ser α-mixing o L2-estable. A partir de una muestra de tamaño n se define una amplia clase de estimadores no paramétricos de la función de densidad f(x) asociada al proceso, y de la función de autorregresión de orden k:r(y) = E(g(Xt+1)/(Xt-k+1 ... Xt) = y), y ∈ Rksiendo g una función real.Se estudian las siguientes propiedades asintóticas de estos estimadores: consistencia puntual (casi segura y en media...
Estimation des densités : risque minimax
Estimation of log-linear-binomial distribution with applications.
Estimators for epidemic alternatives
We introduce and study the behavior of estimators of changes in the mean value of a sequence of independent random variables in the case of so called epidemic alternatives which is one of the variants of the change point problem. The consistency and the limit distribution of the estimators developed for this situation are shown. Moreover, the classical estimators used for `at most change' are examined for the studied situation.
Étude des propriétés asymptotiques des estimateurs des moindres carrés pour des problèmes de régression à phases multiples
Evaluating improvements of records
We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.
Evaluating the bivariate compound generalized Poisson distribution.
Evaluations of expected generalized order statistics in various scale units
We present sharp upper bounds for the deviations of expected generalized order statistics from the population mean in various scale units generated by central absolute moments. No restrictions are imposed on the parameters of the generalized order statistics model. The results are derived by combining the unimodality property of the uniform generalized order statistics with the Moriguti and Hölder inequalities. They generalize evaluations for specific models of ordered observations.
Exact and approximate distributions for the product of Dirichlet components
It is well known that has the beta distribution when and follow the Dirichlet distribution. Linear combinations of the form have also been studied in Provost and Cheong [S. B. Provost and Y.-H. Cheong: On the distribution of linear combinations of the components of a Dirichlet random vector. Canad. J. Statist. 28 (2000)]. In this paper, we derive the exact distribution of the product (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose...
Exact distribution for the generalized F tests
Generalized F statistics are the quotients of convex combinations of central chi-squares divided by their degrees of freedom. Exact expressions are obtained for the distribution of these statistics when the degrees of freedom either in the numerator or in the denominator are even. An example is given to show how these expressions may be used to check the accuracy of Monte-Carlo methods in tabling these distributions. Moreover, when carrying out adaptative tests, these expressions enable us to estimate...