Efficiency and Optimality Properties of a Class of k-Sample Rank Test Against Trend.
Empirical regression quantile processes
We address the problem of estimating quantile-based statistical functionals, when the measured or controlled entities depend on exogenous variables which are not under our control. As a suitable tool we propose the empirical process of the average regression quantiles. It partially masks the effect of covariates and has other properties convenient for applications, e.g. for coherent risk measures of various types in the situations with covariates.
Estimación de la función cuantil y cuantildensidad mediante polinomios de Kantorovic.
En este trabajo se propone un estimador para la función cuantil, basado en polinomios de Kantorovic, como estimador natural, y se prueba que su error absoluto medio es un infinitésimo de orden n-1/2. Mediante simulación se pone de manifiesto que dicho estimador conduce a una reducción sustancial del error absoluto medio frente a la función cuantil muestral y, por otra parte, se compara con el estimador basado en polinomios de Bernstein.
Estimación no paramétrica de la función de distribución.
Sea X una variable aleatoria con función de distribución F(x) y función de densidad f(x) y X1, X2,..., Xn un conjunto de observaciones de la variable que pueden ser dependientes. Se definen dos estimadores no paramétricos generales (uno recursivo y el otro no recursivo) de la función de distribución.Bajo condiciones aceptables se obtiene el sesgo y la varianza y covarianza asintótica de los estimadores definidos. Finalmente se prueban propiedades de consistencia y normalidad asintótica.
Estimating L-functionals for heavy-tailed distributions and application.
Estimating median and other quantiles in nonparametric models
Though widely accepted, in nonparametric models admitting asymmetric distributions the sample median, if n=2k, may be a poor estimator of the population median. Shortcomings of estimators which are not equivariant are presented.
Estimating Survivor Function Using Optimally Selected Order Statistics.
Estimation of a quadratic functional of a density.
Estimation of a System Reliability by Nonparametric Techniques
Estimation of the Distribution Function of Noise in Stationary Processes.
Étude des extrêmes d'une suite stationnaire m-dépendante avec une application relative aux accroissements du processus de Wiener
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.
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 laws for sums of ratios of order statistics from the Pareto distribution
Consider independent and identically distributed random variables {X nk, 1 ≤ k ≤ m, n ≤ 1} from the Pareto distribution. We select two order statistics from each row, X n(i) ≤ X n(j), for 1 ≤ i < j ≤ = m. Then we test to see whether or not Laws of Large Numbers with nonzero limits exist for weighted sums of the random variables R ij = X n(j)/X n(i).
Exponential Convergence Properties of Linear Estimators under Exponential and Uniform Distribution.
Extreme order statistics in an equally correlated Gaussian array
This paper contains the results concerning the weak convergence of d-dimensional extreme order statistics in a Gaussian, equally correlated array. Three types of limit distributions are found and sufficient conditions for the existence of these distributions are given.