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.
Goodness of fit tests for the skew-Laplace distribution.
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.
Goodness-of-fit tests based on characterizations in terms of moments of order statistics
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.
Goodness-of-fit tests based on characterizations of continuous distributions
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].
Goodness-of-fit tests derived from characterizations of continuous distributions
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.
IFS approximations of distribution functions and related optimization problems.
Invariance principles in Hölder spaces.
-Depth-nearest Neighbour Method and its Performance on Skew-normal Distributons
In the present paper we investigate performance of the -depth-nearest classifier. This classifier, proposed recently by Vencálek, uses the concept of data depth to improve the classification method known as the -nearest neighbour. Simulation study which is presented here deals with the two-class classification problem in which the considered distributions belong to the family of skewed normal distributions.
Laws of large numbers for -statistics.