On a class of distribution-free tests for growth curves analyses
On a class of estimators in a multivariate RCA(1) model
This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated...
On a family of bayesian estimators and predictors for a Gumbel model based on the kth lower records
Bayesian estimation for the two parameters of a Gumbel distribution are obtained based on kth lower record values. Prediction, either point or interval, for future kth lower record values is also presented from a Bayesian view point. Some of the results of [4] can be obtained as special cases of our results (k=1).
On a robust significance test for the Cox regression model
A robust significance testing method for the Cox regression model, based on a modified Wald test statistic, is discussed. Using Monte Carlo experiments the asymptotic behavior of the modified robust versions of the Wald statistic is compared with the standard significance test for the Cox model based on the log likelihood ratio test statistic.
On a strongly consistent estimator of the squared L_2-norm of a function
A kernel estimator of the squared -norm of the intensity function of a Poisson random field is defined. It is proved that the estimator is asymptotically unbiased and strongly consistent. The problem of estimating the squared -norm of a function disturbed by a Wiener random field is also considered.
On adaptive estimation in nonlinear regression
On Approximating the Distributions of Friedman's xr2 and Related Statistics.
On asymptotic minimaxity of kernel-based tests
In the problem of signal detection in gaussian white noise we show asymptotic minimaxity of kernel-based tests. The test statistics equal -norms of kernel estimates. The sets of alternatives are essentially nonparametric and are defined as the sets of all signals such that the -norms of signal smoothed by the kernels exceed some constants . The constant depends on the power of noise and as . Similar statements are proved also if an additional information on a signal smoothness is given....
On Asymptotic Minimaxity of Kernel-based Tests
In the problem of signal detection in Gaussian white noise we show asymptotic minimaxity of kernel-based tests. The test statistics equal L2-norms of kernel estimates. The sets of alternatives are essentially nonparametric and are defined as the sets of all signals such that the L2-norms of signal smoothed by the kernels exceed some constants pε > 0. The constant pε depends on the power ϵ of noise and pε → 0 as ε → 0. Similar statements are proved also if an additional information on a signal...
On asymptotic minimaxity of the adaptative kernel estimate of a density function
On bounds for the asymptotic power and on Pitman efficiencies of the Cramer-von Mises test
On bounds of the range of ordered variates II.
On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators
We study the impact of certain transformations within the class of Archimedean copulas. We give some admissibility conditions for these transformations, and define some equivalence classes for both transformations and generators of Archimedean copulas. We extend the r-fold composition of the diagonal section of a copula, from r ∈ N to r ∈ R. This extension, coupled with results on equivalence classes, gives us new expressions of transformations and generators. Estimators deriving directly from these...
On characteristic functions of kth record values from the generalized extreme value distribution and its characterization
Recurrence relations for the marginal, joint and conditional characteristic functions of kth record values from the generalized extreme value distribution are established. These relations are utilized to obtain recurrence relations for single, product and conditional moments of kth record values. Moreover, by making use of the recurrence relations the generalized extreme value distribution is characterized.
On Characterizing Distributions by Conditional Expectations of Functions of Order Statistics.
On consistency of kernel density estimators for randomly censored data : rates holding uniformly over adaptive intervals
On construction of confidence intervals for a mean of dependent data
In the report, the performance of several methods of constructing confidence intervals for a mean of stationary sequence is investigated using extensive simulation study. The studied approaches are sample reuse block methods which do not resort to bootstrap. It turns out that the performance of some known methods strongly depends on a model under consideration and on whether a two-sided or one-sided interval is used. Among the methods studied, the block method based on weak convergence result by...
On continuous convergence and epi-convergence of random functions. Part I: Theory and relations
Continuous convergence and epi-convergence of sequences of random functions are crucial assumptions if mathematical programming problems are approximated on the basis of estimates or via sampling. The paper investigates “almost surely” and “in probability” versions of these convergence notions in more detail. Part I of the paper presents definitions and theoretical results and Part II is focused on sufficient conditions which apply to many models for statistical estimation and stochastic optimization....
On continuous convergence and epi-convergence of random functions. Part II: Sufficient conditions and applications
Part II of the paper aims at providing conditions which may serve as a bridge between existing stability assertions and asymptotic results in probability theory and statistics. Special emphasis is put on functions that are expectations with respect to random probability measures. Discontinuous integrands are also taken into account. The results are illustrated applying them to functions that represent probabilities.
On cumulative process model and its statistical analysis
The notion of the counting process is recalled and the idea of the ‘cumulative’ process is presented. While the counting process describes the sequence of events, by the cumulative process we understand a stochastic process which cumulates random increments at random moments. It is described by an intensity of the random (counting) process of these moments and by a distribution of increments. We derive the martingale – compensator decomposition of the process and then we study the estimator of the...