On Distances and Goodness-of-Fit Tests for Detecting Multimodal Distributions.
On distributions of order statistics for absolutely continuous copulas with applications to reliability
Performance of coherent reliability systems is strongly connected with distributions of order statistics of failure times of components. A crucial assumption here is that the distributions of possibly mutually dependent lifetimes of components are exchangeable and jointly absolutely continuous. Assuming absolute continuity of marginals, we focus on properties of respective copulas and characterize the marginal distribution functions of order statistics that may correspond to absolute continuous...
On Dwass' method for deriving the distribution of rank order statistics
This note presents a critical examination of Dwass' method for obtaining the distribution of rank order statistics defined on random samples obtained from the same continuous population. New situations are discussed for the usefulness of the method.
On EM algorithms and their proximal generalizations
In this paper, we analyze the celebrated EM algorithm from the point of view of proximal point algorithms. More precisely, we study a new type of generalization of the EM procedure introduced in [Chretien and Hero (1998)] and called Kullback-proximal algorithms. The proximal framework allows us to prove new results concerning the cluster points. An essential contribution is a detailed analysis of the case where some cluster points lie on the boundary of the parameter space.
On entropies for random partitions of the unit segment
We prove the complete convergence of Shannon’s, paired, genetic and α-entropy for random partitions of the unit segment. We also derive exact expressions for expectations and variances of the above entropies using special functions.
On estimating the diffusion coefficient : parametric versus nonparametric
On estimating the memory for finitarily markovian processes
On Estimation of Hazard Function
On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane
A method of estimation of intrinsic volume densities for stationary random closed sets in based on estimating volumes of tiny collars has been introduced in T. Mrkvička and J. Rataj, On estimation of intrinsic volume densities of stationary random closed sets, Stoch. Proc. Appl. 118 (2008), 2, 213-231. In this note, a stronger asymptotic consistency is proved in dimension 2. The implementation of the method is discussed in detail. An important step is the determination of dilation radii in the...
On Fourier coefficient estimators consistent in the mean-square sense
The properties of two recursive estimators of the Fourier coefficients of a regression function with respect to a complete orthonormal system of bounded functions (ek) , k=1,2,..., are considered in the case of the observation model , i=1,...,n , where are independent random variables with zero mean and finite variance, , i=1,...,n, form a random sample from a distribution with density ϱ =1/(b-a) (uniform distribution) and are independent of the errors , i=1,...,n . Unbiasedness and mean-square...
On Functional of Order Statistics.
On generalized extreme-value order statistics and moments
On goodness-of-fit for the absence of memory model
Logrank-type and Kolmogorov-type goodness-of-fit tests for the absence of memory model are proposed when the accelerated experiments are done under step-stresses. The power of the test against the approaching alternatives is investigated. The theoretical results are illustrated with simulated data.
On Hodges-Lehmann optimality of LR tests
On interactions in contingency tables
On invariant density estimation for ergodic diffusion processes.
We present a review of several results concerning invariant density estimation by observations of ergodic diffusion process and some related problems. In every problem we propose a lower minimax bound on the risks of all estimators and then we construct an asymptotically efficient estimator.
On Klotz's result on the asymptotic efficiency for the signed rank tests
On -estimators viewed as -estimators
On least squares estimation of Fourier coefficients and of the regression function
On locally most powerful rank tests of independence