On an accuracy of change points
On approximations of transformed chi-squared distributions in statistical applications.
On Bartlett's test for correlation between time series
An explicit formula for the correlation coefficient in a two-dimensional AR(1) process is derived. Approximate critical values for the correlation coefficient between two one-dimensional AR(1) processes are tabulated. They are based on Bartlett’s approximation and on an asymptotic distribution derived by McGregor. The results are compared with critical values obtained from a simulation study.
On Bayesian estimation in an exponential distribution under random censorship
The paper gives some basic ideas of both the construction and investigation of the properties of the Bayesian estimates of certain parametric functions of the parent exponential distribution under the model of random censorship assuming the Koziol–Green model. Various prior distributions are investigated and the corresponding estimates are derived. The stress is put on the asymptotic properties of the estimates with the particular stress on the Bayesian risk. Small sample properties are studied...
On calculation of stationary density of autoregressive processes
An iterative procedure for computation of stationary density of autoregressive processes is proposed. On an example with exponentially distributed white noise it is demonstrated that the procedure converges geometrically fast. The AR(1) and AR(2) models are analyzed in detail.
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 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 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 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 improving sensitivity of the Kalman filter
The impact of additive outliers on a performance of the Kalman filter is discussed and less outlier-sensitive modification of the Kalman filter is proposed. The improved filter is then used to obtain an improved smoothing algorithm and an improved state-space model parameters estimation.
On inconsistency of Hellwig's variable choice method in regression models
It is shown that a popular variable choice method of Hellwig, which is recommended in the Polish econometric textbooks does not enjoy a very basic consistency property. It means in particular that the method may lead to rejection of significant variables in econometric modeling. A simulation study and a real data analysis case are given to support theoretical results.
On selecting the best features in a noisy environment
This paper introduces a novel method for selecting a feature subset yielding an optimal trade-off between class separability and feature space dimensionality. We assume the following feature properties: (a) the features are ordered into a sequence, (b) robustness of the features decreases with an increasing order and (c) higher-order features supply more detailed information about the objects. We present a general algorithm how to find under those assumptions the optimal feature subset. Its performance...
On some two-step density estimation method.
On testing hypotheses in the generalized Skillings-Mack random blocks setting
The testing of the null hypothesis of no treatment effect against the alternative of increasing treatment effect by means of rank statistics is extended from the classical Friedman random blocks model into an unbalanced design allowing treatments not to be applied simultaneously in each random block. The asymptotic normality of the constructed rank test statistic is proved both in the setting not allowing ties and also for models with presence of ties. As a by-product of the proofs a multiple comparisons...
On the choice of the spline density estimators.
On the compound Poisson-gamma distribution
The compound Poisson-gamma variable is the sum of a random sample from a gamma distribution with sample size an independent Poisson random variable. It has received wide ranging applications. In this note, we give an account of its mathematical properties including estimation procedures by the methods of moments and maximum likelihood. Most of the properties given are hitherto unknown.
On the estimation of the autocorrelation function
The autocorrelation function has a very important role in several application areas involving stochastic processes. In fact, it assumes the theoretical base for Spectral analysis, ARMA (and generalizations) modeling, detection, etc. However and as it is well known, the results obtained with the more current estimates of the autocorrelation function (biased or not) are frequently bad, even when we have access to a large number of points. On the other hand, in some applications, we need to perform...
On the generation of correlation matrices.
On the least quares fitting in a linear model.
On the Optimality of Sample-Based Estimates of the Expectation of the Empirical Minimizer***
We study sample-based estimates of the expectation of the function produced by the empirical minimization algorithm. We investigate the extent to which one can estimate the rate of convergence of the empirical minimizer in a data dependent manner. We establish three main results. First, we provide an algorithm that upper bounds the expectation of the empirical minimizer in a completely data-dependent manner. This bound is based on a structural result due to Bartlett and Mendelson, which relates...