On the maximum probability criteria concerning the sequencial decision-making problem.
On the mean and the variance of estimates of Kullback information and relative “useful” information measures
In this paper the mean and the variance of the Maximum Likelihood Estimator (MLE) of Kullback information measure and measure of relative "useful" information are obtained.
On the measurement of stochastical dependence
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let be the empirical distribution function (df) pertaining to independent random variables with continuous df . We investigate the minimizing point of the empirical process , where is another df which differs from . If and are locally Hölder-continuous of order at a point our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let Fn be the empirical distribution function (df) pertaining to independent random variables with continuous df F. We investigate the minimizing point of the empirical process Fn - F0, where F0 is another df which differs from F. If F and F0 are locally Hölder-continuous of order α at a point τ our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the mode-change problem for random measures.
On the moments of normal probability distribution.
On the moments of random variables uniformly distributed over a polytope.
On the most bias-robust linear estimates of the scale parameter of the exponential distribution
On the multivariate skew-normal distribution and its scale mixtures.
On the Natural Selection Rule in General Linear Models.
On the Newcomb-Benford law in models of statistical data.
We consider positive real valued random data X with the decadic representation X = Σi=∞∞Di 10i and the first significant digit D = D(X) in {1,2,...,9} of X defined by the condition D = Di ≥ 1, Di+1 = Di+2 = ... = 0. The data X are said to satisfy the Newcomb-Benford law if P{D=d} = log10(d+1 / d) for all d in {1,2,...,9}. This law holds for example for the data with log10X uniformly distributed on an interval (m,n) where m and n are integers. We show that if log10X has a distribution function...
On the noncentral distribution of the ratio of the extreme roots of the Wishart matrix.
On the Nonnegativity of XX* and its Relevance in Econometrics.
On the Non-Null Distribution of WILCOXON'S Signed Rank Test.
On the Numerical Evaluation of a Sum Involving Binomial Coefficients.
On the optimal continuous experimental design problem
The target of this paper is to provide a compact review of the Optimal Experimental Design, the continuous case. Therefore we are referring to the general nonlinear problem in comparison to the linear one.
On the optimal number of classes in the Pearson goodness-of-fit tests
An asymptotic local power of Pearson chi-squared tests is considered, based on convex mixtures of the null densities with fixed alternative densities when the mixtures tend to the null densities for sample sizes This local power is used to compare the tests with fixed partitions of the observation space of small partition sizes with the tests whose partitions depend on and the partition sizes tend to infinity for . New conditions are presented under which it is asymptotically optimal...
On the Optimality of Differentiated SPR Tests of Composite Hypotheses.
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...