On finite additivity, non-conglomerability and statistical paradoxes.
Some statistical paradoxes arising from the use of non-conglomerable finitely additive distributions are discussed.
On Fisher information inequalities and score functions in non-invertible linear systems.
On formulae for central moments of counting distributions
The aim of this article is to give new formulae for central moments of the binomial, negative binomial, Poisson and logarithmic distributions. We show that they can also be derived from the known recurrence formulae for those moments. Central moments for distributions of the Panjer class are also studied. We expect our formulae to be useful in many applications.
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 measures of skewness
We introduce a concept of functional measures of skewness which can be used in a wider context than some classical measures of asymmetry. The Hotelling and Solomons theorem is generalized.
On Functional of Order Statistics.
On general asymptotic behaviour of order statistics with random index.
On generalized conditional cumulative past inaccuracy measure
The notion of cumulative past inaccuracy (CPI) measure has recently been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order and study the proposed measure for conditionally specified models of two components failed at different time instants, called generalized conditional CPI (GCCPI). Several properties, including the effect of monotone transformation and bounds of GCCPI...
On generalized entropies, Bayesian decisions and statistical diversity
On generalized extreme-value order statistics and moments
On generalized information and divergence measures and their applications: a brief review.
The aim of this review is to give different two-parametric generalizations of the following measures: directed divergence (Kullback and Leibler, 1951), Jensen difference divergence (Burbea and Rao 1982 a,b; Rao, 1982) and Jeffreys invariant divergence (Jeffreys, 1946). These generalizations are put in the unified expression and their properties are studied. The applications of generalized information and divergence measures to comparison of experiments and the connections with Fisher information...
On geometric ergodicity and prediction in nonnegative non-linear autoregressive processes
A non-linear AR(1) process is investigated when the associated white noise is positive. A criterion is derived for the geometric ergodicity of the process. Some explicit formulas are derived for one and two steps ahead extrapolation. Influence of parameter estimation on extrapolation is studied.
On geometry of the set of admissible quadratic estimators of quadratic functions of normal parameters
We consider the problem of admissible quadratic estimation of a linear function of μ² and σ² in n dimensional normal model N(Kμ,σ²Iₙ) under quadratic risk function. After reducing this problem to admissible estimation of a linear function of two quadratic forms, the set of admissible estimators are characterized by giving formulae on the boundary of the set D ⊂ R² of components of the two quadratic forms constituting the set of admissible estimators. Different shapes and topological properties of...
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 Hájek's conjecture in stratified sampling
On Hodges-Lehmann optimality of LR tests
On hypergeometric generalized negative binomial distribution.
On identifiability of mixtures of independent distribution laws
We consider representations of a joint distribution law of a family of categorical random variables (i.e., a multivariate categorical variable) as a mixture of independent distribution laws (i.e. distribution laws according to which random variables are mutually independent). For infinite families of random variables, we describe a class of mixtures with identifiable mixing measure. This class is interesting from a practical point of view as well, as its structure clarifies principles of selecting...
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.