Some problems in sequential analysis
Some problems of exponential smoothing
The paper deals with some practical problems connected with the classical exponential smoothing in time series. The fundamental theorem of the exponential smoothing is extended to the case with missing observations and an interpolation procedure in the framework of the exponential smoothing is described. A simple method of the exponential smoothing for multivariate time series is suggested.
Some problems of prediction of the difference of random variables
Some properties and applications of probability distributions based on MacDonald function
In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types and are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and useful applications...
Some properties and applications of the stuttering generalized Waring distribution.
Some properties of beta functions and the distribution for the product of independent beta random variables.
Products of independent beta random variables appear in a large number of problems in multivariate statistical analysis. In this paper we show how a convenient factorial expansion of gamma ratios can be suitably used in deriving the exact density for a product of independent beta random variables. Possible applications of this result for obtaining the exact densities of the likelihood ratio criteria for testing hypotheses in the multinormal case are also pointed out. For the sake of illustration,...
Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective
Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.Mittag-Leffler functions and their generalizations appear in a large variety of problems in different areas. When we move from total differential equations to fractional equations Mittag-Leffler functions come in naturally. Fractional reaction-diffusion problems in physical sciences and general input-output models in other disciplines are some of the examples in this direction. Some basic properties of Mittag-Leffler functions are...
Some properties of the best linear unbiased estimators in multivariate growth curve models.
Some Properties of the Distribution of an Operational Ridge Estimator.
Some properties of the proportional odds model
Marshall and Olkin (1997) introduced a new family of distributions by adding a tilt parameter. The same family was obtained by Kirmani and Gupta (2001) as the proportional odds model, which had been proposed by Clayton (1974). In this paper, stochastic ordering of distributions from this class and preservation of classes of life distributions by adding a parameter are obtained. The proportional odds family is also considered as a family of weighted distributions.
Some rank tests of independence and the question of their power-function
Some recent results on the law of the iterated logarithm for Banach space valued random variables
Some relationships between the generalized Gumbel and other distributions
Some remarks on comparison of predictors in seemingly unrelated linear mixed models
In this paper, we consider a comparison problem of predictors in the context of linear mixed models. In particular, we assume a set of different seemingly unrelated linear mixed models (SULMMs) allowing correlations among random vectors across the models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of joint unknown vectors under SULMMs and their combined model. We use the matrix rank and inertia...
Some remarks on experimental design
The paper deals with the experimental design which is optimal in the following sense: it satisfies the cost requirements simultaneously with a satisfactory precision of estimates. The underlying regression model is quadratic. The estimates of unknown parameters of the model are explicitly derived.
Some remarks on permutation type tests in linear models
The paper discusses applications of permutation arguments in testing problems in linear models. Particular attention will be paid to the application in L₁-test procedures. Theoretical results will beaccompanied by a simulation study.
Some remarks on sufficiency, invariance and conditional independence.
Some remarks on system reliability
Some Remarks on the Average Sample Number of Sequential and Non-Sequential Tests.
Some remarks on the control of false discovery rate under dependence
We investigate controlling false discovery rate (FDR) under dependence. Our main result is a generalization of the results obtained by Genovese and Wasserman (2004) and Farcomeni (2007).