Approximation properties of multivariate exponential sampling series

In this paper, we generalize the family of exponential sampling series for functions of $n$ variables and study their pointwise and uniform convergence as well as the rate of convergence for the functions belonging to space of $\log$-uniformly continuous functions. Furthermore, we state and prove the generalized Mellin-Taylor's expansion of multivariate functions. Using this expansion we establish pointwise asymptotic behaviour of the series by means of Voronovskaja type theorem.

Implementation of Multivariate Exponential Power Distribution in Discrimination and Classification of Psychological Data and Other applications

Recent advances have shown that some multivariate psychological data are deviating from usual normal assumption either in the tails or kurtosis. Thereby, allowing the call for modelling of such data using more robust elliptically contoured density which includes the normal distribution as a special case. This allowed more flexibility at the kurtosis and tail regions, which is better in handling non-normality in data analysis and also lower the cost of misclassification. The present study employed a robust model for such cases in the context of discrimination and classification of multivariate psychological disorder data using multivariate exponential distribution as an underlining model. Parameters were estimated using the method of maximum likelihood estimation and the discrimination and classification were based on the log likelihood ratio approach. The resulting models relied solidly on the shape parameter, which regulate the tails and the kurtosis, thereby allowed flexibility. This method enable us to lower the cost of misclassification. Some other areas of applications were also considered in the paper.

A parallel algorithm for ridge-penalized estimation of the multivariate exponential family from data of mixed types

Computationally efficient evaluation of penalized estimators of multivariate exponential family distributions is sought. These distributions encompass among others Markov random fields with variates of mixed type (e.g., binary and continuous) as special case of interest. The model parameter is estimated by maximization of the pseudo-likelihood augmented with a convex penalty. The estimator is shown to be consistent. With a world of multi-core computers in mind, a computationally efficient parallel Newton–Raphson algorithm is presented for numerical evaluation of the estimator alongside conditions for its convergence. Parallelization comprises the division of the parameter vector into subvectors that are estimated simultaneously and subsequently aggregated to form an estimate of the original parameter. This approach may also enable efficient numerical evaluation of other high-dimensional estimators. The performance of the proposed estimator and algorithm are evaluated and compared in a simulation study. Finally, the presented methodology is applied to data of an integrative omics study.

Some Properties of Univariate and Multivariate Exponential Power Distributions and Related Topics

In the paper, a survey of the main results concerning univariate and multivariate exponential power (EP) distributions is given, with main attention paid to mixture representations of these laws. The properties of mixing distributions are considered and some asymptotic results based on mixture representations for EP and related distributions are proved. Unlike the conventional analytical approach, here the presentation follows the lines of a kind of arithmetical approach in the space of random variables or vectors. Here the operation of scale mixing in the space of distributions is replaced with the operation of multiplication in the space of random vectors/variables under the assumption that the multipliers are independent. By doing so, the reasoning becomes much simpler, the proofs become shorter and some general features of the distributions under consideration become more vivid. The first part of the paper concerns the univariate case. Some known results are discussed and simple alternative proofs for some of them are presented as well as several new results concerning both EP distributions and some related topics including an extension of Gleser’s theorem on representability of the gamma distribution as a mixture of exponential laws and limit theorems on convergence of the distributions of maximum and minimum random sums to one-sided EP distributions and convergence of the distributions of extreme order statistics in samples with random sizes to the one-sided EP and gamma distributions. The results obtained here open the way to deal with natural multivariate analogs of EP distributions. In the second part of the paper, we discuss the conventionally defined multivariate EP distributions and introduce the notion of projective EP (PEP) distributions. The properties of multivariate EP and PEP distributions are considered as well as limit theorems establishing the conditions for the convergence of multivariate statistics constructed from samples with random sizes (including random sums of random vectors) to multivariate elliptically contoured EP and projective EP laws. The results obtained here give additional theoretical grounds for the applicability of EP and PEP distributions as asymptotic approximations for the statistical regularities observed in data in many fields.

Integration & Volatility across Global Indices in different Time Zones: Some Evidence

This paper examines the association of value instability crosswise over Global Indices of seven securities exchanges. Utilizing every day information of these seven nations situated in various time zones, this paper attempts to call attention to the nearness of nonsynchronous exchanging impacts utilizing open and close logarithmic returns of seven securities exchange files including Indian Indexat the middle. The hilter kilter effect of unpredictability overflow is analyzed by a multivariate exponential general autoregressive restrictive heteroskedastic model utilizing an example of 1742 perceptions taken from Oct 2011 to November 2018. The test outcomes give out many fascinating actualities alongside cost and unpredictability overflow from one market to the next because of time zone impact and additionally, influence impact is seen from the eastern markets' nearby value child Indian file open cost.