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Your search keyword '"Zang, Yishan"' showing total 2 results
Start Over Author "Zang, Yishan" Topic data modeling
2 results on '"Zang, Yishan"'

1. Nonparametric Copula Density Estimation Methodologies.

Author

Provost, Serge B. and Zang, Yishan

Subjects
*PROBABILITY density function, *DENSITY, *DISTRIBUTION (Probability theory), *POLYNOMIAL approximation, *BIVARIATE analysis
Abstract

This paper proposes several methodologies whose objective consists of securing copula density estimates. More specifically, this aim will be achieved by differentiating bivariate least-squares polynomials fitted to Deheuvels' empirical copulas, by making use of Bernstein's approximating polynomials of appropriately selected orders; by differentiating linearized distribution functions evaluated at optimally spaced grid points; and by implementing the kernel density estimation technique in conjunction with a repositioning of the pseudo-observations and a certain criterion for determining suitable bandwidths. Smoother representations of such density estimates can further be secured by approximating them by means of moment-based bivariate polynomials. The various copula density estimation techniques being advocated herein are successfully applied to an actual dataset as well as a random sample generated from a known distribution. [ABSTRACT FROM AUTHOR]

Published
2024
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2. Advances in Moment-Based Distributional Methodologies

Author

Zang, Yishan

Subjects
quadratic forms, Density approximation, classification of tail behavior, quasi-Monte Carlo samples, data modeling, Statistical Methodology
Abstract

This thesis comprises various results that rely on the moments of a distribution or the sample moments associated with a set of observations. Since a sample of size n is uniquely specified by its first n moments, it is pertinent to make use of sample moments for modeling, classification or inference purposes. Three density mixtures are approximated by adjusting in various ways an initial density approximation referred to a base density by means certain moment-based functions, and the accuracy of the resulting density approximants are compared. A similar study is carried out in the context of density estimation. Moreover, it is explained that methodologies that are based on moments are, in fact, ideally suited to model massive data sets. Various types of quasi-Monte Carlo deterministic samples are then compared to randomly generated samples with respect to their distributional representativeness. As well, a novel methodology depending on an arctangent transformation is introduced for classifying the tail behaviour of probability laws. Finally, certain approximations to the distributions of quadratic forms in gamma, inverse Gaussian, binomial and Poisson random variables, which rely on a symbolic expansion of their moments, are proposed.

Published
2019

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