Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs

Abstract: We investigate the convergence rate of approximations by finite sums of rank-1 tensors of solutions of multiparametric elliptic PDEs. Such PDEs arise, for example, in the parametric, deterministic reformulation of elliptic PDEs with random field inputs, based, for example, on the $M$-term truncated Karhunen-Loeve expansion. Our approach could be regarded as either a class of compressed approximations of these solutions or as a new class of iterative elliptic problem solvers for high-dimensional, parametric, elliptic PDEs providing linear scaling complexity in the dimension $M$ of the parameter space. It is based on rank-reduced, tensor-formatted separable approximations of the high-dimensional tensors and matrices involved in the iterative process, combined with the use of spectrally equivalent low-rank tensor-structured preconditioners to the parametric matrices resulting from a finite element discretization of the high-dimensional parametric, deterministic problems. Numerical illustrations for the $M$-dimensional parametric elliptic PDEs resulting from sPDEs on parameter spaces of dimensions $M\leq100$ indicate the advantages of employing low-rank tensor-structured matrix formats in the numerical solution of such problems.

Invalidation of Parametric and Nonparametric Statistical Tests by Concurrent Violation of Two Assumptions

Abstract: To provide counterexamples to some commonly held generalizations about the benefits of nonparametric tests, the author concurrently violated in a simulation study 2 assumptions of parametric statistical significance tests—normality and homogeneity of variance. For various combinations of nonnormal distribution shapes and degrees of variance heterogeneity, the Type I error probability of a non-parametric rank test, the Wilcoxon-Mann-Whitney test, was found to be biased to a far greater extent than that of its parametric counterpart, the Student t test. The Welch-Satterthwaite separate-variances version of the t test, together with a preliminary outlier detection and downweighting procedure, protected the statistical significance level more consistently than the nonparametric test did. Those findings reveal that nonparametric methods are not always acceptable substitutes for parametric methods such as the t test and the F test in research studies when parametric assumptions are not satisfied. They ...

Dependent Evidence Combination Based on Shearman Coefficient and Pearson Coefficient

Abstract: Dempster–Shafer evidence theory is efficient to deal with uncertain information. One assumption of evidence theory is that the source of information should be independent when combined by Dempster’s rule for evidence combination. However, the assumption does not coincide with the reality. A lot of works are done to solve the problem about the independence. The existing method based on the statistical parameter Pearson correlation coefficient discount is one of the feasible methods. However, the Pearson correlation coefficient is only used to characterize the linear correlation between the attributes of the normal distribution. In this paper, a new method is proposed, the Pearson correlation coefficient and Shearman correlation coefficient to generate the discounting factor. Taking the parametric statistic and nonparametric statistic into consideration, the proposed method is more efficient. The experiments on wine data set are illustrated to show the efficiency of our proposed method.