In this paper, the distributions of largest and smallest eigenvalues complex Wishart matrices condition number Gaussian random are derived. These represented by hypergeometric functions matrix arguments, which can be expressed in terms zonal polynomials. Several results derived on polynomials used to evaluate these distributions. Finally, applications numerical analysis statistical hypothesis testing mentioned.

This paper reports upon the design of an expert system at Canada Centre for Remote Sensing updating maps forested areas using Landsat imagery. The is decomposed into a number specialist experts organized in hierarchical fashion around series blackboards which are used communications between different levels. At lowest level hierarchy, acts as interface to low-level, procedural-based, image processing algorithms. A short review systems, with special emphasis on analysis remotely sensed...

The eigenvalue densities of complex central Wishart matrices are investigated with the objective studying an open problem in channel capacity.These represented by hypergeometric functions matrix arguments, which can be expressed terms zonal polynomials.The connection between theory and information is given.This facilitates evaluation most important information-theoretic measure, so-called capacity.In particular, capacity multiple input, output (MIMO) Rayleigh distributed channels fully...

Motivated by the apportionment of diversity analysis due to C. R. Rao, a general approach comparing populations rankers is proposed. Each permutation metric corresponds particular population characteristic that forms basis comparison. Tests hypotheses concerning equality characteristics are developed. Throughout, comparison made with earlier work, most which based on use only Spearman metric. Extension tied rankings discussed. Examples for two groups presented illustrate computational...

For fixed $\theta$, let $X_1, X_2, \cdots$ be a sequence of independent identically distributed random variables having density $f_\theta(x)$. Using sequential Bayes decision theoretic approach we consider the problem estimating any strictly monotone function $g(\theta)$ when error incurred by wrong estimate is measured squared loss and sampling cost $c$ units per observation. A heuristic stopping rule suggested. It shown that excess risk which results using it bounded above terms order $c$.

The problem of $n$ rankings is considered and the asymptotic distributions measures concordance based on rank correlations are derived under null model complete randomness. Bahadur efficiencies computed. A matrix analysis then reveals distribution superior efficiency average Kendall tau. Some interpretation results also made.

Microarray experiments examine the change in transcript levels of tens thousands genes simultaneously. To derive meaningful data, biologists investigate response within specific pathways. Pathways are comprised that interact to carry out a particular biological function. Existing methods for analyzing pathways focus on detecting changes mean or over-representation number differentially expressed relative total pathway. The issue how incorporate influence correlation among is not generally...

A total of $nb$ judges rank $t$ objects $k$ at a time according to $n$ replications BIBD with $b$ blocks. The Durbin statistic is commonly used in this context and equivalent the usual analysis variance on rankings. approach considered here introduce notion compatibility so as define distances between incomplete rankings based metrics space complete Through device we class test statistics which includes special case, derive their asymptotic distributions. This also yields new interpretation...

Motivated by questions arising from the field of statistical genetics, we consider problem testing main, nested, and interaction effects in unbalanced factorial designs. Based on concept composite linear rank statistics, a new notion weighted is proposed. Asymptotic normality statistics established under mild conditions, consistent estimators are developed for corresponding limiting covariance structure. A unified framework to use construct test designs established. The proposed tests...

Abstract The subject of rank correlation has had a rich history. It been used in numerous applications tests for trend and independence. However, little said about how to define when the data are incomplete. practice often ignore missing observations smaller complete record. We propose new class measures which based on notion distance between incomplete rankings. There is potential significant increase efficiency over approach ignores as demonstrated by specific case.

Abstract In testing the null hypothesis of no treatment effects in a randomized block experiment, researcher may restrict attention to an ordered alternative and thereby increase power his test. Jonckheere later Page proposed such test statistics based on Kendall Spearman correlation coefficients. Motivated by notions distance between permutations, we generalize Jonckheere's Page's tests situation which one or more observations are missing from blocks. Conditional pattern observations,...

Since December 2019, many statistical spatial–temporal methods have been developed to track and predict the spread of COVID-19 pandemic. In this paper, we analyzed dataset which includes number biweekly infected cases registered in Ontario from March 2020 end June 2021. We made use Bayesian Spatial–temporal models Area-to-point (ATP) Area-to-area (ATA) Poisson Kriging models. With models, effects government intervention on infection risk are considered while ATP used display pandemic over space.

In the parametric setting, notion of a likelihood function forms basis for development tests hypotheses and estimation parameters. Tests in connection with analysis variance stem entirely from considerations function. On other hand, non procedures have generally been derived without any formal mechanism are often result clever intuition. present article, we propose more approach deriving involving use ranks. Specifically, define motivated by characteristics ranks data demonstrate that this...

Abstract The author proposes a general method for constructing nonparametric tests of hypotheses umbrella alternatives. Such alternatives are relevant when the treatment effect changes in direction after reaching peak. author's class is based on ranks observations. His approach consists defining two sets rankings: first induced by alternative and other data itself. test statistic measures distance between sets. determines asymptotic distribution some special cases distances under both null...