Smooth linear statistics of random permutation matrices, sampled under a general Ewens distribution, exhibit an interesting non-universality phenomenon. Though they have bounded variance, their fluctuations are asymptotically non-Gaussian but infinitely divisible. The fluctuations are asymptotically Gaussian for less smooth linear statistics for which the variance diverges. The degree of smooth...

In most situations the best estimator of a function of the parameter exists, but sometimes it has a complex form and we cannot compute its variance explicitly. Therefore, a lower bound for the variance of an estimator is one of the fundamentals in the estimation theory, because it gives us an idea about the accuracy of an estimator. It is well-known in statistical inference that the Cram&eac...

Practicing managers live in a world of ‘extremes’ but management research is based on Gaussian statistics that rule out those extremes. On occasion, deviation amplifying mutual causal processes among interdependent data points cause extreme events characterized by power laws. They seem ubiquitous; we list 80 kinds of them – half each among natural and social phenomena. We draw a ‘line in the sa...

We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n×n Hermitian matrices as n → ∞. Assuming that the test function of statistics is smooth enough and using the asymptotic formulas by Deift et al for orthogonal polynomials with varying weights, we show first that if the support of the Density of States of ...

Article history: Received 28 April 2010 Available online 27 July 2010 This study investigated the usefulness of social cognitive career theory—SCCT (Lent, Brown, and Hackett, 1994) in predicting interests and goals relating to statistics among psychology students. The participants were 1036 Spanish students who completed measurements of statistics-related mastery experiences, self-efficacy, out...

For comparing the distribution of two samples with multiple endpoints, O'Brien (1984) proposed rank-sum-type test statistics. Huang et al. (2005) extended these statistics to the general nonparametric Behrens-Fisher hypothesis problem and obtained improved test statistics by replacing the ad hoc variance with the asymptotic variance of the rank-sum statistics. In this paper we generalize the wo...

A number of studies revealed that our visual system can extract different types of summary statistics, such as the mean and variance, from sets of items. Although the extraction of such summary statistics has been studied well in isolation, the relationship between these statistics remains unclear. In this study, we explored this issue using an individual differences approach. Observers viewed ...

let x1;x2;...;xn have a jointly multivariate exchangeable normal distribution. in this work we investigate another proof of the independence of x and s2 using order statistics. we also assume that (xi ; yi); i =1; 2;...; n; jointly distributed in bivariate normal and establish the independence of the mean and the variance of concomitants of order statistics.

It is well known that the independence of sample mean and variance characterizes normal distribution. By using Anosov’s theorem, we further investigate analogous characteristic properties in terms some feasible definite statistics. The latter statistics introduced this paper for first time are based on nonnegative, continuous functions ordered arguments with positive degree homogeneity. propose...

We develop and show applications of two new test statistics for deciding if one ARIMA model provides significantly better h-step-ahead forecasts than another, as measured by the difference of approximations to their mean square forecast error. The two statistics differ in the variance estimates used for normalization. Both variance estimates are consistent even when the models considered are in...