A correlation type procedure for assessing multivariate normality

A correlation-type statistic for assessing multivariate normality is described. Its estimated finite sample distribution is tabulated, and its performance against certain alternatives is compared with that of a competing Cramer-von Mises type statistic in a Monte Carlo power study. A set of quadrivariate data is examined as illustration of the procedure.     

ROBUSTNESS OF PROCEDURES FOR THE BEHRENS-FISHER PROBLEMS: EXTENSION TO BIVARIATE NORMAL MIXTURES

In the applied sciences, it is often important to be able to compare the mean values of two populations. However, testing a hypothesis can be complex, if the two populations are heteroscedastic and exhibit non-normality in the data. This paper reviews currently available strategies for the multivariate Behrens-Fisher problem. It then carries out Monte Carlo comparisons of selected procedures to assess their robustness when applied to data from normal mixture distributions. The overall conclusion is that Johansen's procedure appears to work best for small sample data both in terms of empirical power and significance level. Johansen's procedure works reasonably well even with mixture data. The simulation also provides researchers with specific guidelines to follow at the early designing and planning stages of the investigation.     

Robust estimation for ordinal regression

Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot.     

A multivariate solution of the multivariate ranking and selection problem

The problem of selection of the best multivariate population is given a new formulation which does not involve reducing the populations to univariate quantities. This formulation's solution is developed for known, and (using the Heteroscedastic Method) also for unknown, variance-covariance matrices. Preference reversals and arbitrary nonlinear preference functions are explicitly allowed in this new theory     

Estimation of signal to noise ratio using mahalanobis distance

In this paper, we propose some alternative estimatiors to that given by C. G. Khatri and C. R. Rao (1985), for estimating Signal to Noise ratio. Using Pitman Nearness, Condition for prefering one estimator over the other is estabilished. It is shown numerically that estimators corresponding to Entropy loss function are better more oftern than those corresponding to Squared Error loss.     

基于有效预测区域的模糊数据关联

多目标多传感器跟踪系统由数据关联和目标状态估计两部分组成,数据关联是多目标跟踪系统研究的核心。数据关联和目标状态估计两部分既有一定的独立性又有密切的联系,而将两部分合理地结合对提高跟踪系统的性能是重要的。该文以跟踪目标的有效预测区域为依据,利用基于Mahalanobis距离的模糊均值聚类方法解决数据关联问题,在一定程度上将数据关联和目标状态估计两个不同的过程相结合,仿真计算说明了其有效性。     

Long-range correlation analysis of the Wichmann-Hill random number generator

The distribution of points (r _n,r _n+s), n = 0, 1, 2,...whose coordinates are terms at distance s of the pseudorandom sequence generated by the Wichmann and Hill method is studied. It is known that for many congruential generators critical values of the distance s exist such that these points, far from being uniformly distributed, are concentrated on very few lines. An algorithm is described for computing the critical distances within the Wichmann-Hill sequence and the results obtained are compared with those of other linear congruential generators.     

Superiority of the r-k class estimator over some estimators in a misspecified linear model

ABSTRACT

In this article, we discuss the superiority of r-k class estimator over some estimators in a misspecified linear model. We derive the necessary and sufficient conditions for the superiority of the r-k class estimator over each of these estimators under the Mahalanobis loss function by the average loss criterion in the misspecified linear model.     

Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence

The Rényi entropy is a generalisation of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic Rényi entropy and related functionals for the marginal distribution of a stationary m-dependent sequence. The U-statistic estimators under study are based on the number of ε-close vector observations in the corresponding sample. A variety of asymptotic properties for these estimators are obtained (e.g. consistency, asymptotic normality, and Poisson convergence). The results can be used in diverse statistical and computer science problems whenever the conventional independence assumption is too strong (e.g. ε-keys in time series databases and distribution identification problems for dependent samples).