Distribution of multivariate quadratic forms under certain covariance structures

Necessary and sufficient conditions are given for the covariance structure of all the observations in a multivariate factorial experiment under which certain multivariate quadratic forms are independent and distributed as a constant times a Wishart. It is also shown that exact multivariate test statistics can be formed for certain covariance structures of the observations when the assumption of equal covariance matrices for each normal population is relaxed. A characterization is given for the dependency structure between random vectors in which the sample mean and sample covariance matrix have certain properties.     

Statistical tests for random effects in staggered nested designs

In this paper, we present certain statistical tests under a staggered nested design set-up, for the hypotheses that certain variance components are zero. To do so, the particular variance-covariance, structure induced by the staggering is exploited and certain results of multivariate analysis are used. In most problems, the test statistics can be easily computed. An example is provided for illustration and some power computations for comparison of test statistics are shown.     

The Whittle Estimator for Strongly Dependent Stationary Gaussian Fields

In this article we generalize results on the asymptotic behaviour of the Whittle estimator for certain stationary Gaussian long range dependent fields. These results have been established in the one-dimensional case under very general conditions. They require controlling the estimation bias and also giving convergence theorems for certain quadratic forms of the observations. In the multidimensional setting, our main interest will be controlling the bias. This can be done for d ≤ 3 using taper functions, and, depending on the shape of the singularity, also introducing certain regularizing functions. In this last case, however, the estimator will no longer be efficient. We also present certain partial results concerning the convergence to a limiting Gaussian distribution of the associated quadratic forms.     

First-order autoregressive models: A method for obtaining eigenvalues for weighting matrices

Autoregressive models are useful for analysing agricultural field experiments. However, in order to formulate such models, there is a need to specify certain weights reflecting the degree of interaction between neighbouring plots. The eigenvalues for the matrices formed by such weights are usually needed. The paper describes a method for obtaining these eigenvalues, for certain regular patterns.     

The exact nonparametric analysis of a class of experimental designs

This article given an efficient computer algorithm for a certain nonparametric regression method based on Kendall's rank correlation statistics. The method applies to experimental designs for which the set of covariates exhibits certain orthogonality properties, and the dependent variables is continuous. Testing, point and interval estimation, and ties are discussed.     

Two normal approximations to the binomial distribution

Two new normal approximations are proposed for the cumulative binomial distribution when the mean-is reasonably large. Their adequacy is compared with that of certain well-known approximations- The first is recommended for its simplicity and accuracy relative to the standard and Gram-Charlier approximations. The second Is shown to be more accurate than all known approximations for a certain range of the probability of success.     

An alternative version of zero-inflated logarithmic series distribution and some of its applications

An important drawback of the standard logarithmic series distribution (LSD) in several practical applications is that it excludes the zero observation from its support. The LSD with non-negative support is not much studied in the literature. Recently Kumar and Riyaz [On the zero-inflated LSD and its modification. Statistica (accepted for publication). 2013] considered a distribution in this respect namely ‘zero-inflated logarithmic series distribution (ZILSD)’. Through this paper we propose an alternative form of the ZILSD and study some of its properties. We obtain expressions for its probability-generating function, mean and variance, and develop certain recurrence relations for its probabilities, raw moments and factorial moments. The parameters of the model are estimated by the method of moments and the method of maximum likelihood, and certain test procedures are considered for testing the significance of the additional parameter of the distribution. The distribution has been fitted to certain real-life data sets for illustrating its usefulness compared with certain existing models available in the literature. Further, a simulation study is conducted for assessing the performance of the estimators.     

On some aspects of a flexible class of additive Weibull distribution

Here we consider a more flexible class of the additive Weibull distribution of Xie and Lai (Reliab. Eng. Syst. Safety, 1995) and investigate some of its important properties such as expressions for its cumulative distribution function, reliability measures, quantile function, characteristic function, raw moments, incomplete moments, etc. The distribution and moments of order statistics are obtained along with certain structural properties. The maximum-likelihood estimation of the parameters of the distribution is attempted and the usefulness of the model in certain applied areas is illustrated with the help of certain real life data sets.     

Some applications,properties and conjectures for higher order cumulants of a markovian stepping-stone model

This paper investigates certain tridiagonal coefficient matrices from linear differential equations for the joint cumulants of a Markovian stepping-stone model. The model is used to describe the dynamics of insect population growth, and is illustrated with an application to the spread of Africanized honey bees. The coefficient matrices are shown to have certain structure. A conjecture concerning their eigenvalues is proven for a special case of interest, and is also investigated numerically and by symbolic mathematical analysis.     

On optimality of a two-stage sawpling method for binomial populations

We consider a family of two-stage sampling methods for a binomial parameter that guarantee a certain precision. It is shown that, among all such methods, one due to Birnbaum and Healy minimizes the average expected second stage sample size with respect to a certain density on the parameter space. It does not, however, minimize the average expected second stage sample size with respect to the uniform density.     

Robust models in probability sampling

In the estimation of a population mean or total from a random sample, certain methods based on linear models are known to be automatically design consistent, regardless of how well the underlying model describes the population. A sufficient condition is identified for this type of robustness to model failure; the condition, which we call 'internal bias calibration', relates to the combination of a model and the method used to fit it. Included among the internally bias-calibrated models, in addition to the aforementioned linear models, are certain canonical link generalized linear models and nonparametric regressions constructed from them by a particular style of local likelihood fitting. Other models can often be made robust by using a suboptimal fitting method. Thus the class of model-based, but design consistent, analyses is enlarged to include more realistic models for certain types of survey variable such as binary indicators and counts. Particular applications discussed are the estimation of the size of a population subdomain, as arises in tax auditing for example, and the estimation of a bootstrap tail probability.     

Utilizing auxiliary variables in sequential ratio and regression estimation schemes

Ratio and regression estimators for a mean are considered in conjunction with certain sequential sampling schemes. An auxiliary variable is assumed present and both fixed-cost and fixed- width confidence interval stopping rules are investigated. The asymptotic distributions of the estimators are derived as well as optimal probabilities pertinent to the schemes. Comparisons are made with results of certain double sampling procedures. Estimation of the ratio of two means is also considered and the results of a Monte Carlo simulation are included.     

Categorical information and the singular linear model

C. R. Rao (1978) discusses estimation for the common linear model in the case that the variance matrix σ² Q has known singular form Q . In the more general context of inference, this model exhibits certain special features and illustrates how information concerning unknowns can separate into a categorical component and a statistical component. The categorical component establishes that certain parameters are known in value and thus are not part of the statistical inference.     

An estimator for the extreme-value index

Asymptotic normally is derived for a new estimator of the extreme value index under certain conditions.     

The effect of serial correlation on confidence regions for the parmnters of a multivariate normal population

The affect upon the significance levels of confidence regions for the mean of a multivariate normal population are determined for certain violations of the independence assumption.     

中国恩格尔系数下降原因新探

在使用恩格尔系数评价某个国家或地区某个阶段的生活贫富状况时，要结合恩格尔系数的具体影响因素，分清其下降的真正原因。论文从恩格尔系数的计算公式出发，认为它的基本影响因素是物价、品种数、各种消费品或劳务的购买量。利用因子分析法分析了导致居民恩格尔系数下降的五种可能的原因，并联系实际具体阐释。     

On parameter orthogonality in symmetric and skew models

Orthogonal and partly orthogonal reparametrisations are provided for certain wide and important families of univariate continuous distributions. First, the orthogonality of parameters in location-scale symmetric families is extended to symmetric distributions involving a third parameter. This sets the scene for consideration of the four-parameter situation in which skewness is also allowed. It turns out that one specific approach to generating such four-parameter families, that of two-piece distributions with a certain parametrisation restriction, has some attractive features with regard to parameter orthogonality which, to the best of our knowledge, are not shared with other four-parameter distributions. Our work also affords partly orthogonal parametrisations of three-parameter two-piece models.     

On discrimination and classification with multivariate repeated measures data

We study the problem of classification with multiple q-variate observations with and without time effect on each individual. We develop new classification rules for populations with certain structured and unstructured mean vectors and under certain covariance structures. The new classification rules are effective when the number of observations is not large enough to estimate the variance–covariance matrix. Computational schemes for maximum likelihood estimates of required population parameters are given. We apply our findings to two real data sets as well as to a simulated data set.     

Asymptotically optimum estimation of a probability in inverse binomial sampling under general loss functions

The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that satisfies certain assumptions. It is shown that the limit superior of the risk for p asymptotically small has a minimum over all (possibly randomized) estimators. This minimum is achieved by certain non-randomized estimators. The model includes commonly used quality criteria as particular cases. Applications to the non-asymptotic regime are discussed considering specific loss functions, for which minimax estimators are derived.