A statistical analysis of the screening measure of multiple recursive random number generators of orders one and two

This paper presents the results of a comprehensive empirical analysis of the screening measure of multiple recursive generators (MRGs) of orders one and two. Two kinds of screening measures are distinguished: spectral test and lattice test. With regard to these screening measures, two exhaustive searches of the twenty best MRGs of orders one and two are conducted. Some empirical comparisons reveal that the screening procedure with maximum spectral value criterion is preferred in terms of efficiency and thus, is a good way of obtaining ideal MRGs of higher orders. Several extensively tested second-order MRGs are also presented and are therefore recommended.     

Non-parametric testing for the number of change points in a sequence of independent random variables

A non-parametric procedure is derived for testing for the number of change points in a sequence of independent continuously distributed variables when there is no prior information available. The procedure is based on the Kruskal–Wallis test, which is maximized as a function of all possible places of the change points. The procedure consists of a sequence of non-parametric tests of nested hypotheses corresponding to a decreasing number of change points. The properties of this procedure are analyzed by Monte Carlo methods and compared to a parametric procedure for the case that the variables are exponentially distributed. The critical values are given for sample sizes up to 200.     

C55. Quick and accurate rule of thumb for determining the critical value of the coefficient of correlation

Life table analysis techniques in epidemiology depend upon the asymptotic properties of the statistical test methods employed. In some instances, the statistical procedures indicate highly significant results which are, in reality, unjustified. The phenomenon may occur when the asymptotic methods are applied in situations where the cases of interest are few in number. This situation is illustrated by the 20 multiple myeloma deaths observed in the RERF Life Span Study cohort. A permutation test is applied to the life table data, although the test requires the false assumption that the censoring distribution is independent of the radiation dose. A simulation test is developed which does not require equal censoring, which has the same asymptotics as the usual test methods, and which is less likely to overestimate significance in small samples. It is found that both of these small-sample tests provide reasonable numerical solutions. In addition, the simulation test is recommended in general for analyzing life table data with unequal censoring. Finally, by using the small-sample tests, the frequency of death from multiple myeloma is shown to be positively associated with radiation dose (P<0.01).     

A strong law of large number for negatively dependent and non identical distributed random variables in the framework of sublinear expectation

Abstract

In this article, in the framework of sublinear expectation initiated by Peng, we derive a strong law of large numbers (SLLN) for negatively dependent and non identical distributed random variables. This result includes and extends some existing results. Furthermore, we give two examples of our result for applications.     

On improvement in estimating the population mean in simple random sampling

Kadilar and Cingi [Ratio estimators in simple random sampling, Appl. Math. Comput. 151 (3) (2004), pp. 893–902] introduced some ratio-type estimators of finite population mean under simple random sampling. Recently, Kadilar and Cingi [New ratio estimators using correlation coefficient, Interstat 4 (2006), pp. 1–11] have suggested another form of ratio-type estimators by modifying the estimator developed by Singh and Tailor [Use of known correlation coefficient in estimating the finite population mean, Stat. Transit. 6 (2003), pp. 655–560]. Kadilar and Cingi [Improvement in estimating the population mean in simple random sampling, Appl. Math. Lett. 19 (1) (2006), pp. 75–79] have suggested yet another class of ratio-type estimators by taking a weighted average of the two known classes of estimators referenced above. In this article, we propose an alternative form of ratio-type estimators which are better than the competing ratio, regression, and other ratio-type estimators considered here. The results are also supported by the analysis of three real data sets that were considered by Kadilar and Cingi.     

On the Critical Value Behaviour of Multiple Decision Procedures

In this paper we investigate the asymptotic critical value behaviour of certain multiple decision procedures as e.g. simultaneous confidence intervals and simultaneous as well as stepwise multiple test procedures. Supposing that n hypotheses or parameters of interest are under consideration we investigate the critical value behaviour when n increases. More specifically, we answer e.g. the question by which amount the lengths of confidence intervals increase when an additional parameter is added to the statistical analysis. Furthermore, critical values of different multiple decision procedures as for instance step-down and step-up procedures will be compared. Some general theoretic results are derived and applied for various distributions.     

On randomness, determinism and computability

This paper discusses the meaning and relationship of randomness and determinism. A fundamental development of chaotic dynamical systems is given with examples. Such systems are seen to exhibit randomness in the usual sense of unpredictability. The formal definition of randomness in terms of algorithmic incompressibility is also discussed. The role of recursion in computability and randomness is also discussed.     

On comparing,classifying and clustering several dependent regression models

Classifying several regression models fitted on a dataset is one of the most problems in data analysis. In other words, scientists are interested in comparing several regression models that can be used for a dataset. In this paper, an approach will be used to compare and classify several dependent regression models. Then the performance of the proposed method is investigated using simulation study and real example.     

On the LBI criterion for the multivariate one-way random effects model under non-normality

The asymptotic null distribution of the locally best invariant (LBI) test criterion for testing the random effect in the one-way multivariable analysis of variance model is derived under normality and non-normality. The error of the approximation is characterized as O(1/n). The non-null asymptotic distribution is also discussed. In addition to providing a way of obtaining percentage points and p-values, the results of this paper are useful in assessing the robustness of the LBI criterion. Numerical results are presented to illustrate the accuracy of the approximation.     

On the estimation of the most probable number in a serial dilution experiment

The purpose of this paper is to present some alternative estimates for the 'most probable number' of bacteria in a serial dilution experiment. These estimates are directed to be less biased than the ordinary maximum likelihood estimate. A numerical example illustrates the extent to which the variance and the mean square error of these estimates are generally less than those corresponding to the maximum likelihood estimate.     

Computation of the percentage points and the power for the two-sided Kolmogorov-Smirnov one sample test

Two recursive schemes are presented for the calculation of the probabilityP(g(x)≤S _n (x)≤h(x) for allx∈®), whereS _n is the empirical distribution function of a sample from a continuous distribution andh, g are continuous and isotone functions. The results are specialized for the calculation of the distribution and the corresponding percentage points of the test statistic of the two-sided Kolmogorov-Smirnov one sample test. The schemes allow the calculation of the power of the test too. Finally an extensive tabulation of percentage points for the Kolmogorov-Smirnov test is given.     

On Permutation Tests in Multiple Regression and Analysis of Covariance Problems

We introduce distribution-free permutation tests and corresponding estimates for studying the effect of a treatment variable x on a response y. The methods apply in the presence of a multivariate covariate z. They are based on the assumption that the treatment values are assigned randomly to the subjects.     

On Testing the Mean Equivalence of Treatments from Correlated Normal Populations

Let there be k equally correlated treatment populations under consideration, a Studentized range test is proposed to test the hypothesis of average mean equivalence against the alternative hypothesis of inequivalence. The maximum level and minimum power at some least favorable configurations of means are used to calculate the critical value and the required sample size simultaneously when testing a null against an alternative hypothesis. The range test is applied to a real world problem to find out if the stress levels among children at four time periods due to a newly built nearby airport are equivalent.     

Asymptotic properties of kruskal-wallis test and friedman test in the analysis of variance models with random effects

In this paper, asymptotic properties of the Kruskal-Wallis test in the one-way analysis of variance model and that of the Friedman test in the two-way classification model are investigated under alternatives when the treatment effects are random. It is shown that the asymptotic distribution of each statistic is the same as a mixture of central chi-squared variables. Asymptotic comparisons of the tests with respect to their parametric competitors are also performed     

On the distribution of linear combinations of the components of a Dirichlet random vector

On making use of a result of Imhof, an integral representation of the distribution function of linear combinations of the components of a Dirichlet random vector is obtained. In fact, the distributions of several statistics such as Moran and Geary's indices, the Cliff‐Ord statistic for spatial correlation, the sample coefficient of determination, F‐ratios and the sample autocorrelation coefficient can be similarly determined. Linear combinations of the components of Dirichlet random vectors also turn out to be a key component in a decomposition of quadratic forms in spherically symmetric random vectors. An application involving the sample spectrum associated with series generated by ARMA processes is discussed.     

Shrinkage and modification techniques in estimation of variance and the related problems: A review

One of the surprising decision-theoretic results Charles Stein discovered is the inadmissibility of the uniformly minimum variance unbiased estirnator(UMVUE) of the variance of a normal distribution with an unknown mean. Some methods for deriving estimators better than the UMVUE were given by Stein. Brown, Brewster and Zidek. Recently Kubokawa established a novel approach, called the IERD method, by use of which one gets a unified class of improved estimators including their previous procedures. This paper gives a review for a series of these decision-theoretical developments as well as surveys the study of the variance-estimation problem from various aspects. Related to this issue, the paper enumerates several topics with the situations where the usual plain estimators are required to be shrunken or modified, and gives reasonable procedures improving the usual ones through the IERD method.     

On the asymptotic expectation and variance of the number of boundary crossings

Let X₁,X₂,… be independent and identically distributed nonnegative random variables with mean μ, and let S_n = X₁ + … + X_n. For each λ > 0 and each n ≥ 1, let A_n be the interval [λn^Y, ∞), where γ > 1 is a constant. The number of times that S_n is in A_n is denoted by N. As λ tends to zero, the asymtotic behavior of N is studied. Specifically under suitable conditions, the expectation of N is shown to be (μλ^?1)^β + o(λ^?β/2 where β = 1/(γ-1) and the variance of N is shown to be (μλ^?1)^β(βμ¹)²σ² + o(λ^?β) where σ² is the variance of X_n.     

中国循环经济评价体系构建及实证分析

建立一套合理完善的循环经济评价指标体系是循环经济建设的基础性工作,也是考核循环经济发展效果的定量标准。从循环经济的本质和运行机理出发,从物质流分析的视角提出符合中国国情的循环经济发展评价体系并展开相关实证分析,力图由点及面,为中国制定循环经济发展评价体系提供参考。