A linear algebraic algorithm for reducing the support size of t-designs and to generate a basis for trades

A simple linear algebraic algorithm to generate a basis of the null space of a given integral matrix is utilized to present a computer algorithm, which in general, is used to reduce the support size of a given design as in a theorem of FoodyHedayat (Theorem 4.1, 1977), and in particular, it is used to produce a basis for trades. The computations based on this algorithm is of order of a polynomial function.     

High order intersection numbers of t-designs

In this paper we present two generalizations of the results on the intersection numbers of t-designs: the first is related to a result of Ray-Chaudhuri and Wilson (Osaka J. Math. 12 (1975) 737–744) and the second to that of Mendelsohn (in: Studies in Pure Mathematics (Acadamic Press, New Year, 1971)) and Köhler (Discrete Math. 73 (1988/1989) 133–142).     

An optimal property of the “(r,k ) class estimators”

The purpose of this work is to display optimal conditions, in terms of the Mean Square Error criterion of the (r,k) class estimators. This will be done with respect to the ordinary ridge repression, principal components and ordinary least squares estimate.     

Reliabilities for (n,f, k (i,j)) and ⟨n,f, k (i,j)⟩ Systems

The (n,f,k(i,j)):F(? n,f,k(i,j)?:F) system consists of n components ordered in a line or circle, while the system fails if, and only if, there exist at least f failed components OR (AND) at least k consecutive failed components among components i,i + 1,…,j ? 1,j. In this article, we present the system reliability formulae for these systems with product of matrices by means of a two-stage finite Markov chain imbedding approach, a technique first used by Cui et al. (2002 Cui , L. R. , Kuo , W. , Xie , M. ( 2002 ). On (f,g)-out-of-((i,j),n) systems and its reliability . In: Third International Conference on Mathematical Methods in Reliability Methodology and Practice , June 17–20 , Norway , Trondheim , pp. 173 – 176 . [Google Scholar]). In addition, their dual systems, denoted by (n,f,k(i,j)):G and ? n,f,k(i,j)?:G, are also introduced. Two numerical examples are given to illustrate the results.     

On diagnostic devices for proposing half-logistic and inverse half-logistic models using generalized (k) record values

In this work we consider the generalized upper (k) record values (GURV’s) and generalized lower (k) record values (GLRV’s) arising from half-logistic distribution (HLD) and inverse half-logistic distribution (IHLD). We derive some characterization results of HLD based on some moment relations of generalized upper (k) record values and those of generalized lower (k) record values and accordingly devised some diagnostic tools to identify HLD as a model to the distribution of a population. Similar characterization theorems and diagnostic tools are developed for IHLD as well. Simulation studies are conducted to validate the diagnostic tools devised for both HLD and IHLD.     

三阶段DEA模型管理无效率估计注记

由于能够同时调整外部环境与随机误差等因素对效率计算的影响,由Fried et al.(2002)提出的三阶段DEA模型得到了广泛应用。但在对其中的管理无效率进行估计时,国内一些学者误用了Jondrow et al. (1982)的公式。本文给出了适用公式,并进一步给出了使用李双杰等(2007)提出的统一分布假设的三阶段DEA模型管理无效率的估计公式。     

The 1970 US draft lottery revisited: a spatial analysis

Summary.  We revise the result of the 1970 selective service draft lottery in the USA following an open question that was suggested by Fienberg in a paper published in Science in 1971. The result of the drawings can be viewed as a particular spatial pattern which can be analysed by using general spatial tools adapted to our context. Approaches for assessing the complete spatial randomness for this spatial process on a finite support are proposed. More specifically, these approaches involve the number of events in a square window and a k ( r )-based function used to analyse stationary spatial point processes.     

The effects of correlation among observations on the consistency property of sample variance

It is well known that even when the sample observations are correlated and not normal the sample variance, S² converges in probability to E(S²). But the required sample size for S² to be a consistent estimator of E(S²) is an open question. Some light is shed on this question in this paper. In particular the relation between the rate of convergence and the correlation property of the observations is explored. It is shown that the retardation to the rate of convergence is not appreciable if the correlation is moderate but it can be severe for extreme correlations.     

Some Related Minima Stability and Minima Infinite Divisibility of the General Multivariate Pareto Distributions

This article studies the minima stable property of the general multivariate Pareto distributions MP^(k)(I), MP^(k)(II), MP^(k)(III), MP^(k)(IV) which can be applied to characterize the MP^(k) distribution via its weighted ordered coordinates minima and marginal distribution. Also, the multivariate semi-Pareto distribution (denoted by MSP) is discerned in the class of geometric minima infinite divisible and geometric minima stable distributions. If the exponent measure is satisfied by some functional equation, then the geometric minima stable property can be used to characterize the MSP distribution. Finally, the finite sample minima infinite divisible property of the MP^(k)(I), (II), and (IV) distributions is also discussed.     

Combining Unbiased Ridge and Principal Component Regression Estimators

In the presence of multicollinearity problem, ordinary least squares (OLS) estimation is inadequate. To circumvent this problem, two well-known estimation procedures often suggested are the unbiased ridge regression (URR) estimator given by Crouse et al. (1995 Crouse , R. , Jin , C. , Hanumara , R. ( 1995 ). Unbiased ridge estimation with prior information and ridge trace . Commun. Statist. Theor. Meth. 24 : 2341 – 2354 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and the (r, k) class estimator given by Baye and Parker (1984 Baye , M. , Parker , D. ( 1984 ). Combining ridge and principal component regression: a money demand illustration . Commun. Statist. Theor. Meth. 13 : 197 – 205 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). In this article, we proposed a new class of estimators, namely modified (r, k) class ridge regression (MCRR) which includes the OLS, the URR, the (r, k) class, and the principal components regression (PCR) estimators. It is based on a criterion that combines the ideas underlying the URR and the PCR estimators. The standard properties of this new class estimator have been investigated and a numerical illustration is done. The conditions under which the MCRR estimator is better than the other two estimators have been investigated.     

A latent variable model for analyzing mixed longitudinal (k,l)-inflated count and ordinal responses

A random effects model for analyzing mixed longitudinal count and ordinal data is presented where the count response is inflated in two points (k and l) and an (k,l)-Inflated Power series distribution is used as its distribution. A full likelihood-based approach is used to obtain maximum likelihood estimates of parameters of the model. For data with non-ignorable missing values models with probit model for missing mechanism are used.The dependence between longitudinal sequences of responses and inflation parameters are investigated using a random effects approach. Also, to investigate the correlation between mixed ordinal and count responses of each individuals at each time, a shared random effect is used. In order to assess the performance of the model, a simulation study is performed for a case that the count response has (k,l)-Inflated Binomial distribution. Performance comparisons of count-ordinal random effect model, Zero-Inflated ordinal random effects model and (k,l)-Inflated ordinal random effects model are also given. The model is applied to a real social data set from the first two waves of the national longitudinal study of adolescent to adult health (Add Health study). In this data set, the joint responses are the number of days in a month that each individual smoked as the count response and the general health condition of each individual as the ordinal response. For the count response there is incidence of excess values of 0 and 30.     

Applications of schur theory to reliability inference for k of n systems

The results of Hoeffding (1956), Pledger and Proschan (1971), Gleser (1975) and Boland and Proschan (1983) are used to obtain Buehler (1957) 1-α lower confidence limits for the reliability of k of n systems of independent components when the subsystem data have equal sample sizes and the observed failures satisfy certain conditions. To the best of our knowledge, for k ≠ 1 or n, this is the first time the exact optimal lower confidence limits for system reliability have been given. The observed failure vectors are a generalization of key test results for k of n systems, k ≠ n (Soms (1984) and Winterbottom (1974)). Two examples applying the above theory are also given.     

中国股票市场的长期记忆性与趋势预测研究

本文首次在国内利用较新的精准局部似然函数法（Exact Local Whittle）,以上证指数为对象,估计了ARFIMA(p,d,q)模型的长期记忆参数d,并分析了上证指数的趋势性变化。估计结果和稳健性检验均表明,上证指数具有长期记忆性,以上证指数为代表的股票市场并非有效;模拟结果显示,当滚动窗口n=260,带宽m=[n0.65]时,长期记忆参数即估计量d既具备一致性,又具有渐进正态性。在2004年10月8日至2015年11月13日期间,模型给出了8次上涨或下跌的趋势转换信号,其中7次信号是正确的,仅有1次给出了错误信号;股票价格由下跌趋势转为上涨趋势、由上涨趋势转为下跌趋势两种情况相比,记忆参数d在前一种情况时下跌幅度更大,给出的信号更明显。     

A Nonparametric Test for the Ordered Alternative Based on Kendall's Correlation Coefficient

Several methods have been developed for testing the ordered alternative. These include the Jonckheere–Terpstra (JT) test (Jonckheere, 1954 Jonckheere , A. R. ( 1954 ). A distribution free k-sample test against ordered alternatives . Biometrika 41 : 133 – 145 .[Crossref], [Web of Science ®] , [Google Scholar]; Terpstra, 1952 Terpstra , T. ( 1952 ). The asymptotic normality and consistency of Kendall's test against trend when ties are present in one ranking . Indigationes Mathematicae 14 : 327 – 333 . [Google Scholar]), a modified JT test (MJT) (Tryon and Hettmansperger, 1987 Tryon , V. P. , Hettmansperger , T. P. ( 1987 ). A class of nonparametric tests for homogeneity against ordered alternatives . Annals of Statistics 1 : 1061 – 1070 . [Google Scholar]), and a test proposed by Terpstra and Magel (TM) (Terpstra and Magel, 2003 Terpstra , J. T. , Magel , R. C. ( 2003 ). A new nonparametric test for the ordered alternative problem . Journal of Nonparametric Statistics 15 : 289 – 301 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), among others. This article proposes a new method for testing the ordered alternative. The proposed test is based on Kendall's tau statistic. The asymptotic distribution of the test statistic is given. A Monte Carlo simulation study is conducted comparing the estimated powers of the proposed test with existing tests under a variety of sample sizes and distributions.     

Multi-sample test for high-dimensional covariance matrices

In this paper, we propose a new test statistic for testing the equality of high-dimensional covariance matrices for multiple populations. The proposed test statistic generalizes the test of the equality of two population covariance matrices proposed by Li and Chen (2012).     

Joint (k,l)-hurdle random effects models for mixed longitudinal power series and normal outcomes

A random effects model for analyzing mixed longitudinal normal and count outcomes with and without the possibility of non ignorable missing outcomes is presented. The count response is inflated in two points (k and l) and the (k, l)-Hurdle power series is used as its distribution. The new distribution contains, as special submodels, several important distributions which are discussed, such as (k, l)-Hurdle Poisson and (k, l)-Hurdle negative binomial and (k, l)-Hurdle binomial distributions among others. Random effects are used to take into account the correlation between longitudinal outcomes and inflation parameters. A full likelihood-based approach is used to yield maximum likelihood estimates of the model parameters. A simulation study is performed in which for count outcome (k, l)-Hurdle Poisson, (k, l)-Hurdle negative binomial and (k, l)-Hurdle binomial distributions are considered. To illustrate the application of such modelling the longitudinal data of body mass index and the number of joint damage are analyzed.     

Optimal design of experimental epidemics

We consider the optimal design of controlled experimental epidemics or transmission experiments, whose purpose is to inform the practitioner about disease transmission and recovery rates. Our methodology employs Gaussian diffusion approximations, applicable to epidemics that can be modeled as density-dependent Markov processes and involving relatively large numbers of organisms. We focus on finding (i) the optimal times at which to collect data about the state of the system for a small number of discrete observations, (ii) the optimal numbers of susceptible and infective individuals to begin an experiment with, and (iii) the optimal number of replicate epidemics to use. We adopt the popular D-optimality criterion as providing an appropriate objective function for designing our experiments, since this leads to estimates with maximum precision, subject to valid assumptions about parameter values. We demonstrate the broad applicability of our methodology using a diverse array of compartmental epidemic models: a time-homogeneous SIS epidemic, a time-inhomogeneous SI epidemic with exponentially decreasing transmission rates and a partially observed SIR epidemic where the infectious period for an individual has a gamma distribution.