ESTIMATION OF FAMILIAL CORRELATIONS UNDER AUTOREGRESSIVE CIRCULAR COVARIANCE

Circular covariance matrices play an important role in modeling phenomena in numerous epidemiological, communications and physical contexts. In this article, we propose a parsimonious, autoregressive type of circular covariance structure for modeling correlations between the “siblings” of a “family”. This structure, similar to AR(1) structure used in time series models, involves only two parameters. We derive the maximum likelihood estimators of these parameters, and discuss testing of hypotheses about the autoregressive parameter. Estimation of “parent-sib” correlation, namely, the interclass correlation, is also considered. Estimation of the parameters when there are unequal numbers of siblings in different families is also discussed.     

Binomial AR(1) processes: moments,cumulants, and estimation

The modelling and analysis of count-data time series are areas of emerging interest with various applications in practice. We consider the particular case of the binomial AR(1) model, which is well suited for describing binomial counts with a first-order autoregressive serial dependence structure. We derive explicit expressions for the joint (central) moments and cumulants up to order 4. Then, we apply these results for expressing moments and asymptotic distribution of the squared difference estimator as an alternative to the sample autocovariance. We also analyse the asymptotic distribution of the conditional least-squares estimators of the parameters of the binomial AR(1) model. The finite-sample performance of these estimators is investigated in a simulation study, and we apply them to real data about computerized workstations.     

Maximum likelihood estimation for a nearly random walk model

This paper proposes an effective reparameterization method for the maximum likelihood estimation of a nearly random walk ARIMA (1,1,1) model, an important case where standard method of locating the MLE is not satisfactory. This model is equivalent to the permanent and temporary components model that Fama &French (1988) and others used to capture the slow mean reversion behavior of stock prices. The reparameterization method we prppose for estimating the nearly cancelled AR and MA parameters performs satisfactorily. The exact likelihood function based on the transformed parameters is studied. We argue that the region of interest will get magnified and emphasized in the transformed space, thus making the search for MLE more thorough and effective. Substantiai simuiation evidences are provided to demonstrate the effectiveness of the method. The sample size requirement is critical and is discussed in details. For application, this method is applied to estimate a nearly random walk ARIMA (1,1,1) model for NYSE/AMEX value-weighted market return in daily and longer holding-period horizons.     

A note on biasedness of tests of fit

The problem of testing a simple null hypothesis on multinomial distribution is considered. Biasedness of customarily used tests of fit is proved for unequal cell probabilities case.     

基于幂律型分布的动态VaR模型及实证研究

针对金融资产回报时间序列的尖峰厚尾性和波动集聚性,提出了基于AR(1)-GARCH(1,1)模型与幂律型分布相结合计算VaR的方法。用GARCH模型对时间序列建模刻画波动集聚性,用基于幂律型分布的扩展形式拟合GARCH模型的残差分布尾部,刻画回报时间序列的厚尾特征,二者结合更好地描述回报时序的动态波动现象。对上证综指进行实证分析,结果表明本文提出的方法比基于正态分布的GARCH模型和静态幂律尾法更精确。     

鉴定顾客满意的关键因素

“卡诺顾客满意模型”告诉我们,要将资源和管理活动的重点放在关键的顾客需求上,哪些才是关键的顾客需求?本文就该问题展开了研究。作者介绍了应用博弈论和危险分析的方法鉴定顾客对产品和服务不满意的关键因素和能够使顾客愉悦的关键因素,通过一组真实数据及鉴定过程,证实了沙普利值法和归因危险度分析在制订最优市场战略中的理论及实用的优势。本文旨在为企业发现“关键的顾客需求”提供一种量化的方法,为企业的重点管理指明方向,从而不断提高其产品和服务的顾客满意度。      

Effect of dependence on statistics for determination of change

Quite a number of test statistics and estimators for detection of a change in the mean of a series of independent observations were proposed and studied. The purpose of this paper is to examine the behaviour of these statistics if the observations are dependent, particularly, if they form a linear process.     

A Broad Class of Partially Specified Autoregressions on Multi-Casting Data

Extending the bifurcating autoregressive (BAR) process (cf. Cowan and Staudte, 1986 Cowan , R. , Staudte , R. G. ( 1986 ). The bifurcating autoregression model in cell lineage studies . Biometrics 42 : 769 – 783 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) to multi-casting (multi-splitting) data, Hwang and Choi (2009 Hwang , S. Y. , Choi , M. S. ( 2009 ). Modeling and large sample estimation for multi-casting autoregression . Statist. Prob. Lett. 79 : 1943 – 1950 .[Crossref], [Web of Science ®] , [Google Scholar]) introduced multi-casting autoregression (MCAR, for short) defined on multi-casting tree structured data. This article is concerned with the case when the MCAR model is partially specified only through conditional mean and variance without directly imposing autoregressive (AR) structure. The resulting class of models will be referred to as P-MCAR (partially specified MCAR). The P-MCAR considerably enlarges the class of multi-casting models including (as special cases) MCAR, random coefficient MCAR, conditionally heteroscedastic multi-casting models and binomial-thinning processes. Moment structures for this broad P-MCAR class are investigated. Least squares (LS) estimation method is discussed and asymptotic relative efficiency (ARE) of the generalized-LS over ordinary-LS is obtained in a closed form. A simulation study is conducted to illustrate results.     

Valid Resampling of Higher-Order Statistics Using the Linear Process Bootstrap and Autoregressive Sieve Bootstrap

We show that the linear process bootstrap (LPB) and the autoregressive sieve bootstrap (AR sieve) are, in general, not valid for statistics whose large-sample distribution depends on moments of order higher than two, irrespective of whether the data come from a linear time series or not. Inspired by the block-of-blocks bootstrap, we circumvent this non-validity by applying the LPB and AR sieve to suitably blocked data and not to the original data itself. In a simulation study, we compare the LPB, AR sieve, and moving block bootstrap applied directly and to blocked data.