Estimating common parameters of growth curve models under a quadratic loss

Consider the problem of estimating the common matrix of several growth curve models with possibly different unknown covariance matrices under the quadratic loss. The paper gives a combined estimator with a smaller risk than MLE of each growth curve model.     

Estimation and Asymptotic Properties in Periodic GARCH(1, 1) Models

This article studies the probabilistic structure and asymptotic inference of the first-order periodic generalized autoregressive conditional heteroscedasticity (PGARCH(1, 1)) models in which the parameters in volatility process are allowed to switch between different regimes. First, we establish necessary and sufficient conditions for a PGARCH(1, 1) process to have a unique stationary solution (in periodic sense) and for the existence of moments of any order. Second, using the representation of squared PGARCH(1, 1) model as a PARMA(1, 1) model, we then consider Yule-Walker type estimators for the parameters in PGARCH(1, 1) model and derives their consistency and asymptotic normality. The estimator can be surprisingly efficient for quite small numbers of autocorrelations and, in some cases can be more efficient than the least squares estimate (LSE). We use a residual bootstrap to define bootstrap estimators for the Yule-Walker estimates and prove the consistency of this bootstrap method. A set of numerical experiments illustrates the practical relevance of our theoretical results.     

两次国际产业转移本质探讨 ——基于产品生命周期理论视角

 面对今年日益严重的经济衰退，大多数学者主张摒弃现有发展模式，借鉴发达国家发展道路，摆脱困境。本文运用比较分析法，探讨决定这些国家经济发展模式的背景——两次国际产业转移的本质区别，发现产业区域化处于国际产业转移生命周期的成熟阶段，在短期内回归高工资、高资本技术构成、高劳动生产率、高价格和高人均GDP状态，仅仅让发达国家人们享受工业文明的好处，表现为典型的贵族化特点；产业全球化处于标准化阶段，长期性的低工资、低资本技术构成、低劳动生产率、低价格和低人均GDP，让越来越多的发展中国家人们，享受到越来越多的工业文明的实惠，表现为典型的平民化特点。为此中国未来仍然应延续低成本、低工资发展战略，适当产业升级为辅，避免西方产业空心化。     

《说文解字注》中“同体重复字”之形音义探微

重复相同部首而成的字在《说文》中非常有特色。分析显示。该类字的形体具有显著的视觉效果。读音存在不确定性,意义存在多种解读的可能。据此以探索它们的表义规律及如何消除它们的表义局限。     

A class of dynamic piecewise exponential models with random time grid

A novel fully Bayesian approach for modeling survival data with explanatory variables using the Piecewise Exponential Model (PEM) with random time grid is proposed. We consider a class of correlated Gamma prior distributions for the failure rates. Such prior specification is obtained via the dynamic generalized modeling approach jointly with a random time grid for the PEM. A product distribution is considered for modeling the prior uncertainty about the random time grid, turning possible the use of the structure of the Product Partition Model (PPM) to handle the problem. A unifying notation for the construction of the likelihood function of the PEM, suitable for both static and dynamic modeling approaches, is considered. Procedures to evaluate the performance of the proposed model are provided. Two case studies are presented in order to exemplify the methodology. For comparison purposes, the data sets are also fitted using the dynamic model with fixed time grid established in the literature. The results show the superiority of the proposed model.     

The score function and a comparison of various adjustments of the profile likelihood

Several adjustments of the profile likelihood have the common effect of reducing the bias of the associated score function. Hence expansions for the adjusted score functions differ by a term, D_ξ, that has small asymptotic order (n ^?½). The effect of D_ξ on other quantities of interest is studied. In particular, we find the bias and variance of the adjusted maximum-likelihood estimate to be relatively unaffected, while differences in the Bartlett correction depend on D_ξ in a simple way.     

A block bootstrap comparison for sparse chains

In this paper we apply the sequential bootstrap method proposed by Collet et al. [Bootstrap Central Limit theorem for chains of infinite order via Markov approximations, Markov Processes and Related Fields 11(3) (2005), pp. 443–464] to estimate the variance of the empirical mean of a special class of chains of infinite order called sparse chains. For this process, we show that we are able to compute numerically the true value of the standard error with any fixed error.

Our main goal is to present a comparison, for sparse chains, among sequential bootstrap, the block bootstrap method proposed by Künsch [The jackknife and the Bootstrap for general stationary observations, Ann. Statist. 17 (1989), pp. 1217–1241] and improved by Liu and Singh [Moving blocks jackknife and Bootstrap capture week dependence, in Exploring the limits of the Bootstrap, R. Lepage and L. Billard, eds., Wiley, New York, 1992, pp. 225–248] and the bootstrap method proposed by Bühlmann [Blockwise bootstrapped empirical process for stationary sequences, Ann. Statist. 22 (1994), pp. 995–1012].     

Tests for Symmetric Error Distribution in Linear and Nonparametric Regression Models

In linear and nonparametric regression models, the problem of testing for symmetry of the distribution of errors is considered. We propose a test statistic which utilizes the empirical characteristic function of the corresponding residuals. The asymptotic null distribution of the test statistic as well as its behavior under alternatives is investigated. A simulation study compares bootstrap versions of the proposed test to other more standard procedures.     

Recursive computation of the single and product moments of order statistics from the complementary exponential–geometric distribution

The complementary exponential–geometric distribution has been proposed recently as a simple and useful reliability model for analysing lifetime data. For this distribution, some recurrence relations are established for the single and product moments of order statistics. These recurrence relations enable the computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient recursive manner. By using these relations, we have tabulated the means, variances and covariances of order statistics from samples of sizes up to 10 for various values of the shape parameter θ. These values are in turn used to determine the best linear unbiased estimator of the scale parameter β based on complete and Type-II right-censored samples.     

History matters: The impact of reviews and sales of earlier versions of a product on consumer and expert reviews of new editions

Product reviews are assumed to be based on the observable characteristics of the underlying product. However, in the case of new editions in a product series, the determinants may include signals that originate from the reviews and the sales of editions that precede the focal product edition. Our analysis of 577 video games released in a series between 2000 and 2009 indicates that the reviews of earlier versions carry over to the reviews of the sequel by the same type of reviewer. We also find that expert reviews are influenced by the average review of previous editions by consumers and the average sales of previous editions of the product. This suggests that experts tend to adapt to the taste of consumers. Furthermore, it is found that a lack of consensus, between reviewers of a particular type, weakens the impact of average past reviews, whilst it magnifies the impact of the sales of earlier versions.