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.     

On univariate and bivariate generalized gamma convolutions

This paper has two parts. In the first part some results for generalized gamma convolutions (GGCs) are reviewed. A GGC is a limit distribution for sums of independent gamma variables. In the second part, bivariate gamma distributions and bivariate GGCs are considered. New bivariate gamma distributions are derived from shot-noise models. The remarkable property hyperbolic complete monotonicity (HCM) for a function is considered both in the univariate case and in the bivariate case.     

Smoothing parameter selection methods for nonparametric regression with spatially correlated errors

When spatial data are correlated, currently available data‐driven smoothing parameter selection methods for nonparametric regression will often fail to provide useful results. The authors propose a method that adjusts the generalized cross‐validation criterion for the effect of spatial correlation in the case of bivariate local polynomial regression. Their approach uses a pilot fit to the data and the estimation of a parametric covariance model. The method is easy to implement and leads to improved smoothing parameter selection, even when the covariance model is misspecified. The methodology is illustrated using water chemistry data collected in a survey of lakes in the Northeastern United States.     

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.     

现代民间文艺学源起歌谣探因——以刘半农为考察中心

文章以刘半农为考察中心,结合当时国内外政治、文化、学术背景,中国的文学传统和歌谣的特点,对现代民间文艺学发端于歌谣的原因进行了探讨。认为,刘半农的成长环境、个性、人生经历和文学生涯等,共同塑造了他诗人的心态基础,养成了他偏爱歌谣、重视语言本身的审美特性和追求自然、率真、写实的审美风格。这对歌谣运动的发起有着重要的影响。     

Variance reduction for kernel estimators in clustered/longitudinal data analysis

We develop a variance reduction method for the seemingly unrelated (SUR) kernel estimator of Wang (2003). We show that the quadratic interpolation method introduced in Cheng et al. (2007) works for the SUR kernel estimator. For a given point of estimation, Cheng et al. (2007) define a variance reduced local linear estimate as a linear combination of classical estimates at three nearby points. We develop an analogous variance reduction method for SUR kernel estimators in clustered/longitudinal models and perform simulation studies which demonstrate the efficacy of our variance reduction method in finite sample settings.