Bayes shrinkage estimator for consistency assessment of treatment effects in multi-regional clinical trials

The primary objective of a multi-regional clinical trial is to investigate the overall efficacy of the drug across regions and evaluate the possibility of applying the overall trial result to some specific region. A challenge arises when there is not enough regional sample size. We focus on the problem of evaluating applicability of a drug to a specific region of interest under the criterion of preserving a certain proportion of the overall treatment effect in the region. We propose a variant of James-Stein shrinkage estimator in the empirical Bayes context for the region-specific treatment effect. The estimator has the features of accommodating the between-region variation and finiteness correction of bias. We also propose a truncated version of the proposed shrinkage estimator to further protect risk in the presence of extreme value of regional treatment effect. Based on the proposed estimator, we provide the consistency assessment criterion and sample size calculation for the region of interest. Simulations are conducted to demonstrate the performance of the proposed estimators in comparison with some existing methods. A hypothetical example is presented to illustrate the application of the proposed method.     

Infill asymptotics for adaptive kernel estimators of spatial intensity

We apply the Abramson principle to define adaptive kernel estimators for the intensity function of a spatial point process. We derive asymptotic expansions for the bias and variance under the regime that n independent copies of a simple point process in Euclidean space are superposed. The method is illustrated by means of a simple example and applied to tornado data.     

The performance of alternative estimators for the probit model with first-order serial correlation 1

The purpose of the paper is to evaluate the relative performance of two generalized conditional moment (GCM) estimators in terms of their mean squared errors, for the Probit model with first-order serial correlation. The first estimator is a linearized one-step estimator described by Poirier and Ruud (1988). The second one is defined in the present paper. Monte Car10 experiments suggest that the GCM estimators outperform the ordinary Probit estimator. The two GCM estimators do almost equally well, except that the second one may be easier to calculate, especially in large samples.     

Smooth tail-index estimation

The two parametric distribution functions appearing in the extreme-value theory – the generalized extreme-value distribution and the generalized Pareto distribution – have log-concave densities if the extreme-value index γ∈[?1, 0]. Replacing the order statistics in tail-index estimators by their corresponding quantiles from the distribution function that is based on the estimated log-concave density ? f _n leads to novel smooth quantile and tail-index estimators. These new estimators aim at estimating the tail index especially in small samples. Acting as a smoother of the empirical distribution function, the log-concave distribution function estimator reduces estimation variability to a much greater extent than it introduces bias. As a consequence, Monte Carlo simulations demonstrate that the smoothed version of the estimators are well superior to their non-smoothed counterparts, in terms of mean-squared error.     

Results concerning the generalized partially linear single-index model

The central topic of this article is the estimation of parameters of the generalized partially linear single-index model (GPLSIM). Two numerical optimization procedures are presented and an S-plus program based on these procedures is compared to a program by Wand in a simulation setting. The results from these simulations indicate that the estimates for the new procedures are as good, if not better, than Wand's. Also, this program is much more flexible than Wand's since it can handle more general models. Other simulations are also conducted. The first compares the effects of using linear interpolation versus spline interpolation in an optimization procedure. The results indicate that by using spline interpolation one gets more stable estimates at a cost of increased computational time. A second simulation was conducted to assess the performance of a method for estimating the variance of alpha. A third set of simulations is carried out to determine the best criterion for testing that one of the elements of alpha is equal to zero. The GPLSIM is applied to a water quality data set and the results indicate an interesting relationship between gastrointestinal illness and turbidity (cloudiness) of drinking water.     

Rank invariant tests with left truncated and interval censored data

Peto and Peto (1972) have studied rank invariant tests to compare two survival curves for right censored data. We apply their tests, including the logrank test and the generalized Wilcoxon test, to left truncated and interval censored data. The significance levels of the tests are approximated by Monte Carlo permutation tests. Simulation studies are conducted to show their size and power under different distributional differences. In particular, the logrank test works well under the Cox proportional hazards alternatives, as for the usual right censored data. The methods are illustrated by the analysis of the Massachusetts Health Care Panel Study dataset.     

Tests for generalized exponential laws based on the empirical Mellin transform

Recently, many standard families of distributions have been generalized by exponentiating their cumulative distribution function (CDF). In this paper, test statistics are constructed based on CDF–transformed observations and the corresponding moments of arbitrary positive order. Simulation results for generalized exponential distributions show that the proposed test compares well with standard methods based on the empirical distribution function.     

Estimating the variance of the sample median

The small-sample bias and root mean squared error of several distribution-free estimators of the variance of the sample median are examined. A new estimator is proposed that is easy to compute and tends to have the smallest bias and root mean squared error.     

《广绝交论》写作时间的考订及其意义

有关刘孝标《广绝交论》的写作时间，学术界主要有天监七年、天监九年两种观点。考察刘孝标在天监年间的行迹不难发现，天监十一年是刘孝标生平思想变化的重要转折点，以此为界，他由之前的汲汲于仕途功名彻底转向拒弃名利、向往隐逸。这一思想心态的蜕变，是《广绝交论》一文的基本创作前提，该文即作于此年。     

Bayesian analysis of multivariate stochastic volatility with skew return distribution

Multivariate stochastic volatility models with skew distributions are proposed. Exploiting Cholesky stochastic volatility modeling, univariate stochastic volatility processes with leverage effect and generalized hyperbolic skew t-distributions are embedded to multivariate analysis with time-varying correlations. Bayesian modeling allows this approach to provide parsimonious skew structure and to easily scale up for high-dimensional problem. Analyses of daily stock returns are illustrated. Empirical results show that the time-varying correlations and the sparse skew structure contribute to improved prediction performance and Value-at-Risk forecasts.