Controlling Bayes directional false discovery rate in random effects model

Starting with a decision theoretic formulation of simultaneous testing of null hypotheses against two-sided alternatives, a procedure controlling the Bayesian directional false discovery rate (BDFDR) is developed through controlling the posterior directional false discovery rate (PDFDR). This is an alternative to Lewis and Thayer [2004. A loss function related to the FDR for random effects multiple comparison. J. Statist. Plann. Inference 125, 49–58.] with a better control of the BDFDR. Moreover, it is optimum in the sense of being the non-randomized part of the procedure maximizing the posterior expectation of the directional per-comparison power rate given the data, while controlling the PDFDR. A corresponding empirical Bayes method is proposed in the context of one-way random effects model. Simulation study shows that the proposed Bayes and empirical Bayes methods perform much better from a Bayesian perspective than the procedures available in the literature.     

Asymptotically efficient estimation in response adaptive trials

We examine the issue of asymptotic efficiency of estimation for response adaptive designs of clinical trials, from which the collected data set contains a dependency structure. We establish the asymptotic lower bound of exponential rates for consistent estimators. Under certain regularity conditions, we show that the maximum likelihood estimator achieves the asymptotic lower bound for response adaptive trials with dichotomous responses. Furthermore, it is shown that the maximum likelihood estimator of the treatment effect is asymptotically efficient in the Bahadur sense for response adaptive clinical trials.     

Star-shaped distributions and their generalizations

Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. We generalize elliptically contoured densities to “star-shaped distributions” with concentric star-shaped contours and show that many results in the former case continue to hold in the more general case. We develop a general theory in the framework of abstract group invariance so that the results can be applied to other cases as well, especially those involving random matrices.     

Statistical estimation errors of VaR under ARCH returns

In this paper we discuss some problems of existing methods for calculating the Value-at-Risk (VaR) in ARCH setting. It should be noted that the commonly used approaches often confuse the true innovations with the empirical residuals, i.e., estimation errors for unknown ARCH parameters are ignored. We adjust this by using the asymptotics of the residual empirical process, and propose a feasible VaR which, according to the spirit of VaR, keeps the assets away from a specified risk with high confidence level. Its meaningfulness in comparison with the usual VaR will be illustrated clearly by numerical studies.     

DYNAMIC FACTOR MODELS

This paper introduces nonlinear dynamic factor models for various applications related to risk analysis. Traditional factor models represent the dynamics of processes driven by movements of latent variables, called the factors. Our approach extends this setup by introducing factors defined as random dynamic parameters and stochastic autocorrelated simulators. This class of factor models can represent processes with time varying conditional mean, variance, skewness and excess kurtosis. Applications discussed in the paper include dynamic risk analysis, such as risk in price variations (models with stochastic mean and volatility), extreme risks (models with stochastic tails), risk on asset liquidity (stochastic volatility duration models), and moral hazard in insurance analysis.

We propose estimation procedures for models with the marginal density of the series and factor dynamics parameterized by distinct subsets of parameters. Such a partitioning of the parameter vector found in many applications allows to simplify considerably statistical inference. We develop a two- stage Maximum Likelihood method, called the Finite Memory Maximum Likelihood, which is easy to implement in the presence of multiple factors. We also discuss simulation based estimation, testing, prediction and filtering.     

A remark on the Bahadur representation of sample quantiles for negatively associated sequences

Under mild conditions, we investigate further the Bahadur representation of sample quantiles for negatively associated sequences, whose convergence rate is faster than the corresponding one in Ling (2008).     

Estimation of the scale parameter of the half-logistic distribution with multiply type II censored sample

In this paper, we consider the maximum likelihood and Bayes estimation of the scale parameter of the half-logistic distribution based on a multiply type II censored sample. However, the maximum likelihood estimator(MLE) and Bayes estimator do not exist in an explicit form for the scale parameter. We consider a simple method of deriving an explicit estimator by approximating the likelihood function and discuss the asymptotic variances of MLE and approximate MLE. Also, an approximation based on the Laplace approximation (Tierney & Kadane, 1986) is used to obtain the Bayes estimator. In order to compare the MLE, approximate MLE and Bayes estimates of the scale parameter, Monte Carlo simulation is used.     

基于ISM模型的水文水资源工程专业课程体系分析

文章通过建立递阶结构模型的实用方法,对水文水资源工程专业最有特色的、最主要的七门课程进行了分析并绘制了多极递阶有向图,从而给出了该专业主要课程的体系结构。     

Lattice and Schröder paths with periodic boundaries

We consider paths in the plane with (1,0$1,0$), (0,1$0,1$), and (a,b$a,b$)-steps that start at the origin, end at height n$n$, and stay strictly to the left of a given non-decreasing right boundary. We show that if the boundary is periodic and has slope at most b/a$b/a$, then the ordinary generating function for the number of such paths ending at height n   is algebraic. Our argument is in two parts. We use a simple combinatorial decomposition to obtain an Appell relation or “umbral” generating function, in which the power zⁿ$z^n$ is replaced by a power series of the form zⁿ_φn(z),$z^n{\phi }_n(z),$ where _φn(0)=1.${\phi }_n(0)=1.$ Then we convert (in an explicit way) the umbral generating function to an ordinary generating function by solving a system of linear equations and a polynomial equation. This conversion implies that the ordinary generating function is algebraic. We give several concrete examples, including an alternative way to solve the tennis ball problem.     

Large sample interval mapping method for genetic trait loci in finite regression mixture models

This article investigates the large sample interval mapping method for genetic trait loci (GTL) in a finite non-linear regression mixture model. The general model includes most commonly used kernel functions, such as exponential family mixture, logistic regression mixture and generalized linear mixture models, as special cases. The populations derived from either the backcross or intercross design are considered. In particular, unlike all existing results in the literature in the finite mixture models, the large sample results presented in this paper do not require the boundness condition on the parametric space. Therefore, the large sample theory presented in this article possesses general applicability to the interval mapping method of GTL in genetic research. The limiting null distribution of the likelihood ratio test statistics can be utilized easily to determine the threshold values or p-values required in the interval mapping. The limiting distribution is proved to be free of the parameter values of null model and free of the choice of a kernel function. Extension to the multiple marker interval GTL detection is also discussed. Simulation study results show favorable performance of the asymptotic procedure when sample sizes are moderate.