© Institute of Mathematical Statistics, 2004 LOWER TAIL PROBABILITIES FOR GAUSSIAN PROCESSES (2009)
Let X = (Xt)t∈S be a real-valued Gaussian random process indexed by S with mean zero. General upper and lower estimates are given for the lower tail probability P(sup t∈S (Xt − Xt0) ≤ x) as x...
Berry-Esseen Bounds for Projections of Coordinate Symmetric Random Vectors (2009)
Goldstein, Larry; University Of Southern California; Larry@math.usc.edu, Shao, Qi-Man; Hong Kong University Of Science And Technology; Maqmshao@ust.hk
For a coordinate symmetric random vector (Y1,...,Yn) = Y∈ Rn, that is, one satisfying (Y1,...,Yn) =d (e1Y1,...,enYn) for all (e1,..,en) ∈ {-1,1}n, for...
Chen, Xia, Li, Wenbo V., Rosinski, Jan, Shao, Qi-Man
In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes. We also show that a fractional...
Stein's Method of Exchangeable Pairs with Application to the Curie-Weiss Model (2009)
Chatterjee, Sourav, Shao, Qi-Man
Let $(W, W')$ be an exchangeable pair. Assume that $$E(W-W' | W) = g(W)+r(W),$$ where $g(W)$ is a dominated term and $r(W)$ is negligible. Let $G(t) = \int_0^t g(s) ds$ and define $p(t) = c_1 e^{-c_0...
Cram'er Type Moderate deviations for the Maximum of Self-normalized Sums (2009)
Hu, Zhishui; USTC; Huzs@ustc.edu.cn, Shao, Qi-Man; HKUST; Maqmshao@ust.hk, Wang, Qiying; University Of Sydney; Qiying@maths.usyd.edu.au
Let { X, Xi , i ≥ 1} be i.i.d. random variables, Sk be the partial sum and Vn2 = ∑1&le i&le n Xi2. Assume that E(X)=0 and E(X4) < ∞. In this paper we discuss the moderate deviations of...
Liu, Wei-Dong, Lin, Zhengyan, Shao, Qi-Man
Let $\mathbf{X}_1,...,\mathbf{X}_n$ be a random sample from a $p$-dimensional population distribution. Assume that $c_1n^{\alpha}\leq p\leq c_2n^{\alpha}$ for some positive constants $c_1,c_2$ and...
Large and Moderate Deviations for Hotelling's T-squared Statistic (2007)
. Let X;X 1 ; X 2 ; ::: be i.i.d. R d -valued random variables. We prove large and moderate deviations for Hotelling's T 2 -statistic when X is in the generalized domain of attraction of the...
On Parameters Of Increasing Dimensions (2007)
. In statistical analyses the complexity of a chosen model is often related to the size of available data. One important question is whether the asymptotic distribution of the parameter estimates...
Self-Normalized Moderate And Large Deviations (2007)
. Let fX n ; n 1g be i.i.d. R d -valued random variables. We prove Partial Large Deviation Principles (PLDP) for self-normalized partial sums with minimal or no moment assumptions, for both moderate...
Self-Normalized Large Deviations In Vector Spaces (2007)
. In this short note we define and study properties of Partial Large Deviation Principles (PLDP), using them to extend Cram'er's theorem to self-normalized partial sums of i.i.d. random...
Do Stock Returns Follow A Finite Variance Distribution? 1 (2007)
In this paper we propose a test statistic to discriminate between models with nite variance and models with in nite variance. The test statistic is the ratio of the sample standard deviation and the...
Amir Dembo, Bjorn Poonen, Qi-man Shao, Ofer Zeitouni
Consider a polynomial of large degree n whose coecients are independent, identically distributed, non-degenerate random variables having zero mean and nite moments of all orders. We show that such a...
A Normal Comparison Inequality and Its Applications (2007)
Abstract. Let = ( i; 1 i n) and = ( i; 1 i n) be standard normal random variables with covariance matrices R 1
UNIVERSITY OF DELAWARE AND (2007)
ABSTRACT We show that a special setting of the well-known Gaussian correlation conjecture, namely for sets of equal measure, can be useful in proving the existence of small ball constants. We hope...
SELF-NORMALIZED MODERATE DEVIATIONS AND LILS By Amir Dembo 1 (2007)
Abstract. Let fXn; n 1g be i.i.d. R d-valued random variables. We prove Partial Moderate Deviation Principles for self-normalized partial sums subject to minimal moment assumptions. Applications to...
Amir Dembo, Bjorn Poonen, Qi-man Shao, Ofer Zeitouni
Consider a polynomial of large degree n whose coecients are independent, identically distributed, nondegenerate random variables having zero mean and nite moments of all orders. We show that such a...
Normal approximation for nonlinear statistics using a concentration inequality approach (2007)
Chen, Louis H. Y., Shao, Qi-Man
Let $T$ be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry--Esseen type bounds for $T$ are obtained. The bounds are the best...
Large and Moderate Deviations for Hotelling's T^2-Statistics (2006)
Dembo, Amir; Stanford University; Amir@stat.stanford.edu, Shao, Qi-Man; Hong Kong University Of Science And Technology; Maqmshao@ust.hk
Let X , X1, X 2 , ... be i.i.d. R d-valued random variables. We prove large and moderate deviations for Hotelling's T2-statistic when X is in the generalized domain of attraction of the normal...
On discriminating between long-range dependence and changes in mean (2006)
Berkes, István, Horváth, Lajos, Kokoszka, Piotr, Shao, Qi-Man
We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null...
On discriminating between long-range dependence and changes in mean (2006)
Berkes, István, Horváth, Lajos, Kokoszka, Piotr, Shao, Qi-Man
We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null...
A calibrated scenario generation model for heavy-tailed risk factors (2006)
Shao, Qi-Man, Wang, Hao, Yu, Hao
In this paper, a calibrated scenario generation model for multivariate risk factors with heavy-tailed distributions is developed. This model includes the standard and classical model of scenario...
A calibrated scenario generation model for heavy-tailed risk factors (2006)
Shao, Qi-Man, Wang, Hao, Yu, Hao
In this paper, a calibrated scenario generation model for multivariate risk factors with heavy-tailed distributions is developed. This model includes the standard and classical model of scenario...
A calibrated scenario generation model for heavy-tailed risk factors (2006)
Shao, Qi-Man, Wang, Hao, Yu, Hao
In this paper, a calibrated scenario generation model for multivariate risk factors with heavy-tailed distributions is developed. This model includes the standard and classical model of scenario...
Saddlepoint approximation for Student's t-statistic with no moment conditions (2005)
Jing, Bing-Yi, Shao, Qi-Man, Zhou, Wang
A saddlepoint approximation of the Student's t-statistic was derived by Daniels and Young [Biometrika 78 (1991) 169-179] under the very stringent exponential moment condition that requires that the...
Saddlepoint approximation for Student’s t-statistic with no moment conditions (2004)
Jing, Bing-Yi, Shao, Qi-Man, Zhou, Wang
A saddlepoint approximation of the Student’s t-statistic was derived by Daniels and Young [Biometrika 78 (1991) 169–179] under the very stringent exponential moment condition that requires that...
Normal approximation under local dependence (2004)
Chen, Louis H. Y., Shao, Qi-Man
We establish both uniform and nonuniform error bounds of the Berry-Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best...
Normal approximation under local dependence (2004)
Chen, Louis H. Y., Shao, Qi-Man
We establish both uniform and nonuniform error bounds of the Berry–Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best...
Asymptotic Distributions and Berry-Esseen Bounds for Sums of Record Values (2004)
Shao, Qi-Man; University Of Oregon And National University Of Singapore; Qmshao@darkwing.uoregon.edu, Su, Chun; University Of Science An Technology Of China; Suchun@ustc.edu.cn, Wei, Gang; Hong Kong Baptist University; Gwei@hkbu.edu.hk
Let Un, n >= 1 be independent uniformly distributed random variables, and Yn, n >= 1 be independent and identically distributed non-negative random variables with finite third moments. Denote Sn the...
Lower tail probabilities for Gaussian processes (2004)
Let $X=(X_t)_{t \in S}$ be a real-valued Gaussian random process indexed by S with mean zero. General upper and lower estimates are given for the lower tail probability $\mathbb{P}(\sup_{t \in S}...
Self-normalized Cramér-type large deviations for independent random variables (2003)
Jing, Bing-Yi, Shao, Qi-Man, Wang, Qiying
Let $X_1, X_2, \ldots $ be independent random variables with zero means and finite variances. It is well known that a finite exponential moment assumption is necessary for a Cramér-type large...
Self-normalized Cramér-type large deviations for independent random variables (2003)
Wang, Qiying, Jing, Bing-Yi, Shao, Qi-Man
Let X1, X2, ... be independent random variables with zero means and finite variances. It is well known that a finite exponential moment assumption is necessary for a Cramér-type large deviation...
Bootstrapping the Student t-Statistic (2001)
Mason, David M., Shao, Qi-Man.
Let $X_1\ldots,X_n, n \geq 1$, be independent, identically distributed random variables and consider the Student $t$-statistic $T_n$ based upon these random variables. Giné, Götze and Mason (1997)...
Capture time of Brownian pursuits (2001)
Let B 0; B 1; ; B n be independent standard Brownian motions, starting at 0. We investigate the tail of the capture time n = infft> 0: B i (t) b i = B 0 (t) for some 1 i ng where 0 i 1; 1 i n. In...
Edited by C.R. Rao and D. Shanbhag. 1
Random polynomials having few or no real zeros (2000)
Dembo, Amir, Poonen, Bjorn, Shao, Qi-Man, Zeitouni, Ofer
Consider a polynomial of large degree n whose coefficients are independent, identically distributed, nondegenerate random variables having zero mean and finite moments of all orders. We show that...
Lower tail probabilities of Gaussian processes (2000)
Abstract: Let X = (Xt)t∈S be a real valued Gaussian random process indexed by S with mean zero. General upper and lower estimates are given for the lower tail probability P supt∈S(Xt − Xt0) ≤...
Random Polynomials Having Few or No Real Zeros (2000)
Amir Dembo, Bjorn Poonen, Qi-man Shao, Ofer Zeitouni
Consider a polynomial of large degree n whose coecients are independent, identically distributed, nondegenerate random variables having zero mean and nite moments of all orders. We show that such a...
Random Polynomials Having Few or No Real Zeros (2000)
Amir Dembo, Bjorn Poonen, Qi-man Shao, Ofer Zeitouni
Consider a polynomial of large degree n whose coe#cients are independent, identically distributed, nondegenerate random variables having zero mean and finite moments of all orders. We show that such...
A Test Statistic and Its Application in Modelling Daily Stock Returns (1999)
Shao, Qi-Man, Yu, Hao, Yu, Jun
In this paper we propose a test statistic to discriminate bctween models with finite variance and models with infinite variance. The test statistic is the ratio of the sample standard deviation and...
Limit theorems for quadratic forms with applications to Whittle's estimate (1999)
We establish strong and weak approximations for quadratic forms of weakly and strongly dependent random variables and obtain necessary and sufficient conditions for the weak convergence of weighted...
Monte Carlo Estimation of Bayesian Credible and HPD Intervals (1998)
This paper considers how to estimate Bayesian credible and highest probability density (HPD) intervals for parameters of interest and provides a simple Monte Carlo approach to approximate these...
Constraints on the parameters in a Bayesian hierarchical model typically make Bayesian computation and analysis complicated. As Gelfand, Smith and Lee (1992) remarked, it is almost impossible to...
Monte Carlo methods for Bayesian analysis of constrained parameter problems (1998)
Constraints on the parameters in a Bayesian hierarchical model typically make Bayesian computation and analysis complicated. Posterior densities that contain analytically intractable integrals as...
On Monte Carlo methods for estimating ratios of normalizing constants (1997)
Recently, estimating ratios of normalizing constants has played an important role in Bayesian computations. Applications of estimating ratios of normalizing constants arise in many aspects of...
Self-normalized large deviations (1997)
Let ${X, X_n, n \geq 1}$ be a sequence of independent and identically distributed random variables. The classical Cramér-Chernoff large deviation states that $\lim_{n\to\infty} n^{-1} \ln...
Estimating Ratios of Normalizing Constants for Densities with Different Dimensions (1997)
In Bayesian inference, a Bayes factor is defined as the ratio of posterior odds versus prior odds where posterior odds is simply a ratio of the normalizing constants of two posterior densities. In...
We obtain strong Bahadur representations for a general class of M-estimators that satisfies $\Sigma_i \psi (x_i, \theta) = o(\delta_n)$, where the $x_i$'s are independent but not necessarily...
Weak convergence for weighted empirical processes of dependent sequences (1996)
In this paper we establish weak convergence theorems for weighted empirical processes of strong mixing, $\rho$-mixing and associated sequences. We apply these results to obtain weak convergence of...
Limit theorem for maximum of standardized U-statistics with an application (1996)
We show that the maximally selected standardized U-statistic goes in distribution to an infinite sum of weighted chi-square random variables in the degenerate case. The result is applied to the...
Let ${X_n, 1 \leq n < \infty}$ be a sequence of independent identically distributed random variables in the domain of attraction of a stable law with index $0 < \alpha < 2$. The limit of...
Performance study of marginal posterior density estimation via Kullback-Leibler divergence
Bayesian computation, conditional marginal density estimation, importance-weighted marginal density estimation, kernel density estimation, Markov chain Monte Carlo, Primary 62E25, secondary 62A15,...
Ming-Hui Chen, Joseph G. Ibrahim, Qi-Man Shao
In this paper, we carry out an in-depth theoretical investigation of Bayesian inference for the Cox regression model. We establish necessary and sufficient conditions for posterior propriety of the...
Existence of Bayesian Estimates for the Polychotomous Quantal Response Models
Improper prior, logit model, log-log model, posterior distribution, probit model,
Partition-Weighted Monte Carlo Estimation
Bayesian computation, importance sampling, Markov chain Monte Carlo, posterior distribution, simulation,
Bahadur efficiency and robustness of studentized score tests
Bahadur slope, efficiency, influence function, score test,
On Parameters of Increasing Dimensions
In statistical analyses the complexity of a chosen model is often related to the size of available data. One important question is whether the asymptotic distribution of the parameter estimates...
Properties of Prior and Posterior Distributions for Multivariate Categorical Response Data Models
In this article, we model multivariate categorical (binary and ordinal) response data using a very rich class of scale mixture of multivariate normal (SMMVN) link functions to accommodate heavy...
A note on estimation of variance for [rho]-mixing sequences
Let {Xn, n [greater-or-equal, slanted] 1} be a stationary [rho]-mixing sequence of random variables with EX1 = , EX12+[delta] for some and Var Sn --> [infinity] as n --> [infinity]. This note...
A note on the almost sure central limit theorem for weakly dependent random variables
We give here an almost sure central limit theorem for associated sequences, strongly mixing and p-mixing sequences under the same conditions that assure that the central limit theorem holds.
A new proof on the distribution of the local time of a Wiener process
Let W(t) be a standard Wiener process with local time L(x, t). It is well-known that, as stochastic processes, L(0, t) and supo [less-than-or-equals, slant] s [less-than-or-equals, slant] tW(s) have...
A note on dichotomy theorems for integrals of stable processes
We find necessary and sufficient conditions for the almost sure finiteness of weighted integrals of stable processes with parameters [alpha] = 1 and [beta] [not equal to] 0.
Complete convergence for [alpha]-mixing sequences
In this note we estimate the convergence rate of strong law for [alpha]-mixing sequences under the nearly best possible condition on the mixing rate.
Maximum likelihood inference for the Cox regression model with applications to missing covariates
Chen, Ming-Hui, Ibrahim, Joseph G., Shao, Qi-Man
In this paper, we carry out an in-depth theoretical investigation for existence of maximum likelihood estimates for the Cox model [D.R. Cox, Regression models and life tables (with discussion),...