Asymptotic normality of a nonparametric estimator of sample coverage (2009)
This paper establishes a necessary and sufficient condition for the asymptotic normality of the nonparametric estimator of sample coverage proposed by Good [Biometrica 40 (1953) 237--264]. This new...
General maximum likelihood empirical Bayes estimation of normal means (2009)
We propose a general maximum likelihood empirical Bayes (GMLEB) method for the estimation of a mean vector based on observations with i.i.d. normal errors. We prove that under mild moment conditions...
A Probability Model for Combining Ranks (2009)
Ofer Melnik, Yehuda Vardi, Cun-hui Zhang
Abstract. Mixed Group Ranks is a parametric method for combining rank based classi ers that is e ective for many-class problems. Its parametric structure combines qualities of voting methods with...
RISK BOUNDS IN ISOTONIC REGRESSION (2009)
Nonasymptotic risk bounds are provided for maximum likelihood-type isotonic estimators of an unknown nondecreasing regression function, with general average loss at design points. These bounds are...
INVITED PAPER COMPOUND DECISION THEORY AND EMPIRICAL BAYES METHODS (2009)
acclaimed as “two breakthroughs ” by Neyman (1962), are the most important contributions of Herbert Robbins to statistics. The purpose of this paper is to provide a brief description of his work...
A group bridge approach for variable selection (2009)
Huang, Jian, Ma, Shuange, Xie, Huiliang, Zhang, Cun-Hui
In multiple regression problems when covariates can be naturally grouped, it is important to carry out feature selection at the group and within-group individual variable levels simultaneously. The...
AN EXTENSION OF THE HARDY-LITTLEWOOD (2008)
Strong Law, Zhidong Bai, Philip E. Cheng, Cun-hui Zhang, National Sun, Academia Sinica
Abstract: A strong law is established for linear statistics that are weighted sums of a random sample. Using an observation of Cheng (1995a) about the Bernstein and Kolmogorov inequalities, we...
Concave Learners for Rankboost (2008)
Ofer Melnik, Yehuda Vardi, Cun-hui Zhang, Donald Geman
Rankboost has been shown to be an effective algorithm for combining ranks. However, its ability to generalize well and not overfit is directly related to the choice of weak learner, in the sense that...
LINEAR REGRESSION WITH INTERVAL CENSORED DATA (2008)
This paper concerns linear regression with interval censored data. M-estimators for the regression coefficients are derived. Asymptotic consistency and normality of the M-estimators are obtained via...
D. Brown, Andrew V. Carter, Mark G. Low, Cun-hui Zhang
This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This...
AN INVARIANT SELECTION RULE FOR MULTI-TREATMENT TRIAL WITH LINEAR PRIOR PREFERENCE (2008)
T. Timothy Chen, Cun-hui Zhang
Abstract: In clinical trials, asymmetric designs are often used to reflect prior preference of treatments based on factors other than efficacy, such as toxicity and cost. We consider the case where...
Continuous Generalized Gradient Descent (2008)
This article derives characterizations and computational algorithms for continuous general gradient descent trajectories in high-dimensional parameter spaces for statistical model selection,...
LEAST SQUARES ESTIMATORS OF THE MODE OF A UNIMODAL REGRESSION FUNCTION (2008)
Jyh-ming Shoung, Cun-hui Zhang
In this paper, we consider nonparametric least squares estimators of the mode of an unknown unimodal regression function. We establish almost sure convergence of these estimators with nearly optimal...
SUMMARY. Let f(x|θ) be a known parametric family of probability density functions with respect to a σ-finite measure µ. The density function f(x) of a random variable X belongs to a mixture model...
The sparsity and bias of the Lasso selection in high-dimensional linear regression (2008)
Meinshausen and Buhlmann [Ann. Statist. 34 (2006) 1436--1462] showed that, for neighborhood selection in Gaussian graphical models, under a neighborhood stability condition, the LASSO is consistent,...
Discussion: One-step sparse estimates in nonconcave penalized likelihood models (2008)
Discussion of ``One-step sparse estimates in nonconcave penalized likelihood models'' [arXiv:0808.1012]
The Iterated Lasso for High-Dimensional Logistic Regression (2008)
Jian Huang, Shuange Ma, Cun-hui Zhang
We consider an iterated Lasso approach for variable selection and estimation in sparse, high-dimensional logistic regression models. In this approach, we use the Lasso (Tibshirani 1996) to obtain an...
Hungarian Academy of Sciences (2007)
G Unter Rote, William Steiger, Cun-hui Zhang
Points P 1,..., Pn in the unit square define a convex n-chain if they are below y = x and, together with P 0 = (0, 0) and Pn+1 = (1, 1), they are in convex position. Under uniform probability, we...
Complex Datasets and Inverse Problems. Tomography, Networks and Beyond (2007)
Liu, Regina, Strawderman, William, Zhang, Cun-Hui
This book is a collection of papers dedicated to the memory of Yehuda Vardi. Yehuda was the chair of the Department of Statistics of Rutgers University when he passed away unexpectedly on January 13,...
What is the real size of a sampled network? The case of the Internet (2007)
Viger, Fabien, Barrat, Alain, Dall'Asta, Luca, Zhang, Cun-Hui, Kolaczyk, Eric D.
Most data concerning the topology of complex networks are the result of mapping projects which bear intrinsic limitations and cannot give access to complete, unbiased datasets. A particularly...
What is the real size of a sampled network? The case of the Internet (2007)
Viger, Fabien, Barrat, Alain, Dall'Asta, Luca, Zhang, Cun-Hui, Kolaczyk, Eric D.
Most data concerning the topology of complex networks are the result of mapping projects which bear intrinsic limitations and cannot give access to complete, unbiased datasets. A particularly...
A Group Bridge Approach for Variable Selection (2007)
Jian Huang, Shuangge Ma, Huiliang Xie, Cun-hui Zhang
In multiple regression problems when covariates can be naturally grouped, it is important to carry out feature selection at the group and within-group individual variable levels simultaneously. The...
Nonlinear renewal theorems for random walks with perturbations of intermediate order (2006)
We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is...
A Conversation with Yuan Shih Chow (2006)
Ying, Zhiliang, Zhang, Cun-Hui
Yuan Shih Chow was born in Hubei province in China, on September 1, 1924. The eldest child of a local militia and political leader, he grew up in war and turmoil. His hometown was on the front line...
Estimation of sums of random variables: Examples and information bounds (2006)
This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and...
A Conversation with Yuan Shih Chow (2006)
Ying, Zhiliang, Zhang, Cun-Hui
Yuan Shih Chow was born in Hubei province in China, on September 1, 1924. The eldest child of a local militia and political leader, he grew up in war and turmoil. His hometown was on the front line...
Adaptive Lasso for sparse highdimensional regression (2006)
Jian Huang, Shuangge Ma, Cun-hui Zhang
Summary. We study the asymptotic properties of adaptive LASSO estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. We...
Adaptive Lasso for sparse highdimensional regression (2006)
Jian Huang, Shuangge Ma, Cun-hui Zhang
Summary. We study the asymptotic properties of the adaptive Lasso estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. We...
Network Inference from TraceRoute Measurements: Internet Topology `Species' (2005)
Viger, Fabien, Barrat, Alain, Dall'Asta, Luca, Zhang, Cun-Hui, Kolaczyk, Eric D.
Internet mapping projects generally consist in sampling the network from a limited set of sources by using traceroute probes. This methodology, akin to the merging of spanning trees from the...
Estimation of sums of random variables: Examples and information bounds (2005)
This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and...
General empirical Bayes wavelet methods and exactly adaptive minimax estimation (2005)
In many statistical problems, stochastic signals can be represented as a sequence of noisy wavelet coefficients. In this paper, we develop general empirical Bayes methods for the estimation of true...
Brown, Lawrence D., Carter, Andrew V., Low, Mark G., Zhang, Cun-Hui
This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This...
On optimality of bold play for primitive casinos in the presence of inflation (2005)
Chen, Robert W., Shepp, Larry A., Yao, Yi-Ching, Zhang, Cun-Hui
Mr. G owes $100000 to a loan shark, and will be killed at dawn if the loan is not repaid in full. Mr. G has $20000, but partial payments are not accepted, and he has no other source of income or...
General empirical Bayes wavelet methods and exactly adaptive minimax estimation (2005)
In many statistical problems, stochastic signals can be represented as a sequence of noisy wavelet coefficients. In this paper, we develop general empirical Bayes methods for the estimation of true...
Network Inference from TraceRoute Measurements: Internet Topology `Species' (2005)
Viger, Fabien, Barrat, Alain, Dall'Asta, Luca, Zhang, Cun-Hui, Kolaczyk, Eric D.
Internet mapping projects generally consist in sampling the network from a limited set of sources by using traceroute probes. This methodology, akin to the merging of spanning trees from the...
Network Inference from TraceRoute Measurements: Internet Topology `Species' (2005)
Viger, Fabien, Barrat, Alain, Dall'Asta, Luca, Zhang, Cun-Hui, Kolaczyk, Eric D.
Internet mapping projects generally consist in sampling the network from a limited set of sources by using traceroute probes. This methodology, akin to the merging of spanning trees from the...
Estimation of sums of random variables: Examples and information (2005)
This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and...
General empirical Bayes wavelet methods and exactly adaptive minimax estimation. Ann (2005)
In many statistical problems, stochastic signals can be represented as a sequence of noisy wavelet coefficients. In this paper, we develop general empirical Bayes methods for the estimation of true...
A two-way semilinear model for normalization and analysis of cDNA microarray data (2005)
Jian Huang, Hsun-chih Kuo, Irina Koroleva, Cun-hui Zhang, Marcelo Bento Soares
Microarray analysis is a technology for monitoring gene expression levels on a large scale and has been widely used in functional genomics. A challenging issue in the analysis of microarray data is...
Asymptotic Analysis of a Two-Way Semiparametric Regression Model for Microarray Data (2005)
statistics
Jian Huang, Deli Wang, Cun-hui Zhang
1 ABSTRACT A basic question in analyzing cDNA microarray data is normalization. The purpose of normalization is to remove systematic bias in the observed expression values by establishing a...
A two-way semilinear model for normalization and analysis of cDNA microarray data (2005)
Jian Huang, Deli Wang, Cun-hui Zhang
ABSTRACT A basic question in analyzing cDNA microarray data is normalization, the purpose of which is to remove systematic bias in the observed expression values by establishing a normalization curve...
Brown, Lawrence D., Carter, Andrew V., Low, Mark G., Zhang, Cun-Hui
This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This...
Mixed group ranks: preference and confidence in classifier combination (2004)
Ofer Melnik, Yehuda Vardi, Cun-hui Zhang
Abstract—Classifier combination holds the potential of improving performance by combining the results of multiple classifers. For domains with very large numbers of classes, such as biometrics, we...
Asymptotic equivalence theory for nonparametric regression with random design (2002)
Brown, Lawrence D., Cai, T. Tony, Low, Mark G., Zhang, Cun-Hui
This paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on an unknown regression or...
Risk bounds in isotonic regression (2002)
Nonasymptotic risk bounds are provided for maximum likelihood-type isotonic estimators of an unknown nondecreasing regression function, with general average loss at design points. These bounds are...
A robust clustering method and visualization tool based on data depth (2002)
Rebecka Jornsten, Yehuda Vardi, Cun-hui Zhang
Abstract. We present a robust clustering method based on a modi ed Weiszfeld algorithm for the multivariate median, and associated data depth. The multivariate medians are used to represent the...
On the bitplane compression of microarray images (2002)
Rebecka Jornsten, Yehuda Vardi, Cun-hui Zhang
Abstract. The microarray image technology is anewand powerful tool for studying the expression of thousands of genes simultaneously. Methods for image processing and statistical analysis are still...
Asymptotic equivalence theory for nonparametric regression with random design (2002)
D. Brown, T. Tony Cai, Mark G. Low, Cun-hui Zhang
This paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on an unknown regression or...
Asymptotic equivalence theory for nonparametric regression with random design (2002)
Lawrence D. Brown, T. Tony Cai, Mark G. Low, Cun-hui Zhang
This paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on the unknown regression/drift...
On the Bitplane Compression of Microarray Images (2002)
Rebecka Jörnsten, Yehuda Vardi, Cun-hui Zhang
The microarray image technology is a new and powerful tool for studying the expression of thousands of genes simultaneously. Methods for image processing and statistical analysis are still under...
A Robust Clustering Method and Visualization Tool Based on Data Depth (2002)
Rebecka Jörnsten, Yehuda Vardi, Cun-hui Zhang
We present a robust clustering method based on a modified Weiszfeld algorithm for the multivariate median, and associated data depth. The multivariate medians are used to represent the clusters,...
Least squares estimators of the mode of a unimodal regression function (2001)
Shoung, Jyh-Ming, Zhang, Cun-Hui
In this paper, we consider nonparametric least squares estimators of the mode of an unknown unimodal regression function. We establish almost sure convergence of these estimators with nearly optimal...
Two-sample tests for growth curves under dependent right censoring (2001)
Vardi, Yehuda, Ying, Zhiliang, Zhang, Cun-Hui
In many tumour growth inhibition studies, tumour sizes are recorded over a period of time, forming a growth curve for each experimental animal. A frequently asked question in these studies is whether...
This paper concerns moment and tail probability inequalities and the strong law of large numbers for $U$-statistics with nonnegative or symmetrized kernels and their multisample and decoupled...
Sub-Bernoulli functions, moment inequalities and strong laws for nonnegative and symmetrized (1999)
This paper concerns moment and tail probability inequalities and the strong law of large numbers for U-statistics with nonnegative or symmetrized kernels and their multisample and decoupled versions....
Yehuda Vardi, Cun-hui Zhang, Location Problem
Abstract. This paper gives a new, simple, monotonically convergent, algorithm for the Fermat-Weber location problem, with extensions covering more general cost functions. 1. Introduction and main...
Linear regression with interval censored data (1998)
This paper concerns linear regression with interval censored data. $M$-estimators for the regression coefficients are derived. Asymptotic consistency and normality of the $M$-estimators are obtained...
Asymptotic nonequivalence of nonparametric experiments when the smoothness index is ½ (1998)
Brown, Lawrence D., Zhang, Cun-Hui
An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric...
on Fast Functional Magnetic Resonance Imaging via Prolate Wavelets 1 (1998)
Cun-hui Zhang, Communicated Ronald, R. Coifman
Our objective is to improve the time-resolution of functional magnetic resonance imaging by sampling only a small fraction of the Fourier transform of the spin density and using a prolate wavelet...
Asymptotic nonequivalence of nonparametric experiments when the smoothness index is 1/2 (1998)
An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric...
A Central Limit Theorem for Convex Chains in the Square (1998)
Imre Barany, G Rote, Günter Rote, William Steiger, William Steiger, Cun-hui Zhang, ...
Points P 1 , ...,Pn in the unit square define a convex n-chain if they are below y = x and, together with P 0 = (0, 0) and Pn+1 = (1, 1), they are in convex position. Under uniform probability, we...
A Central Limit Theorem for Convex Chains in the Square (1998)
Imre Bárány, G Rote, Günter Rote, William Steiger, William Steiger, ...
Points P 1 , ..., P n in the unit square define a convex n-chain if they are below y = x and, together with P 0 =(0, 0) and P n+1 = (1, 1), they are in convex position. Under uniform probability, we...
Fast Functional Magnetic Resonance Imaging via Wavelets (1998)
. Our objective is to improve the time-resolution of functional magnetic resonance imaging by sampling only a small fraction of the Fourier transform of the spin density, and using a wavelet filter...
Imre Bárány, Günter Rote, Cun-hui Zhang, William Steiger
Points P1,...,Pn in the unit square define a convex n-chain if they are below y = x and, together with P0 =(0,0) and Pn+1 =(1,1), they are in convex position. Under uniform probability, we prove an...
Topics in Statistical Estimation and Control. (1997)
Robbins, Herbert, Zhang, Cun-Hui
Methods of statistical design and inference were obtained for treatment effects under certain data-based allocation rules which are potentially useful when ethical concern is the major factor or when...
Empirical Bayes and compound estimation of normal means (1997)
Abstract: This article concerns the canonical empirical Bayes problem of estimating normal means under squared-error loss. General empirical estimators are derived which are asymptotically minimax...
Linear regression with doubly censored data (1996)
Linear regression with doubly censored responses is considered. Buckley-James-Ritov-type estimators are proposed. Semiparametric information and projective scores are discussed. An expansion of the...
Strong law of large numbers for sums of products (1996)
Let $X, X_n, n \ge 1$, be a sequence of independent identically distributed random variables. We give necessary and sufficient conditions for the strong law of large numbers n^{-k/p} \sum_{1\lei_1...
Abstract: This paper concerns the global performance of modifications of the kernel estimators considered in Zhang (1995) for a mixing density function g based on a sample from f(x) = �...
Estimating a multiplicative treatment effect under biased allocation (1991)
ROBBINS, HERBERT, ZHANG, CUN-HUI
Suppose that, given θ, x is Poisson with mean θ, while, given θ, y is Poisson with mean αθ or βθ according as treatment 1 or treatment 2 is used. Moreover, suppose that treatment 1 is used if...
The multivariate L1-median and associated data depth
This paper gives three related results: (i) a new, simple, fast, monotonically converging algorithm for deriving the L1-median of a data cloud in ℝd, a problem that can be traced to Fermat and has...
Efficiency of the u,v method of estimation
Robbins, Herbert, Zhang, Cun-Hui
Given a pool of motorists, how do we estimate the total intensity of those who had a prespecified number of traffic accidents in the past year? We previously have proposed the u,v method as a...
The multivariate L1-median and associated data depth
This paper gives three related results: (i) a new, simple, fast, monotonically converging algorithm for deriving the L1-median of a data cloud in ℝd, a problem that can be traced to Fermat and has...
Efficiency of the u,v method of estimation
Robbins, Herbert, Zhang, Cun-Hui
Given a pool of motorists, how do we estimate the total intensity of those who had a prespecified number of traffic accidents in the past year? We previously have proposed the u,v method as a...
A group bridge approach for variable selection
Jian Huang, Shuange Ma, Huiliang Xie, Cun-Hui Zhang
In multiple regression problems when covariates can be naturally grouped, it is important to carry out feature selection at the group and within-group individual variable levels simultaneously. The...