Papers by Eitan Greenshtein
Sequential Analysis, 1992
The Annals of Statistics, 1996
Bernoulli, 2000
Let $\{X_t\}$, $t\in \R$ , <math overflow="scroll"> <mi>t</mi> <mo... more Let $\{X_t\}$, $t\in \R$ , <math overflow="scroll"> <mi>t</mi> <mo>∈</mo><mo rspace="thinmathspace" lspace="0em">R</mo> </math> , be a stochastic process. Suppose that the process may not be continuously observed, yet an inference which is related to its probabilistic parameters, or to its sample path, is required. The main purpose of this paper is to study sampling plans. A sampling plan is a method
Institute of Mathematical Statistics Lecture Notes - Monograph Series, 2009
We consider the compound decision problem of estimating a vector of n parameters, known up to a p... more We consider the compound decision problem of estimating a vector of n parameters, known up to a permutation, corresponding to n independent observations, and discuss the difference between two symmetric classes of estimators. The first and larger class is restricted to the set of all permutation invariant estimators. The second class is restricted further to simple symmetric procedures. That is, estimators such that each parameter is estimated by a function of the corresponding observation alone. We show that under mild conditions, the minimal total squared error risks over these two classes are asymptotically equivalent up to essentially O(1) difference.
Journal of Applied Probability, 1998
Abstract Let X=(X 1,..., X n) be a random binary vector, with a known joint distribution P. It is... more Abstract Let X=(X 1,..., X n) be a random binary vector, with a known joint distribution P. It is necessary to inspect the coordinates sequentially in order to determine if X i= 0 for every i, i= 1,..., n. We find bounds for the ratio of the expected number of coordinates inspected using ...
Random matrix theory lies at the confluence of several areas of mathematics, especially number th... more Random matrix theory lies at the confluence of several areas of mathematics, especially number theory, combinatorics, dynamical systems, diffusion processes, probability and statistics. At the same time, random matrix theory may hold the key to solving critical problems for a broad ...
We elaborate on a deconvolution method, used to estimate the empirical distribution of unknown pa... more We elaborate on a deconvolution method, used to estimate the empirical distribution of unknown parameters, as suggested recently by Efron . It is applied to estimating the empirical distribution of the 'sampling probabilities' of m sampled items. The estimated empirical distribution is used to modify the Horvitz-Thompson estimator. The performance of the modified Horvitz-Thompson estimator is studied in two examples. In one example the sampling probabilities are estimated based on the number of visits until a response was obtained. The other example is based on real data from panel sampling, where in four consecutive months there are corresponding four attempts to interview each member in a panel. The sampling probabilities are estimated based on the number of successful attempts.
We study the problem of incorporating covariates in a compound decision setup. It is desired to e... more We study the problem of incorporating covariates in a compound decision setup. It is desired to estimate the means of $n$ response variables, which are independent and normally distributed, and each is accompanied by a vector of covariates. We suggest a method that involves non-parametric empirical Bayes techniques and may be viewed as a generalization of the celebrated Fay-Herriot (1979) method. Some optimality properties of our method are proved. We also compare it numerically with Fay-Herriot and other methods, using a `semi-real' data set that involves spatio-temporal covariates, where the goal is to estimate certain proportions in many small areas (Statistical-Areas)
Statistica Sinica, 2013
ABSTRACT We study the problem of incorporating covariates in a compound decision setup. It is des... more ABSTRACT We study the problem of incorporating covariates in a compound decision setup. It is desired to estimate the means of n response variables that are independent and normally distributed, each accompanied by a vector of covariates. We suggest a method that involves non-parametric empirical Bayes techniques and may be viewed as a generalization of the celebrated Fay-Herriot (1979) method. Some optimality properties of our method are proved. We also compare it numerically with Fay-Herriot and other methods, in a real data situation where the goal is to estimate certain proportions in many small areas. We also demonstrate our approach through the baseball data set originally analyzed by Brown (2008).
Sequential Analysis, 1998
We investigate sampling plans in time sequential testing af snrvival distributions, when the stud... more We investigate sampling plans in time sequential testing af snrvival distributions, when the study time is fixed. We obtain the asymptotic value of optimal sampling plans as the error probabilities of the test approach zero.
Uploads
Papers by Eitan Greenshtein