arXiv subjects

E. Greenshtein

Publications and source records attributed to E. Greenshtein.

4 recordsLinked to original sources

arXiv2014

Empirical Bayes improvement of Kalman filter type of estimators

We consider the problem of estimating the means $μ_i$ of $n$ random variables $Y_i \sim N(μ_i,1)$, $i=1,\ldots ,n$. Assuming some structure on the $μ$ process, e.g., a state space model, one may use a summary statistics for the contribution of the rest of the observations to the estimation of $μ_i$. The most important example for this is the Kalman filter. We introduce a non-linear improvement of the standard weighted average of the given summary statistics and $Y_i$ itself, using empirical Bayes methods. The improvement is obtained under mild assumptions. It is strict when the process that governs the states $μ_1,\ldots,μ_n $ is not a linear Gaussian state-space model. We consider both the sequential and the retrospective estimation problems.

math.ST↗

arXiv2013

The Poisson Compound Decision Problem Revisited

The compound decision problem for a vector of independent Poisson random variables with possibly different means has half a century old solution. However, it appears that the classical solution needs smoothing adjustment even when there are many observations and relatively small means such that the empirical distribution is close to its mean. We discuss three such adjustments. We also present another approach that first transforms the problem into the normal compound decision problem.

math.ST↗

arXiv2011

Re-calibration of sample means

We consider the problem of calibration and the GREG method as suggested and studied in Deville and Sarndal (1992). We show that a GREG type estimator is typically not minimal variance unbiased estimator even asymptotically. We suggest a similar estimator which is unbiased but is asymptotically with a minimal variance.

stat.ME↗

arXiv2010

Compound decision in the presence of proxies with an application to spatio-temporal data

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)

math.ST↗