Topic

# Stein's unbiased risk estimate

About: Stein's unbiased risk estimate is a research topic. Over the lifetime, 2423 publications have been published within this topic receiving 59188 citations.

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TL;DR: In this article, the effect size estimator of Glass's estimator, the sample mean difference divided by the sample standard deviation, is studied in the context of an explicit statistical model.

Abstract: Glass's estimator of effect size, the sample mean difference divided by the sample standard deviation, is studied in the context of an explicit statistical model. The exact distribution of Glass's estimator is obtained and the estimator is shown to have a small sample bias. The minimum variance unbiased estimator is obtained and shown to have uniformly smaller variance than Glass's (biased) estimator. Measurement error is shown to attenuate estimates of effect size and a correction is given. The effects of measurement invalidity are discussed. Expressions for weights that yield the most precise weighted estimate of effect size are also derived.

3,206 citations

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TL;DR: This brief note presents a general proof that the estimator is unbiased for cluster-correlated data regardless of the setting.

Abstract: There is a simple robust variance estimator for cluster-correlated data. While this estimator is well known, it is poorly documented, and its wide range of applicability is often not understood. The estimator is widely used in sample survey research, but the results in the sample survey literature are not easily applied because of complications due to unequal probability sampling. This brief note presents a general proof that the estimator is unbiased for cluster-correlated data regardless of the setting. The result is not new, but a simple and general reference is not readily available. The use of the method will benefit from a general explanation of its wide applicability.

2,373 citations

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TL;DR: In this paper, a prediction rule is constructed on the basis of some data, and then the error rate of this rule is estimated in classifying future observations using cross-validation.

Abstract: We construct a prediction rule on the basis of some data, and then wish to estimate the error rate of this rule in classifying future observations. Cross-validation provides a nearly unbiased estimate, using only the original data. Cross-validation turns out to be related closely to the bootstrap estimate of the error rate. This article has two purposes: to understand better the theoretical basis of the prediction problem, and to investigate some related estimators, which seem to offer considerably improved estimation in small samples.

2,195 citations

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TL;DR: In this paper, a generalized moments estimator is proposed for the autoregressive parameter in a widely considered spatial autocorrelation model. But, as discussed in this paper, the (quasi) maximum likelihood estimator may not be computationally feasible in many cases involving moderate or large-sized samples.

Abstract: This paper is concerned with the estimation of the autoregressive parameter in a widely considered spatial autocorrelation model. The typical estimator for this parameter considered in the literature is the (quasi) maximum likelihood estimator corresponding to a normal density. However, as discussed in this paper, the (quasi) maximum likelihood estimator may not be computationally feasible in many cases involving moderate- or large-sized samples. In this paper we suggest a generalized moments estimator that is computationally simple irrespective of the sample size. We provide results concerning the large and small sample properties of this estimator.

1,414 citations

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TL;DR: A new estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment is presented, which has significant advantages over multiple histogram reweighting methods for combining data from multiple states.

Abstract: We present a new estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment. The estimator, which we term the multistate Bennett acceptance ratio (MBAR) estimator because it reduces to the Bennett acceptance ratio when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a solution to the estimating equations in many cases. Additionally, an estimate of the statistical uncertainty is provided for all estimated quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equilibrium data collected from multiple states. We illustrate this method by producing a highly precise estimate of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under constant force bias.

939 citations