Mean squared error of empirical predictor

By J. N. K. Rao, Jiming Jiang, Kalyan Das. 2004

294 citations recorded by the source corpus.

The term empirical predictor refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML estimators are used for the second stage. We obtain second-order approximation to the MSE as well as an estimator of the MSE correct to the same order. The general results are applied to mixed linear models to obtain a second-order approximation to the MSE of the empirical best linear unbiased predictor (EBLUP) of a linear mixed effect and an estimator of the MSE of EBLUP whose bias is correct to second order. The general mixed linear model includes the mixed ANOVA model and the longitudinal model as special cases.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/67ff4f537d359e346619213fb6e525fd4454b21d

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In Statistics and Probability

Citations in the corpus

Mixed model prediction and small area estimation (2006, methodology): “Chatterjee et al. (2006) showed that the Chatterjee-Lahiri parametric bootstrap methods can be extended to a very general normal mixed linear model considered in Das et al. (2004).”
Best Predictive Small Area Estimation (2011, methodology): “A well-known precision measure for a predictor is the mean squared prediction error (MSPE; e.g., Prasad and Rao 1990; Das, Jiang, and Rao 2004).”
Estimation of Finite Population Domain Means (2006, background): “The last condition of b holds if, for example, θ̂ is truncated (e.g., Das et al. 2004, p. 826).”
Nonparametric estimation of mean-squared prediction error in nested-error regression models (2005, unknown): “To alleviate it, Prasad and Rao [27] constructed second-order correct mean-squared error estimators under normal models.”
New important developments in small area estimation (2013, methodology): “Datta, Rao and Torabi (2010) propose to replace the estimator x̄i of xi by its maximum likelihood estimator (MLE) under the model. The corresponding PB of Ȳi (assuming that the other model parameters are known) is the same as the PB of Ghosh and Sinha (2007), but with Bi replaced by B̃i = (niσ 2 u +”
Bootstrap mean squared error of a small-area EBLUP (2008, unknown): “13 studied the approximation of the MSE for a wider class of models, including ANOVA and longitudinal random effects models, when variance components are estimated by ML or RML.”
Non‐parametric small area estimation using penalized spline regression (2008, methodology): “S ′VSI−1/+o ( L2n n ) , where l denotes the restricted maximum likelihood log-likelihood function, and the derivatives are all evaluated at the true parameter values (see theorem 3.1 of Das et al. (2004)).”
Empirical likelihood for small area estimation (2011, background): “[2002], Das et al. [2004], Jiang & Lahiri [2006]).”
Nonparametric small area estimation using penalized spline regression (2005, unknown): “This proof builds on the work of Das et al. (2004). First we compute the orders of magnitude of the quantities dj = {tr(PBjPBj)} (j = 1, 2, 3), which are, respectively, O( √ n/Ln), O(n/Ln) and O(T/Ln).”