Empirical Bayes prediction intervals in a normal regression model: higher order asymptotics

Basu, Ruma; Ghosh, Jayanta K.; Mukerjee, Rahul

doi:10.1016/s0167-7152(03)00083-x

Cited by 23 publications

(21 citation statements)

References 2 publications

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“…This is an extension of the results of Basu et al (2003) and Datta et al (2002) to the nested error regression model and to the finite population model with unbalanced sample sizes and unknown components of variance. The corrected confidence intervals have been numerically shown to be superior to the conventional confidence interval based on the sample mean in terms of the coverage probability and the expected width of the interval.…”

Section: Discussionmentioning

confidence: 93%

“…Since we specify a nested error regression model and the extended finite population model in this paper, we want to develop closed form confidence intervals based on the Taylor series expansion. This method has been used by Basu, Ghosh, and Mukerjee (2003) and Datta, Ghosh, Smith, and Lahiri (2002), who derived the asymptotically corrected empirical Bayes confidence interval in the Fay-Herriot model with a known error variance.…”

Section: Introductionmentioning

confidence: 99%

“…This method was used in Basu et al (2003) and Datta et al (2002) for the Fay-Herriot model. Another approach to constructing stable confidence intervals is to use the estimator of the mean squared error (MSE) of µ EB i ( ψ) instead of (σ 2 /n i )(1 −γ i ).…”

Section: Introductionmentioning

confidence: 99%

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Corrected empirical Bayes confidence intervals in nested error regression models

Kubokawa

2010

Journal of the Korean Statistical Society

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a b s t r a c tIn the small area estimation, the empirical best linear unbiased predictor (EBLUP) or the empirical Bayes estimator (EB) in the linear mixed model is recognized to be useful because it gives a stable and reliable estimate for a mean of a small area. In practical situations where EBLUP is applied to real data, it is important to evaluate how much EBLUP is reliable. One method for the purpose is to construct a confidence interval based on EBLUP. In this paper, we obtain an asymptotically corrected empirical Bayes confidence interval in a nested error regression model with unbalanced sample sizes and unknown components of variance. The coverage probability is shown to satisfy the confidence level in the second-order asymptotics. It is numerically revealed that the corrected confidence interval is superior to the conventional confidence interval based on the sample mean in terms of the coverage probability and the expected width of the interval. Finally, it is applied to the posted land price data in Tokyo and the neighboring prefecture.

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Section: Discussionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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Corrected empirical Bayes confidence intervals in nested error regression models

Kubokawa

2010

Journal of the Korean Statistical Society

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“…Some link functions in generalized LME models can deal with cases where dependent variables are restricted to Y t ≥ 0 [35]. However, the prediction intervals for the random-effects in the LME model are well developed [17,39,5,14,53]. It is useful to applying the prediction intervals in business operations is useful in knowing whether a randomeffect exists.…”

Section: Discussionmentioning

confidence: 99%

Advantage of make-to-stock strategy based on linear mixed-effect model: a comparison with regression, autoregressive, times series, and exponential smoothing models

Liao

Chiu

2017

Croat. Oper. Res. Rev.

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Abstract. In the past few decades, demand forecasting has become relatively difficult due to rapid changes in the global environment. This research illustrates the use of the make-to-stock (MTS) production strategy in order to explain how forecasting plays an essential role in business management. The linear mixed-effect (LME) model has been extensively developed and is widely applied in various fields. However, no study has used the LME model for business forecasting. We suggest that the LME model be used as a tool for prediction and to overcome environment complexity. The data analysis is based on real data in an international display company, where the company needs accurate demand forecasting before adopting a MTS strategy. The forecasting result from the LME model is compared to the commonly used approaches, including the regression model, autoregressive model, times series model, and exponential smoothing model, with the results revealing that prediction performance provided by the LME model is more stable than using the other methods. Furthermore, product types in the data are regarded as a random effect in the LME model, hence demands of all types can be predicted simultaneously using a single LME model. However, some approaches require splitting the data into different type categories, and then predicting the type demand by establishing a model for each type. This feature also demonstrates the practicability of the LME model in real business operations.

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“…pðx m jÞ ¼ P 2 i¼1 i gðx m j i Þ: The EB approach has been used recently in various fields in statistics, including sequential estimation [9], reliability [4,20,21], multivariate analysis [7,15], nonparametric estimation [16,17], and some other estimation problems [2,13,14]. In this article, we aim to find an EB decision rule for classification in pattern recognition, which is close to the a.o.…”

Section: The Eb Decision Rule and Stochasticmentioning

confidence: 99%

Two algorithms for classification on quality control

Chang

2010

Journal of the Chinese Institute of Industrial Engineers

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In this article, no probability density and no prior probability are assumed for the good and defective classes, except possibly two means. A sequence of unidentified input lifetimes is used to estimate the percentages of two classes. After the classifier system is put into use, the new coming unidentified input lifetime can improve the percentages. A Monte Carlo simulation study with exponential or Weibull or gamma distribution on life is presented to demonstrate the classification. The study can be widely used in quality control.

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Empirical Bayes prediction intervals in a normal regression model: higher order asymptotics

Cited by 23 publications

References 2 publications

Corrected empirical Bayes confidence intervals in nested error regression models

Corrected empirical Bayes confidence intervals in nested error regression models

Advantage of make-to-stock strategy based on linear mixed-effect model: a comparison with regression, autoregressive, times series, and exponential smoothing models

Two algorithms for classification on quality control

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