### Abstract

Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is traditionally measured by the mean squared prediction error (MSPE), and interval estimates are generally constructed using estimates of the MSPE. Such methods have shortcomings like under-coverage or over-coverage, excessive length and lack of interpretability. We propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled EBLUP. The bootstrap histogram is highly accurate, and differs from the true EBLUP distribution by only 0(d^{3}n^{-3/2}), where d is the number of parameters and n the number of observations. This result is used to obtain highly accurate prediction intervals. Simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models.

Original language | English (US) |
---|---|

Pages (from-to) | 1221-1245 |

Number of pages | 25 |

Journal | Annals of Statistics |

Volume | 36 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2008 |

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### Keywords

- Bootstrap
- Coverage accuracy
- Linear mixed model
- Prediction interval
- Predictive distribution
- Small area

### Cite this

*Annals of Statistics*,

*36*(3), 1221-1245. https://doi.org/10.1214/07-AOS512

**Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models.** / Chatterjee, Snigdhansu; Lahiri, Partha; Li, Huilin.

Research output: Contribution to journal › Article

*Annals of Statistics*, vol. 36, no. 3, pp. 1221-1245. https://doi.org/10.1214/07-AOS512

}

TY - JOUR

T1 - Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models

AU - Chatterjee, Snigdhansu

AU - Lahiri, Partha

AU - Li, Huilin

PY - 2008/6/1

Y1 - 2008/6/1

N2 - Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is traditionally measured by the mean squared prediction error (MSPE), and interval estimates are generally constructed using estimates of the MSPE. Such methods have shortcomings like under-coverage or over-coverage, excessive length and lack of interpretability. We propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled EBLUP. The bootstrap histogram is highly accurate, and differs from the true EBLUP distribution by only 0(d3n-3/2), where d is the number of parameters and n the number of observations. This result is used to obtain highly accurate prediction intervals. Simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models.

AB - Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is traditionally measured by the mean squared prediction error (MSPE), and interval estimates are generally constructed using estimates of the MSPE. Such methods have shortcomings like under-coverage or over-coverage, excessive length and lack of interpretability. We propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled EBLUP. The bootstrap histogram is highly accurate, and differs from the true EBLUP distribution by only 0(d3n-3/2), where d is the number of parameters and n the number of observations. This result is used to obtain highly accurate prediction intervals. Simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models.

KW - Bootstrap

KW - Coverage accuracy

KW - Linear mixed model

KW - Prediction interval

KW - Predictive distribution

KW - Small area

UR - http://www.scopus.com/inward/record.url?scp=51049100175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51049100175&partnerID=8YFLogxK

U2 - 10.1214/07-AOS512

DO - 10.1214/07-AOS512

M3 - Article

AN - SCOPUS:51049100175

VL - 36

SP - 1221

EP - 1245

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 3

ER -