### Abstract

SUMMARY: This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {ø_{i}}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic t_{i}(θ) for ø_{i} is from an exponential family and hence complete. By imposing the assumption that the ø_{i}'s are generated from an unspecified distribution function Q, we show that for this class of distributions the conditional score function for θ (Lindsay, 1982) with oslhas_{i} estimated by E_{Q}{oslhas_{i} /t_{i}(θ)} is optimal in a sense similar to that of Cox & Reid (1987) and Liang (1987). Two empirical Bayes estimates of ø, along with the maximum likelihood estimate of ø_{i} are compared through simulations in terms of θ estimation.

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

Pages (from-to) | 261-270 |

Number of pages | 10 |

Journal | Biometrika |

Volume | 79 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1992 |

### Fingerprint

### Keywords

- Conditional score function
- Conjugate prior
- Empirical Bayes
- Linear Bayes
- Maximum likelihood estimate
- Nuisance parameters

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Mathematics(all)
- Statistics and Probability
- Agricultural and Biological Sciences (miscellaneous)
- Agricultural and Biological Sciences(all)

### Cite this

*Biometrika*,

*79*(2), 261-270. https://doi.org/10.1093/biomet/79.2.261

**Empirical Bayes and conditional inference with many nuisance parameters.** / Liang, Kung Yee; Tsou, Daniel.

Research output: Contribution to journal › Article

*Biometrika*, vol. 79, no. 2, pp. 261-270. https://doi.org/10.1093/biomet/79.2.261

}

TY - JOUR

T1 - Empirical Bayes and conditional inference with many nuisance parameters

AU - Liang, Kung Yee

AU - Tsou, Daniel

PY - 1992/6

Y1 - 1992/6

N2 - SUMMARY: This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of distributions the conditional score function for θ (Lindsay, 1982) with oslhasi estimated by EQ{oslhasi /ti(θ)} is optimal in a sense similar to that of Cox & Reid (1987) and Liang (1987). Two empirical Bayes estimates of ø, along with the maximum likelihood estimate of øi are compared through simulations in terms of θ estimation.

AB - SUMMARY: This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of distributions the conditional score function for θ (Lindsay, 1982) with oslhasi estimated by EQ{oslhasi /ti(θ)} is optimal in a sense similar to that of Cox & Reid (1987) and Liang (1987). Two empirical Bayes estimates of ø, along with the maximum likelihood estimate of øi are compared through simulations in terms of θ estimation.

KW - Conditional score function

KW - Conjugate prior

KW - Empirical Bayes

KW - Linear Bayes

KW - Maximum likelihood estimate

KW - Nuisance parameters

UR - http://www.scopus.com/inward/record.url?scp=0008780098&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0008780098&partnerID=8YFLogxK

U2 - 10.1093/biomet/79.2.261

DO - 10.1093/biomet/79.2.261

M3 - Article

AN - SCOPUS:0008780098

VL - 79

SP - 261

EP - 270

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 2

ER -