Reference Priors For Non-Normal Two-Sample Problems

C. Fernández, M.F.J. Steel

Research output: Working paper › Discussion paper › Other research output

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Abstract

The reference prior algorithm (Berger and Bernardo, 1992) is applied to locationscale models with any regular sampling density. A number of two-sample problems is analyzed in this general context, extending the dierence, ratio and product of Normal means problems outside Normality, while explicitly considering possibly dierent sizes for each sample. Since the reference prior turns out to be improper in all cases, we examine existence of the resulting posterior distribution and its moments under sampling from scale mixtures of Normals. In the context of an empirical example, it is shown that a reference posterior analysis is numerically feasible and can display some sensitivity to the actual sampling distributions. This illustrates the practical importance of questioning the Normality assumption.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages21
Volume1997-104
Publication statusPublished - 1997

Publication series

NameCentER Discussion Paper
Volume1997-104

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Reference Prior
Two-sample Problem
Normality
Scale Mixture
Sampling Distribution
Posterior distribution
Moment
Context
Model

Keywords

  • Behrens-Fisher problem
  • Fieller-Creasy problem
  • Gibbs sampling
  • Jeffreys' prior
  • location-scale model
  • posterior existence
  • product of means
  • scale mixtures of normals
  • skewness

Cite this

Fernández, C., & Steel, M. F. J. (1997). Reference Priors For Non-Normal Two-Sample Problems. (CentER Discussion Paper; Vol. 1997-104). Tilburg: Econometrics.
Fernández, C. ; Steel, M.F.J. / Reference Priors For Non-Normal Two-Sample Problems. Tilburg : Econometrics, 1997. (CentER Discussion Paper).
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abstract = "The reference prior algorithm (Berger and Bernardo, 1992) is applied to locationscale models with any regular sampling density. A number of two-sample problems is analyzed in this general context, extending the dierence, ratio and product of Normal means problems outside Normality, while explicitly considering possibly dierent sizes for each sample. Since the reference prior turns out to be improper in all cases, we examine existence of the resulting posterior distribution and its moments under sampling from scale mixtures of Normals. In the context of an empirical example, it is shown that a reference posterior analysis is numerically feasible and can display some sensitivity to the actual sampling distributions. This illustrates the practical importance of questioning the Normality assumption.",
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note = "Pagination: 21",
year = "1997",
language = "English",
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Fernández, C & Steel, MFJ 1997 'Reference Priors For Non-Normal Two-Sample Problems' CentER Discussion Paper, vol. 1997-104, Econometrics, Tilburg.

Reference Priors For Non-Normal Two-Sample Problems. / Fernández, C.; Steel, M.F.J.

Tilburg : Econometrics, 1997. (CentER Discussion Paper; Vol. 1997-104).

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Reference Priors For Non-Normal Two-Sample Problems

AU - Fernández, C.

AU - Steel, M.F.J.

N1 - Pagination: 21

PY - 1997

Y1 - 1997

N2 - The reference prior algorithm (Berger and Bernardo, 1992) is applied to locationscale models with any regular sampling density. A number of two-sample problems is analyzed in this general context, extending the dierence, ratio and product of Normal means problems outside Normality, while explicitly considering possibly dierent sizes for each sample. Since the reference prior turns out to be improper in all cases, we examine existence of the resulting posterior distribution and its moments under sampling from scale mixtures of Normals. In the context of an empirical example, it is shown that a reference posterior analysis is numerically feasible and can display some sensitivity to the actual sampling distributions. This illustrates the practical importance of questioning the Normality assumption.

AB - The reference prior algorithm (Berger and Bernardo, 1992) is applied to locationscale models with any regular sampling density. A number of two-sample problems is analyzed in this general context, extending the dierence, ratio and product of Normal means problems outside Normality, while explicitly considering possibly dierent sizes for each sample. Since the reference prior turns out to be improper in all cases, we examine existence of the resulting posterior distribution and its moments under sampling from scale mixtures of Normals. In the context of an empirical example, it is shown that a reference posterior analysis is numerically feasible and can display some sensitivity to the actual sampling distributions. This illustrates the practical importance of questioning the Normality assumption.

KW - Behrens-Fisher problem

KW - Fieller-Creasy problem

KW - Gibbs sampling

KW - Jeffreys' prior

KW - location-scale model

KW - posterior existence

KW - product of means

KW - scale mixtures of normals

KW - skewness

M3 - Discussion paper

VL - 1997-104

T3 - CentER Discussion Paper

BT - Reference Priors For Non-Normal Two-Sample Problems

PB - Econometrics

CY - Tilburg

ER -

Fernández C, Steel MFJ. Reference Priors For Non-Normal Two-Sample Problems. Tilburg: Econometrics. 1997. (CentER Discussion Paper).

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