Integrated likelihoods in models with stratum nuisance parameters

Riccardo De Bin; Nicola Sartori; Thomas A. Severini

doi:10.1214/15-EJS1045

Integrated likelihoods in models with stratum nuisance parameters

Riccardo De Bin, Nicola Sartori, Thomas A. Severini

Statistics and Data Science

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Frequentist inference about a parameter of interest in presence of a nuisance parameter can be based on an integrated likelihood function. We analyze the behaviour of inferential quantities based on such a pseudolikelihood in a two-index-asymptotics framework, in which both sample size and dimension of the nuisance parameter may diverge to infinity. We show that a properly chosen integrated likelihood largely outperforms standard likelihood methods, such as those based on the profile likelihood. These results are confirmed by simulation studies, in which comparisons with modified profile likelihood are also considered.

Original language	English (US)
Pages (from-to)	1474-1491
Number of pages	18
Journal	Electronic Journal of Statistics
Volume	9
Issue number	1
DOIs	https://doi.org/10.1214/15-EJS1045
State	Published - 2015

Funding

RDB was partially supported by grant BO3139/4-1 from the German Science Foundation Massachusetts Department of Fish and Game, (DFG). NS was partially supported by Progetto di Ateneo (CPDA131553), Universit`a degli Studi di Padova. The work of TAS was supported by the NSFNational Science Foundation.

Keywords

Modified profile likelihood
Non stationary autoregressive model
Profile likelihood
Profile score bias
Two-index asymptotics

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1214/15-EJS1045

Cite this

@article{d7f0ab028b4042e39a4fa0300ce1d5e7,

title = "Integrated likelihoods in models with stratum nuisance parameters",

abstract = "Frequentist inference about a parameter of interest in presence of a nuisance parameter can be based on an integrated likelihood function. We analyze the behaviour of inferential quantities based on such a pseudolikelihood in a two-index-asymptotics framework, in which both sample size and dimension of the nuisance parameter may diverge to infinity. We show that a properly chosen integrated likelihood largely outperforms standard likelihood methods, such as those based on the profile likelihood. These results are confirmed by simulation studies, in which comparisons with modified profile likelihood are also considered.",

keywords = "Modified profile likelihood, Non stationary autoregressive model, Profile likelihood, Profile score bias, Two-index asymptotics",

author = "{De Bin}, Riccardo and Nicola Sartori and Severini, {Thomas A.}",

year = "2015",

doi = "10.1214/15-EJS1045",

language = "English (US)",

volume = "9",

pages = "1474--1491",

journal = "Electronic Journal of Statistics",

issn = "1935-7524",

publisher = "Institute of Mathematical Statistics",

number = "1",

}

TY - JOUR

T1 - Integrated likelihoods in models with stratum nuisance parameters

AU - De Bin, Riccardo

AU - Sartori, Nicola

AU - Severini, Thomas A.

PY - 2015

Y1 - 2015

N2 - Frequentist inference about a parameter of interest in presence of a nuisance parameter can be based on an integrated likelihood function. We analyze the behaviour of inferential quantities based on such a pseudolikelihood in a two-index-asymptotics framework, in which both sample size and dimension of the nuisance parameter may diverge to infinity. We show that a properly chosen integrated likelihood largely outperforms standard likelihood methods, such as those based on the profile likelihood. These results are confirmed by simulation studies, in which comparisons with modified profile likelihood are also considered.

AB - Frequentist inference about a parameter of interest in presence of a nuisance parameter can be based on an integrated likelihood function. We analyze the behaviour of inferential quantities based on such a pseudolikelihood in a two-index-asymptotics framework, in which both sample size and dimension of the nuisance parameter may diverge to infinity. We show that a properly chosen integrated likelihood largely outperforms standard likelihood methods, such as those based on the profile likelihood. These results are confirmed by simulation studies, in which comparisons with modified profile likelihood are also considered.

KW - Modified profile likelihood

KW - Non stationary autoregressive model

KW - Profile likelihood

KW - Profile score bias

KW - Two-index asymptotics

UR - http://www.scopus.com/inward/record.url?scp=84982746810&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84982746810&partnerID=8YFLogxK

U2 - 10.1214/15-EJS1045

DO - 10.1214/15-EJS1045

M3 - Article

AN - SCOPUS:84982746810

SN - 1935-7524

VL - 9

SP - 1474

EP - 1491

JO - Electronic Journal of Statistics

JF - Electronic Journal of Statistics

IS - 1

ER -

Integrated likelihoods in models with stratum nuisance parameters

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this