Efficiency combined with simplicity: new testing procedures for Generalized Inverse Gaussian models

Angelo Koudou and Christophe Ley ()

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2014, vol. 23, issue 4, 708-724

Abstract: The standard efficient testing procedures in the Generalized Inverse Gaussian (GIG) family (also known as Halphen Type A family) are likelihood ratio tests, and hence rely on Maximum Likelihood (ML) estimation of the three parameters of the GIG. The particular form of GIG densities, involving modified Bessel functions, prevents in general form a closed-form expression for ML estimators, which are obtained at the expense of complex numerical approximation methods. On the contrary, Method of Moments (MM) estimators allow for concise expressions, but tests based on these estimators suffer from a lack of efficiency as compared to likelihood ratio tests. This is why, in recent years, trade-offs between ML and MM estimators have been proposed, resulting in simpler yet not completely efficient estimators and tests. In the present paper, we do not propose such a trade-off but rather an optimal combination of both methods, our tests inheriting efficiency from an ML-like construction and simplicity from the MM estimators of the nuisance parameters. This goal shall be reached by attacking the problem from a new angle, namely via the Le Cam methodology. Besides providing simple efficient testing methods, the theoretical background of this methodology further allows us to write out explicitly power expressions for our tests. A Monte Carlo simulation study shows that, also at small sample sizes, our simpler procedures do at least as good as the complex likelihood ratio tests. We conclude the paper by applying our findings on two real-data sets. Copyright Sociedad de Estadística e Investigación Operativa 2014

Keywords: Asymptotic linearity; GIG distributions; IG distributions; Maximin tests; Uniform local asymptotic normality; Primary 62F03; Secondary 62F05 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s11749-014-0378-2 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:testjl:v:23:y:2014:i:4:p:708-724

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/11749/PS2

DOI: 10.1007/s11749-014-0378-2

Access Statistics for this article

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research is currently edited by Alfonso Gordaliza and Ana F. Militino

More articles in TEST: An Official Journal of the Spanish Society of Statistics and Operations Research from Springer, Sociedad de Estadística e Investigación Operativa
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().