Electronic Journal of Statistics

A note on the local power of the LR, Wald, score and gradient tests

Artur J. Lemonte and Silvia L.P. Ferrari

Full-text: Open access

Abstract

This paper examines the local power of the likelihood ratio, Wald, score and gradient tests under the presence of a scalar parameter, ϕ say, that is orthogonal to the remaining parameters. We show that some of the coefficients that define the local powers remain unchanged regardless of whether ϕ is known or needs to be estimated, whereas the others can be written as the sum of two terms, the first of which being the corresponding term obtained as if ϕ were known, and the second, an additional term yielded by the fact that ϕ is unknown. The contribution of each set of parameters on the local powers of the tests can then be examined. Various implications of our main result are stated and discussed. Several examples are presented for illustrative purposes.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 421-434.

Dates
First available in Project Euclid: 19 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1332162335

Digital Object Identifier
doi:10.1214/12-EJS678

Mathematical Reviews number (MathSciNet)
MR2988414

Zentralblatt MATH identifier
1336.62061

Keywords
asymptotic expansions gradient test likelihood ratio test local power score test wald test

Citation

Lemonte, Artur J.; Ferrari, Silvia L.P. A note on the local power of the LR, Wald, score and gradient tests. Electron. J. Statist. 6 (2012), 421--434. doi:10.1214/12-EJS678. https://projecteuclid.org/euclid.ejs/1332162335


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