Hypothesis Tests with a Repeatedly Singular Information Matrix

70 Pages Posted: 3 Mar 2020

See all articles by Dante Amengual

Dante Amengual

Centre for Monetary and Financial Studies (CEMFI)

Xinyue Bei

Duke University

Enrique Sentana

Centro de Estudios Monetarios y Financieros (CEMFI); Financial Markets Group; Centre for Economic Policy Research (CEPR)

Date Written: February 2020

Abstract

We study score-type tests in likelihood contexts in which the nullity of the information matrix under the null is larger than one, thereby generalizing earlier results in the literature. Examples include multivariate skew normal distributions, Hermite expansions of Gaussian copulas, purely non-linear predictive regressions, multiplicative seasonal time series models and multivariate regression models with selectivity. Our proposal, which involves higher order derivatives, is asymptotically equivalent to the likelihood ratio but only requires estimation under the null. We conduct extensive Monte Carlo exercises that study the finite sample size and power properties of our proposal and compare it to alternative approaches.

Keywords: Generalized extremum tests, Higher-order identifiability, Likelihood ratio test, Non-Gaussian copulas, Predictive regressions, Skew normal distributions

JEL Classification: C12, C22, C34, C46, C58

Suggested Citation

Amengual, Dante and Bei, Xinyue and Sentana, Enrique, Hypothesis Tests with a Repeatedly Singular Information Matrix (February 2020). CEPR Discussion Paper No. DP14415, Available at SSRN: https://ssrn.com/abstract=3547348

Dante Amengual (Contact Author)

Centre for Monetary and Financial Studies (CEMFI) ( email )

Casado del Alisal 5
28014 Madrid
Spain

Xinyue Bei

Duke University ( email )

100 Fuqua Drive
Durham, NC 27708-0204
United States

Enrique Sentana

Centro de Estudios Monetarios y Financieros (CEMFI) ( email )

Casado del Alisal 5
28014 Madrid
Spain
+34 91 429 0551 (Phone)
+34 91 429 1056 (Fax)

HOME PAGE: http://www.cemfi.es/~sentana/

Financial Markets Group

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London School of Economics & Political Science (LSE)
London WC2A 2AE
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+44 20 7955 7002 (Phone)
+44 20 7852 3580 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

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