Score-type tests for normal mixtures

Dante Amengual (), Xinyue Bei (), Marine Carrasco and Enrique Sentana
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Dante Amengual: CEMFI, Centro de Estudios Monetarios y Financieros, https://www.cemfi.es/
Xinyue Bei: Duke University, https://duke.edu/

Working Papers from CEMFI

Abstract: Testing normality against discrete normal mixtures is complex because some parameters turn increasingly underidentified along alternative ways of approaching the null, others are inequality constrained, and several higher-order derivatives become identically 0. These problems make the maximum of the alternative model log-likelihood function numerically unreliable. We propose score-type tests asymptotically equivalent to the likelihood ratio as the largest of two simple intuitive statistics that only require estimation under the null. One novelty of our approach is that we treat symmetrically both ways of writing the null hypothesis without excluding any region of the parameter space. We derive the asymptotic distribution of our tests under the null and sequences of local alternatives. We also show that their asymptotic distribution is the same whether applied to observations or standardized residuals from heteroskedastic regression models. Finally, we study their power in simulations and apply them to the residuals of Mincer earnings functions.

Keywords: Generalized extremum tests; higher-order identifiability; likelihood ratio test; Mincer equations. (search for similar items in EconPapers)
JEL-codes: C12 C46 (search for similar items in EconPapers)
Date: 2022-12
New Economics Papers: this item is included in nep-ecm
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Related works:
Journal Article: Score-type tests for normal mixtures (2025)
Working Paper: Score-type tests for normal mixtures (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:cmf:wpaper:wp2022_2213

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