Journal of Statistical Planning and Inference 124 (2004) 423 – 437 www.elsevier.com/locate/jspi An improved test for heteroskedasticity using adjusted modied prole likelihood inference Silvia L.P. Ferrari a ; ∗ , Audrey H.M.A. Cysneiros b , Francisco Cribari-Neto b a Departamento de Estat stica, IME, Universidade de S˜ ao Paulo, Caixa Postal 66281, S˜ ao Paulo/SP 05311-970, Brazil b Departamento de Estat stica, CCEN, Universidade Federal de Pernambuco, Cidade Universit aria, Recife/PE 50740-540, Brazil Received 12 October 2002; accepted 7 April 2003 Abstract This paper addresses the issue of testing for heteroskedasticity in linear regression models. We derive a Bartlett adjustment to the modied prole likelihood ratio test (J. Roy. Statist. Soc. B 49 (1987) 1) for heteroskedasticity in the normal linear regression model. Our results generalize those in Ferrari and Cribari-Neto (Statist. Probab. Lett. 57 (2002) 353), since they allow for a vector-valued structure for the parameter that denes the skedastic function. Monte Carlo evidence shows that the proposed test displays reliable nite-sample behavior, outperforming the original likelihood ratio test, the Bartlett-corrected likelihood ratio test, and the modied prole likelihood ratio test. c 2003 Elsevier B.V. All rights reserved. Keywords: Bartlett correction; Heteroskedasticity; Likelihood ratio test; Nuisance parameters; Prole likelihood 1. Introduction Linear regression models are oftentimes used to model the behavior of a variable of interest conditional on a set of explanatory variables. In practical applications, it is common for these models to include a heteroskedastic structure, thus indicating that the conditional variances are not constant across observations. Since the modeling strate- gies are dierent when such variances are not constant, it is important to rst test * Corresponding author. E-mail addresses: sferrari@ime.usp.br (S.L.P. Ferrari), audrey@de.ufpe.br (A.H.M.A. Cysneiros), cribari@ufpe.br (F. Cribari-Neto). 0378-3758/$ - see front matter c 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0378-3758(03)00210-6