HYPOTHESES TESTING FOR ERROR-IN-VARIABLES MODELS

PATRICIA GIMENEZ^{1,2}, HELENO BOLFARINE^{1} AND ENRICO A. COLOSIMO^{1,3}

1Departamento de Estatística, IME/USP, Caixa Postal 20570, 01452-990, São Paulo-SP, Brazil

2Departamento de Matemática - FCEYN/UNMDP, Funes 3350, C.P. 7600, Mar del Plata-BS.AS., Argentina

3Departamento de Estatística, ICEx/UFMG, Caixa Postal 702, 30161-970, Belo Horizonte-MG, Brazil

(Received December 4, 1997; revised April 12, 1999)

Abstract. In this paper, hypotheses testing based on a corrected score function are considered. Five different testing statistics are proposed and their asymptotic distributions are investigated. It is shown that the statistics are asymptotically distributed according to the chisquare distribution or can be written as a linear combination of chisquare random variables with one degree of freedom. A small scale numerical Monte Carlo study is presented in order to compare the empirical size and power of the proposed tests. A comparative calibration example is used to illustrate the results obtained.

Key words and phrases: Asymptotic tests, comparative calibration, consistent estimator, measurement error, naive test.