A point optimal test for heteroscedastic disturbances

The Invariance of Tests of Disturbance Specification to Multicollinearity

“…A wide range of tests for autocorrelation, heteroscedasticity and normality have been investigated for dependence on X only through M . These include: all those surveyed by Judge, Griffiths, Hill and Lee (1980, chapters 4.2, 4.3, 5.4); those of Szroeter (1978), White (19801, King (1985) and Evans and King (1985); Bickel's (1978) robust tests and tests for special cases of heteroscedasticity, resulting from outliers with non-homogeneous disturbance variance and from random coefficient models (see Breusch and Pagan (1979)); and tests for non-normality based on OLS and LUS residuals, or their order statistics. Only those of Durbin and Sims, for first-order autoregression, are affected by multicollinearity.…”

The power and robustness properties of tests for heteroskedasticity when the regressors are trended

“…3 ) above. The chcrice of valuea for h and the critical vslut.5 for nperatiorializi!lg this test has heen disc~~sseii exhaustively-in Evans and King ( 1985a). Critical values for this test are derived ~cc(:~r.dingly.…”

On the Optimality of Some Tests of the Error Covariance Matrix in the Linear Regression Model

“…49-50, andKing (1980), theorem 3, show that the test is most powerful invariant (MPI) for known (),. and Evans and King (1985) advocate these point optimal tests for detecting first-order AR disturbances and heteroscedastic disturbances respectively.…”

“…the use of conditional distributions, and investigates some of these issues. Specifically, we give an alternative justification for the so-called point optimal tests, advocated by Evans and King (1985) and , by showing that they are the most powerful similar (MPS) test. We also derive the locally best similar (LBS) test for the one-sided alternative problem and the locally best unbiased similar (LBUS) test for the two-sided alternative.…”