Non-constant variance (heteroscedasticity) is common in regression data, and many tests have been proposed for detecting it. This paper shows that the properties of likelihood-based tests can be improved by using the modified profile likelihood of Cox and Reid. A modified likelihood ratio test and modified score tests are derived, and both theoretical and intuitive justifications are given for the improved properties of the tests. The results of a Monte Carlo study are mentioned, which show that, whereas the ordinary likelihood ratio test can be very anticonservative, the modified test holds its null size well and is more powerful than the other tests. For non-normal error distributions, Studentized tests hold their size well (without being overconservative), even for long-tailed error distributions. Under short-tailed error distributions, likelihood ratio or Studentized score tests are most powerful, depending on the degree of heteroscedasticity. The modified versions of the score tests consistently outperform the unmodified versions. The use of these tests is demonstrated through analysis of data on the volatility of stock prices.
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Journal of the Royal Statistical Society. Series C (Applied Statistics)
© 1994 Royal Statistical Society
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