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21.
We consider the regression model yi = ?(xi ) + ε in which the function ? or its pth derivative ?(p) may have a discontinuity at some unknown point τ. By fitting local polynomials from the left and right, we test the null that ?(p) is continuous against the alternative that ?(p)(τ?) ≠ ?(p)(τ+). We obtain Darling-Erdös type limit theorems for the test statistics under the null hypothesis of no change, as well as their limits in probability under the alternative. Consistency of the related change-point estimators is also established. 相似文献
22.
We give a complete asymptotic characterization of the supremum of weighted empirical spacings processes. 相似文献