WEIGHTED TESTS FOR A CHANGE IN THE REGRESSION SLOPE
Statistics & Risk Modeling
For a given data set it may be required to discover if a change has been occurred. This is can be conducted using change-point analysis. Let X 1 , X 2 , ...,X n be independent randomvariab les with respective continuous distribution functions F 1 , F 2 , ..., F n such that F i (0)=0 for all i.We consider the problem of testing the null hypothesis that F 1 = F 2 = ...= F n against the alternative of r-changes in the distribution functions of this sequence at unknown times 1<[nτ 1 ]<[nτ 2 ]< ....
... τ 1 ]<[nτ 2 ]< .... <[nτ r ]<n, where[ y] is the integer part of y. We study the asymptotic theory of change-point processes which are defined in terms of the emp irical process. We propose and study new weighted non-parametric change-point test statistics for a possible change in distribution function of a data set. The paper is organized as follows. In Section 2 we will consider the above multip le change-point problem in the case of at most two change-points (AMTC), i.e. r=2. In Section 3 we generalize the AMTC results to the case of ≥ 2. The proposed new change-point test statistics are presented in Sect ion 4. A lso, the asymptotic distributions of the proposed test statistics are derived in Sect ion 4. In Section 5, we propose new test statistics for the case of at most one change point. We study the applicability o f the proposed tests through a Monte Carlo study in section 6.