An Extension of the Csörgő-Horváth Functional Limit Theorem and Its Applications to Changepoint Problems
✍ Scribed by D. Ferger
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 384 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0047-259X
No coin nor oath required. For personal study only.
✦ Synopsis
Consider a triangular array (X_{1}^{n}, \ldots, X_{n}^{n}, n \in \mathbb{N}), of rowwise independent random clements with values in a measurable space. Suppose there exists (\theta \in[0,1)) such that (X_{1}^{n}, \ldots, X_{\left.\left[n^{n}\right}\right]}^{n}) have distribution (v_{1}) and (X_{\left[n^{n}\right]+1}^{n}, \ldots, X_{n}^{n}) have distribution (v_{2}). Csörgö and Horváth derived an invariance principle for a one-time parameter process, which is the foundation of a test for (H_{0}: 0=0) versus (H_{1}: \theta \in(0,1)). We are interested in the more complex test problem (\tilde{H}{0}: \theta \in \Theta{0}) versus (\tilde{H}{1}: \theta \notin \Theta{0}), where (\Theta_{0} \subseteq(0,1)). To treat this new situation, we extend the Csörgö-Horvath result in proving a functional limit theorem for a suitable two-time parameter process. We briefly sketch several applications of our result. Especially, the power of the Csörgö-Horváth test is investigated in detail. 1994 Academic Press, Inc.