# zbMATH — the first resource for mathematics

Asymptotic efficient estimation of the change point with unknown distributions. (English) Zbl 0714.62027
Summary: Suppose $$X_ 1,...,X_ n$$ are distributed according to a probability measure under which $$X_ 1,...,X_ n$$ are independent, $$X_ i\sim F_ 0$$, for $$i=1,...,[\theta_ nn]$$ and $$X_ i\sim F^{(n)}$$ for $$i=[\theta_ nn]+1,...,n$$, where [x] denotes the integer part of x.
We consider the asymptotic efficient estimation of $$\theta_ n$$ when the distributions are not known. Our estimator is efficient in the sense that if $$F^{(n)}=F_{\eta_ n}$$, $$\eta_ n\to 0$$ and $$\{F_{\eta}\}$$ is a regular one-dimensional parametric family of distributions, then the estimator is asymptotically equivalent to the best regular estimator.

##### MSC:
 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference
Full Text: