Chris A. J. Klaassen — Page 2

arXiv2002

Asymptotically efficient estimation of linear functionals in inverse regression models

In this paper we will discuss a procedure to improve the usual estimator of a linear functional of the unknown regression function in inverse nonparametric regression models. In Klaassen, Lee, and Ruymgaart (2001) it has been proved that this traditional estimator is not asymptotically efficient (in the sense of the Hájek - Le Cam convolution theorem) except, possibly, when the error distribution is normal. Since this estimator, however, is still root-n consistent a procedure in Bickel, Klaassen, Ritov, and Wellner (1993) applies to construct a modification which is asymptotically efficient. A self-contained proof of the asymptotic efficiency is included.

math.ST↗

arXiv2001

Discrete Spacings

Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring units have length less than $k$. When centered and scaled by $n^{-1/2}$ the resulting numbers of spacings of length $1, 2,..., k-1$ have simultaneously a limiting normal distribution as $n\to\infty$. This is proved by the classical method of moments.

math.PR↗