On the increments of partial sum processes with multidimensional indices
โ Scribed by Josef Steinebach
- Publisher
- Springer
- Year
- 1983
- Tongue
- English
- Weight
- 446 KB
- Volume
- 63
- Category
- Article
- ISSN
- 1432-2064
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The author studies the almost sure behaviour of the increments of the partially observed empirical process and derives some functional laws of the iterated logarithm for this process. Application to nonparametric density estimation is presented.
Let {X,; n~>l} be a stationary sequence of random variables with finite variance, and dN(2) be the finite Fourier transform based on data Xi .... ,AN. Let AN(t), 0~<t~<l be the normalized process of partial sums of the finite Fourier transforms. In general, AN does not converge to a Gaussian process
Let \(\left\{X, X_{n} ; \vec{n} \in \mathbb{N}^{d}\right\}\) be a field of independent identically distributed real random variables, \(0<p<2\), and \(\left\{a_{\bar{n}, \bar{k}} ;(\bar{n}, \bar{k}) \in \mathbb{N}^{d} \times \mathbb{N}^{d}, \bar{k} \leqslant \bar{n}\right\}\) a triangular array of r