✦ LIBER ✦

On unbiased density estimation for ergodic diffusion

✍ Scribed by Yu.A. Kutoyants

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 316 KB
Volume: 34
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(96)00174-5

No coin nor oath required. For personal study only.

✦ Synopsis

Two classes of unbiased estimators of the density function of ergodic distribution for the diffusion process of observations are proposed. The estimators are square-root consistent and asymptotically normal. This curious situation is entirely different from the case of discrete-time models (Davis 1977) where the unbiased estimator rarely exists and usually the estimators are not square-root consistent.

📜 SIMILAR VOLUMES

On efficient estimation of invariant den

On efficient estimation of invariant density for ergodic diffusion processes

✍ Ilia Negri 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 96 KB

The problem of nonparametric invariant density function estimation of an ergodic di usion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is established. The asymptotic risk considered measures the distance between the estimators and the density that

On confidence intervals for distribution

On confidence intervals for distribution function and density of ergodic diffusion process

✍ D. Dehay; Yu.A. Kutoyants 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 228 KB

In the problems of invariant distribution and density estimation of an ergodic di usion process, the asymptotic variances of many estimators can be represented as some mathematical expectations with respect to the invariant law. Therefore, the construction of the conÿdence intervals requires the est

Ergodic theorems for transient one-dimen

Ergodic theorems for transient one-dimensional diffusions

✍ K.B. Athreya; A.P.N. Weerasinghe 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 431 KB

Logarithmic Estimates for the Density of

Logarithmic Estimates for the Density of Hypoelliptic Two-Parameter Diffusions

✍ A. Kohatsu-Higa; D. Márquez-Carreras; M. Sanz-Solé 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 221 KB

We consider a hypoelliptic two-parameter diffusion. We first prove a sharp upper bound in small time (s, t) ¥ [0, 1] 2 for the L p -moments of the inverse of the Malliavin matrix of the diffusion process. Second, we establish the behaviour of 2e 2 log p s, t (x, y), as e a 0, where x is the initial

Ergodic control problem for one-dimensio

Ergodic control problem for one-dimensional diffusions with near-monotone cost

✍ A. Bensoussan; V. Borkar 📂 Article 📅 1984 🏛 Elsevier Science 🌐 English ⚖ 366 KB

On an Unbiased Variance Estimator for th

On an Unbiased Variance Estimator for the WILCOXON-MANN-WHITNEY-Statistic Based on Ranks

✍ Dr. R. Hilgers 📂 Article 📅 1981 🏛 John Wiley and Sons 🌐 English ⚖ 320 KB 👁 2 views

## Abstract For some applications of the WILCOXON‐MANN‐WHITNEY‐statistic its variance has to be estimated. So e.g. for the test of POTTHOFF (1963) to detect differences in medians of two symmetric distributions as well as for the computation of approximate, confidence bounds for the probability __P