๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Asymptotic normality of the kernel estimate of a probability density function under association

โœ Scribed by George G. Roussas

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
123 KB
Volume
50
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

โœฆ Synopsis

The sole purpose of this paper is to establish asymptotic normality of the usual kernel estimate of the marginal probability density function of a strictly stationary sequence of associated random variables. In much of the discussions and derivations, the term association is used to include both positively and negatively associated random variables. The method of proof follows the familiar pattern for dependent situations of using large and small blocks. A result made available in the literature recently is instrumental in the derivations.

๐Ÿ“œ SIMILAR VOLUMES

On the asymptotic normality of multistag
On the asymptotic normality of multistage integrated density derivatives kernel estimators
โœ Carlos Tenreiro ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 264 KB

The estimation of integrated density derivatives is a crucial problem which arises in data-based methods for choosing the bandwidth of kernel and histogram estimators. In this paper, we establish the asymptotic normality of a multistage kernel estimator of such quantities, by showing that under some

Exact asymptotic L1-error of a kernel de
Exact asymptotic L1-error of a kernel density estimator under censored data
โœ Mohamed Lemdani; Elias Ould-Saฤฑฬˆd ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 139 KB

In this paper, we give the exact asymptotic L 1 -error for the kernel estimator of the density function from censored data. We also give asymptotically optimal bandwidths. Strong approximation of the product-limit estimator by a Gaussian process is used to obtain the result.