𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Hilbert kernel density estimate

✍ Scribed by Luc Devroye; Adam Krzyżak

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
124 KB
Volume
44
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

✦ Synopsis

Let X be an R d -valued random variable with unknown density f. Let X1; : : : ; Xn be i.i.d. random variables drawn from f. We study the pointwise convergence of a new class of density estimates, of which the most striking member is the Hilbert kernel estimate

where V d is the volume of the unit ball in R d . This is particularly interesting as this density estimate is basically of the format of the kernel estimate (except for the log n factor in front) and the kernel estimate does not have a smoothing parameter.

📜 SIMILAR VOLUMES

The Hilbert Kernel Regression Estimate
The Hilbert Kernel Regression Estimate
✍ Luc Devroye; Laszlo Györfi; Adam Krzyżak 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 410 KB

Let (X, Y ) be an R d \_R-valued regression pair, where X has a density and Y is bounded. If n i.i.d. samples are drawn from this distribution, the Nadaraya Watson kernel regression estimate in R d with Hilbert kernel K(x)=1Â&x& d is shown to converge weakly for all such regression pairs. We also sh

On kernel density estimation near endpoi
On kernel density estimation near endpoints
✍ Shunpu Zhang; Rohana J. Karunamuni 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 144 KB

In this paper, we consider the estimation problem of f(0), the value of density f at the left endpoint 0. Nonparametric estimation of f( 0) is rather formidable due to boundary e ects that occur in nonparametric curve estimation. It is well known that the usual kernel density estimates require modiÿ

On the Accuracy of Binned Kernel Density
On the Accuracy of Binned Kernel Density Estimators
✍ Peter Hall; M.P. Wand 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 515 KB

The accuracy of the binned kernel density estimator is studied for general binning rules. We derive mean squared error results for the closeness of this estimator to both the true density and the unbinned kernel estimator. The binning rule and smoothness of the kernel function are shown to influence