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An algorithm for QMC integration using low-discrepancy lattice sets

Vojtěch Franěk (2008)

Commentationes Mathematicae Universitatis Carolinae

Many low-discrepancy sets are suitable for quasi-Monte Carlo integration. Skriganov showed that the intersections of suitable lattices with the unit cube have low discrepancy. We introduce an algorithm based on linear programming which scales any given lattice appropriately and computes its intersection with the unit cube. We compare the quality of numerical integration using these low-discrepancy lattice sets with approximations using other known (quasi-)Monte Carlo methods. The comparison is based...

An alternative extension of the k-means algorithm for clustering categorical data

Ohn San, Van-Nam Huynh, Yoshiteru Nakamori (2004)

International Journal of Applied Mathematics and Computer Science

Most of the earlier work on clustering has mainly been focused on numerical data whose inherent geometric properties can be exploited to naturally define distance functions between data points. Recently, the problem of clustering categorical data has started drawing interest. However, the computational cost makes most of the previous algorithms unacceptable for clustering very large databases. The -means algorithm is well known for its efficiency in this respect. At the same time, working only on...

An approximate necessary condition for the optimal bandwidth selector in kernel density estimation

L. Gajek, A. Lenic (1993)

Applicationes Mathematicae

An approximate necessary condition for the optimal bandwidth choice is derived. This condition is used to construct an iterative bandwidth selector. The algorithm is based on resampling and step-wise fitting the bandwidth to the density estimator from the previous iteration. Examples show fast convergence of the algorithm to the bandwidth value which is surprisingly close to the optimal one no matter what is the initial knowledge on the unknown density.

An asymptotically unbiased moment estimator of a negative extreme value index

Frederico Caeiro, M. Ivette Gomes (2010)

Discussiones Mathematicae Probability and Statistics

In this paper we consider a new class of consistent semi-parametric estimators of a negative extreme value index, based on the set of the k largest observations. This class of estimators depends on a control or tuning parameter, which enables us to have access to an estimator with a null second-order component of asymptotic bias, and with a rather interesting mean squared error, as a function of k. We study the consistency and asymptotic normality of the proposed estimators. Their finite sample...

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