Statistical estimation

Statistical Topology Using the Nonparametric Density Estimation and Bootstrap Algorithm

This paper presents approximate confidence intervals for each function of parameters in a Banach space based on a bootstrap algorithm. We apply kernel density approach to estimate the persistence landscape. In addition, we evaluate the quality distribution function estimator of random variables using integrated mean square error (IMSE). The results of simulation studies show a significant impro...

Statistical Modelling and Estimation

Statistical Estimation of Measure Invariants

New invariants of measures, called the β-statentropy, are described. They are similar to the entropy and the HP -spectrum for dimensions. The βstatentropy admits construction of a statistical estimator calculated by n independent points distributed in accordance with a given measure. The accuracy of this estimator is O(n−c), where c is some constant, and the complexity of calculation is O(n2). ...

The Dantzig Selector : Statistical Estimation

given just a single parameter t. Two active-set methods were described in [11], with some concern about efficiency if p were large, where X is n× p . Later when basis pursuit de-noising (BPDN) was introduced [2], the intention was to deal with p very large and to allow X to be a sparse matrix or a fast operator. A primal–dual interior method was used to solve the associated quadratic program, b...

Statistical estimation with model selection

The purpose of this paper is to explain the interest and importance of (approximate) models and model selection in Statistics. Starting from the very elementary example of histograms we present a general notion of finite dimensional model for statistical estimation and we explain what type of risk bounds can be expected from the use of one such model. We then give the performance of suitable mo...