A study on statistical theory via the Bernstein polynomial/asymmetric kernel and its application

2016 Fiscal Year Final Research Report

• Project/Area Number: 26330030
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Hokkaido University
• Principal Investigator: Kakizawa Yoshihide 北海道大学, 経済学研究科, 教授 (30281778)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: ノンパラメトリック法 / 密度推定

Outline of Final Research Achievements

In this study, we focus on the asymmetric kernel methods to estimate the probability density function for nonnegative data. Especially, we have proposed (i) a family of asymmetric kernel density estimators, depending on the so-called density generator that plays a role of an infinite dimensional parameter, and (ii) a family of Amoroso kernel density estimators, including the gamma/inverse gamma/inverse Gaussian/reciprocal inverse Gaussian/Birnbaum-Saunders/log-normal kernel density estimators as special cases of these families. Also, we have discussed (iii) some bias-reduced density estimators. We have established their asymptotic properties (bias, variance, mean integrated squared error, and so on), as well as the (pointwise) strong consistency and asymptotic normality. The simulation studies have been conducted to confirm our theoretical results.

Free Research Field

統計科学、数理統計学