Development of alternative methods of parameter estimation to the EM algorithm using missing data

2023 Fiscal Year Final Research Report

• Project/Area Number: 18K11205
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60030:Statistical science-related
• Research Institution: Kansai University
• Principal Investigator: Takai Keiji 関西大学, 商学部, 教授 (20572019)
• Project Period (FY): 2018-04-01 – 2024-03-31
• Keywords: 欠測データ / 不完全データ / フィッシャースコアリング / 加速法

Outline of Final Research Achievements

The purpose of this study is to develop an alternative to the EM algorithm (hereafter referred to as EM) that is currently used as the standard method for estimating parameters in statistical models with missing data. First, we developed a Fisher scoring for incomplete data, which is an improvement of the Fisher scoring method, to overcome the shortcomings of conventional EM. This method provides a better convergence speed, faster than that of general EM, and also derive the error variances that couldn't be obtained with EM. Second, we developed another parameter estimation method applicable to the gamma distribution and its mixtures. This method has the property of being able to automatically find initial values. This method has the property that it never fails in the process of computation, unlike ordinary computation methods including the Newton-Raphson method.

Free Research Field

統計学

Academic Significance and Societal Importance of the Research Achievements

本研究では統計モデルのパラメータを推定するための数値計算の方法を開発した．本研究で得られた成果の一つである不完全データのフィッシャースコアリングは，計算スピードとしては早い部類には入らない．しかし，本研究により，その計算過程は本質的には最急降下法となっていることや，その計算プロセスが既存のEMアルゴリズムに近いことなどの解析を行なうことができた．これにより本研究のようなEMアルゴリズムの単純な改善では超一次収束を達成できないことが示唆されている．