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

• 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
• Project Status: Completed (Fiscal Year 2023)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• 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 / 情報量規準 / ガンマ分布 / ガンマ混合分布 / EMアルゴリズム / MAR / 欠測値 / 情報量基準 / 非正定値行列 / 因子分析 / 最尤推定 / ニュートン法

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.

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．

Research Products

• [Journal Article] Model Selection with Missing Data Embedded in Missing-at-Random Data (2023)
  • Author(s): Takai Keiji、Hayashi Kenichi
  • Journal Title: Stats Volume: 6 Issue: 2 Pages: 495-505
  • DOI: 10.3390/stats6020031
  • Peer Reviewed / Open Access
• [Journal Article] Incomplete-data Fisher scoring method with steplength adjustment (article) Author (2020)
  • Author(s): Keiji Takai
  • Journal Title: Statistics and Computing Volume: 30 Issue: 4 Pages: 871-886
  • DOI: 10.1007/s11222-020-09923-z
  • Peer Reviewed / Open Access
• [Journal Article] On the use of the selection matrix in the maximum likelihood estimation of normal distribution models with missing data (2017)
  • Author(s): Takai Keiji
  • Journal Title: Communications in Statistics - Theory and Methods Volume: 47 Issue: 14 Pages: 1-16
  • DOI: 10.1080/03610926.2017.1353631
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Presentation] ガンマ混合分布のパラメータ推定 (2023)
  • Author(s): 高井啓二
  • Organizer: 日本計算機統計学会 第37回大会
• [Presentation] A bisection estimation method for a Gamma distribution and the Gamma-related distributions (2023)
  • Author(s): Keiji TAKAI
  • Organizer: The 12th conference of the Asian Regional Section of the International Association for Statistical Computing (IASC-ARS 2023).
  • Int'l Joint Research
• [Presentation] 負の二項分布モデルによるチラシ掲載効果の検証 (2021)
  • Author(s): 高井啓二
  • Organizer: 関西 大学 RISS(Research Institute for Socionetwork Strategies of Kansai University) セミナー「広告効果測定，視線追跡データとパスデータの融合」
• [Presentation] 欠測データを用いたフィッシャースコアリング法 (2019)
  • Author(s): 高井啓二
  • Organizer: 科 研費シンポジウム「高次元複雑データの統計モデリング」
• [Presentation] パラメータ分割による不完全データフィッシャースコアリング (2018)
  • Author(s): 高井啓二
  • Organizer: 統計関連学会連合大会 2018