ESTIMATING THE MISSING VALUE IN ONE-WAY ANOVA UNDER LONG-TAILED SYMMETRIC ERROR DISTRIBUTIONS

Aydin D., ŞENOĞLU B.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, vol.36, no.2, pp.523-538, 2018 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 2
  • Publication Date: 2018
  • Journal Name: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Academic Search Premier, Directory of Open Access Journals
  • Page Numbers: pp.523-538
  • Keywords: Missing value, one-way ANOVA, LTS distribution, EM algorithm, MML methodology, LEAST-SQUARES ESTIMATION, T-DISTRIBUTION, VARIANCE, TRANSFORMATIONS, LIKELIHOOD, IMPUTATION, NORMALITY, ALGORITHM
  • Ankara University Affiliated: Yes

Abstract

In practice, missing values are widely seen and create serious problems in almost all statistical analysis. In this study, to deal with missing values, we propose estimators for missing value in one-way analysis of variance (ANOVA) when the distribution of error terms is long-tailed symmetric (LTS). We use methodologies known as maximum likelihood (ML), modified maximum likelihood (MML) and least squares (LS) in estimating missing value. Expectation and maximization (EM) algorithm is used for computing ML estimate of missing value. We compare the efficiencies of LS, ML and MML estimators of missing value via Monte Carlo simulation study. Simulation results show that ML estimator of missing value is the most efficient among the others. The usefulness of the proposed estimators is illustrated by peak discharge data example taken from civil engineering.