Estimation and testing in one-way anova when the errors are skew-normal Estimación y pruebas de hipótesis en ANOVA a una vía cuando los errores se distribuyen como normal sesgados

Celik N., ŞENOĞLU B., ARSLAN O.

Revista Colombiana de Estadistica, vol.38, no.1, pp.75-91, 2015 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.15446/rce.v38n1.48802
  • Journal Name: Revista Colombiana de Estadistica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.75-91
  • Keywords: Algorithm, ANOVA, Iteratively, Likelihood, Modified, Monte Carlo, Reweighting, Robustness, Simulation, Skew-Normal
  • Ankara University Affiliated: Yes

Abstract

© 2015 Revista Colombiana de Estadística. All right received.We consider one-way analysis of variance (ANOVA) model when the error terms have skew- normal distribution. We obtain the estimators of the model parameters by using the maximum likelihood (ML) and the modified maximum likelihood (MML) methodologies (see, Tiku 1967). In the ML method, iteratively reweighting algorithm (IRA) is used to solve the likelihood equations. The MML approach is a non-iterative method used to obtain the explicit estimators of model parameters. We also propose new test statistics based on these estimators for testing the equality of treatment effects. Simulation results show that the proposed estimators and the tests based on them are more efficient and robust than the corresponding normal theory solutions. Also, real data is analysed to show the performance of the proposed estimators and the tests.