Analysis of variance in experimental design with nonnormal error distributions

Senoglu, B
Tiku, ML
We consider a two-way classification model with interaction and assume that the errors have a location-scale nonnormal distribution. From an application of the modified likelihood estimation, we obtain efficient and robust estimators of the parameters. We define F statistics for testing main effects and interaction. We analyze the Box-Cox data and show that the method developed in this paper gives accurate results besides being easy theoretically and computationally.


Analysis of variance and linear contrasts in experimental design with generalized secant hyperbolic distribution
Yilmaz, Yidiz E.; Akkaya, Ayşen (Elsevier BV, 2008-07-01)
We consider one-way classification model in experimental design when the errors have generalized secant hyperbolic distribution. We obtain efficient and robust estimators for block effects by using the modified maximum likelihood estimation (MML) methodology. A test statistic analogous to the normal-theory F statistic is defined to test block effects. We also define a test statistic for testing linear contrasts. It is shown that test statistics based on MML estimators are efficient and robust. The methodolo...
Estimating parameters in autoregressive models in non-normal situations: Asymmetric innovations
Akkaya, Ayşen (2001-01-01)
The estimation of coefficients in a simple autoregressive model is considered in a supposedly difficult situation where the innovations have an asymmetric distribution. Two distributions, gamma and generalized logistic, are considered for illustration. Closed form estimators are obtained and shown to be efficient and robust. Efficiencies of least squares estimators are evaluated and shown to be very low. This work is an extension of that of Tiku, Wong and Bian [1] who give solutions for a simple AR(I) model
Experimental design with short-tailed and long-tailed symmetric error distributions
Yilmaz, Yıldız Elif; Akkaya, Ayşen; Department of Statistics (2004)
One-way and two-way classification models in experimental design for both balanced and unbalanced cases are considered when the errors have Generalized Secant Hyperbolic distribution. Efficient and robust estimators for main and interaction effects are obtained by using the modified maximum likelihood estimation (MML) technique. The test statistics analogous to the normal-theory F statistics are defined to test main and interaction effects and a test statistic for testing linear contrasts is defined. It is ...
Estimation and hypothesis testing in BIB design and robustness
Tiku, Moti L.; ŞENOĞLU, BİRDAL (Elsevier BV, 2009-07-01)
Modified maximum likelihood estimators of the unknown parameters in a BIB design under non-normality of error distributions are obtained. They are shown to be more efficient and robust than the traditional least squares estimators. A test statistic for testing a linear contrast among treatment effects is developed. A real life example is given.
Linear contrasts in experimental design with non-identical error distributions
Senoglu, B; Tiku, ML (Wiley, 2002-01-01)
Estimation of linear contrasts in experimental design, and testing their assumed values, is considered when the error distributions from block to block are not necessarily identical. The normal-theory solutions are shown to have low efficiencies as compared to the solutions presented here.
Citation Formats
B. Senoglu and M. Tiku, “Analysis of variance in experimental design with nonnormal error distributions,” COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, pp. 1335–1352, 2001, Accessed: 00, 2020. [Online]. Available: