Analysis of variance and linear contrasts in experimental design with generalized secant hyperbolic distribution

Date

2008-07-01

Author

Yilmaz, Yidiz E.
Akkaya, Ayşen

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

232
views

0
downloads

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 methodology readily extends to unbalanced designs.

Subject Keywords

Applied Mathematics, Computational Mathematics

URI

https://hdl.handle.net/11511/41631

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/j.cam.2007.06.001

Collections

Department of Statistics, Article

Suggestions

OpenMETU
Core

Dynamic programming for a Markov-switching jump-diffusion Azevedo, N.; Pinheiro, D.; Weber, Gerhard Wilhelm (Elsevier BV, 2014-09-01) We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman's optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton-Jacobi-Belman equation, which turns out to be a partial in...
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.
Estimation in bivariate nonnormal distributions with stochastic variance functions Tiku, Moti L.; İslam, Muhammed Qamarul; SAZAK, HAKAN SAVAŞ (Elsevier BV, 2008-01-01) Data sets in numerous areas of application can be modelled by symmetric bivariate nonnormal distributions. Estimation of parameters in such situations is considered when the mean and variance of one variable is a linear and a positive function of the other variable. This is typically true of bivariate t distribution. The resulting estimators are found to be remarkably efficient. Hypothesis testing procedures are developed and shown to be robust and powerful. Real life examples are given.
Accurate numerical bounds for the spectral points of singular Sturm-Liouville problems over 0 < x < infinity Taşeli, Hasan (Elsevier BV, 2004-03-01) The eigenvalues of singular Sturm-Liouville problems defined over the semi-infinite positive real axis are examined on a truncated interval 0<x<l as functions of the boundary point l. As a basic theoretical result, it is shown that the eigenvalues of the truncated interval problems satisfying Dirichlet and Neumann boundary conditions provide, respectively, upper and lower bounds to the eigenvalues of the original problem. Moreover, the unperturbed system in a perturbation problem, where l remains sufficient...
A model for the computation of quantum billiards with arbitrary shapes Erhan, Inci M.; Taşeli, Hasan (Elsevier BV, 2006-10-01) An expansion method for the stationary Schrodinger equation of a three-dimensional quantum billiard system whose boundary is defined by an arbitrary analytic function is introduced. The method is based on a coordinate transformation and an expansion in spherical harmonics. The effectiveness is verified and confirmed by a numerical example, which is a billiard system depending on a parameter.

Citation Formats

Y. E. Yilmaz and A. Akkaya, “Analysis of variance and linear contrasts in experimental design with generalized secant hyperbolic distribution,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 545–553, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41631.