Estimation in bivariate nonnormal distributions with stochastic variance functions

Tiku, Moti L.
İslam, Muhammed Qamarul
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.


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.
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...
Derivative free multilevel optimization methods
Pekmen, Bengisen; Karasözen, Bülent; Department of Scientific Computing (2009)
Derivative free optimization algorithms are implementations of trust region based derivative-free methods using multivariate polynomial interpolation. These are designed to minimize smooth functions whose derivatives are not available or costly to compute. The trust region based multilevel optimization algorithms for solving large scale unconstrained optimization problems resulting by discretization of partial differential equations (PDEs), make use of different discretization levels to reduce the computati...
Image segmentation and smoothing via partial differential equations
Özmen, Neslihan; Leblebicioğlu, Mehmet Kemal; Department of Scientific Computing (2009)
In image processing, partial differential equation (PDE) based approaches have been extensively used in segmentation and smoothing applications. The Perona-Malik nonlinear diffusion model is the first PDE based method used in the image smoothing tasks. Afterwards the classical Mumford-Shah model was developed to solve both image segmentation and smoothing problems and it is based on the minimization of an energy functional. It has numerous application areas such as edge detection, motion analysis, medical i...
Manguoğlu, Murat; Sameh, Ahmed H.; Grama, Ananth (Society for Industrial & Applied Mathematics (SIAM), 2010-01-01)
The emergence of multicore architectures and highly scalable platforms motivates the development of novel algorithms and techniques that emphasize concurrency and are tolerant of deep memory hierarchies, as opposed to minimizing raw FLOP counts. While direct solvers are reliable, they are often slow and memory-intensive for large problems. Iterative solvers, on the other hand, are more efficient but, in the absence of robust preconditioners, lack reliability. While preconditioners based on incomplete factor...
Citation Formats
M. L. Tiku, M. Q. İslam, and H. S. SAZAK, “Estimation in bivariate nonnormal distributions with stochastic variance functions,” COMPUTATIONAL STATISTICS & DATA ANALYSIS, pp. 1728–1745, 2008, Accessed: 00, 2020. [Online]. Available: