Estimating parameters of a multiple autoregressive model by the modified maximum likelihood method

Akkaya, Ayşen
We consider a multiple autoregressive model with non-normal error distributions, the latter being more prevalent in practice than the usually assumed normal distribution. Since the maximum likelihood equations have convergence problems (Puthenpura and Sinha, 1986) [11], we work Out modified maximum likelihood equations by expressing the maximum likelihood equations in terms of ordered residuals and linearizing intractable nonlinear functions (Tiku and Suresh, 1992) [8]. The solutions, called modified maximum estimators, are explicit functions of sample observations and therefore easy to compute. They are under some very general regularity conditions asymptotically unbiased and efficient (Vaughan and Tiku, 2000) [4]. We show that for small sample sizes, they have negligible bias and are considerably more efficient than the traditional least Squares estimators. We show that Our estimators are robust to plausible deviations from an assumed distribution and are therefore enormously advantageous as compared to the least squares estimation. We give a real life example.


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...
Counting Boolean functions with specified values in their Walsh spectrum
Uyan, Erdener; Calik, Cagdas; Doğanaksoy, Ali (Elsevier BV, 2014-03-15)
The problem of counting Boolean functions with specified number s of Walsh coefficients omega in their Walsh spectrum is discussed in this paper. Strategies to solve this problem shall help solving many more problems related to desired cryptographic features of Boolean functions such as nonlinearity, resiliency, algebraic immunity, etc. In an attempt to study this problem, we present a new framework of solutions. We give results for vertical bar omega vertical bar >= 2(n-1) and for all s, in line with a pre...
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.
Manguoğlu, Murat (Society for Industrial & Applied Mathematics (SIAM), 2019-01-01)
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with a relatively small number of negative eigenvalues. The proposed scheme consists of an outer minimum residual (MINRES) iteration, preconditioned by an inner conjugate gradient (CG) iteration in which CG can be further preconditioned. The robustness of the proposed scheme is illustrated by solving indefinite linear systems that arise in t...
Citation Formats
Ö. TÜRKER BAYRAK and A. Akkaya, “Estimating parameters of a multiple autoregressive model by the modified maximum likelihood method,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 1763–1772, 2010, Accessed: 00, 2020. [Online]. Available: