We consider the problem of inference about skewness parameter in skew-normal distribution and it's difficulties. An approximately maximum likelihood estimator that is based on some prior information is proposed. Finally the efficiency of proposed estimator is assessed both theoretically and by a simulation study.

In this article, we study parameter estimation of the logarithmic series distribution. A well-known method of estimation is the maximum likelihood estimate (MLE) and this method for this distribution resulted in a biased estimator for the small sample size datasets. The goal here is to reduce the bias and root mean square error of MLE of the unknown parameter. Employing the Cox and Snell method, a closed-form expression for the bias-reduction of the maximum likelihood estimator of the parameter is obtained. Moreover, the parametric Bootstrap bias correction of the maximum likelihood estimator is studied. The performance of the proposed estimators is investigated via Monte Carlo simulation studies. The numerical results show that the analytical bias-corrected estimator performs better than bootstrapped-based estimator and MLE for small sample sizes. Also, certain useful characterizations of this distribution are presented. An example via a real dataset is presented for the illustrative purposes.

This paper presents a new estimator for the speech enhancement using codebook. Codebook-based speech enhancement method separates the noise and speech from each other and synthesizes the enhanced speech signal by optimally selecting the speech codebook indexes. This method can enhance the noisy speech with signal to noise ratio of less than zero decibel. In this method it is very important to select the correct codebook indexes. Therefore, in this paper, the maximum likelihood estimator is proposed for speech and noise by applying auditory quality-enhancing weights. The relation of this estimator is also used as a distance function in the design of codebooks. This method is simulated for different speakers and noises. The results show the proposed maximum likelihood estimator leads to better speech enhancement than the euclidean distance estimator. The proposed method is also more successful in dealing with non-stationary or stationary noises and negative or positive SNRs than other methods. The cost of the superior quality enhancement in this method is the requirement to a relatively time-consuming signal processing.

In this paper, we first introduce semi-parametric heteroscedastic hierarchical models. Then, we define a new version of the empirical likelihood function (Restricted Joint Empirical likelihood) and use it to obtain the shrinkage estimators of the models' parameters in these models. Under different assumptions, a simulation study investigates the better performance of the restricted joint empirical likelihood function in the analysis of semi-parametric heterogeneity hierarchical models. Furthermore, we analyze an actual data set using the RJEL method.

The paper was to reduce biased estimation using new approach (Penalized Maximum Likelihood Estimation (PMLE) Method) in Logistic Regression. For this aim, unreal four small data sets were randomly generated. Maximum Likelihood Estimation (MLE) and PMLE Methods were applied and compared for separation case including biased estimation in Logistic Regression when one of the cells in 2 x 2 tables becomes equal to zero (separation problem). Parameters1 and their standard error obtained by using MLE for four data sets were 12.56±257.8, 13.46±264.3, 13.42±210.3, and 13.41±180.4, respectively, meaning that MLE’s are biased estimates. Corresponding values for PMLE method were found 2.28 ± 1.81, 3.05 ± 1.59, 3.45 ± 1.53, and 3.45 ± 1.53, respectively, meaning that PMLE’s was unbiased estimates. It is clear that standard error value for data set 1 reduced from 257.8 to 1.81 when using PMLE method for separation problem. According to PMLE Method, the odds of being coronary heart disease risk for smokers were increased 21.08 times than that for non-smokers smoking in data set 2, which is significant at 1% level. The odds of being coronary heart disease risk for smokers were increased 31.63 times than that for non-smokers in data set 3 (P < 0.001). The odds of being coronary heart disease risk for smokers were increased 41.93 times than that for non-smokers in data set 4. When one of the cells in 2 x 2 contingency tables becomes equal to zero, PMLE was more superior to MLE Method because PMLE Method may be performed unbiased (reliable) estimation.

Directional statistics are very useful tools to model the phenomenon that are characterized by the angles. Recently, various disciplines including biology, astronomy, meteorology and bioinformatics have paid attention to use these distributions. Particularly, it was shown in biological researches that there are two pair angles describing, relatively, the complete geometrical and spatial structures of a protein in the three dimensional space. There is a distribution, called bivariate Von-Mises, to represent the position of the atoms based upon the values of these angles in a probabilistic manner. In this paper, considering an especial case of this density (cosine model), the properties of distribution including the numbers of modes and its approximation by the bivariate normal distribution are first studied. Then, to estimate the parameters using the pseudo-likelihood method is described. The theoretical materials are evaluated in simulation studies and the application of the cosine model in a real example is presented.

The present work focuses on the second order Markov chain model which arises in a variety of settings and is well-suited to be modeled in many applications. The efficiency of the maximum quasi-likelihood estimators with the full maximum likelihood estimators for second order Markov chain models are given, besides the limiting normality results on the asymptotic properties of the associated estimates. Some efficiency calculations are also given to discuss the feasibility and computational complexity of the QL approach relative to the full likelihood approach.