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.

The mixed effects model is one of the powerful statistical approaches used to model the relationship between the response variable and some predictors in analyzing data with a hierarchical structure. The ESTIMATION of parameters in these models is often done following either the least squares error or MAXIMUM LIKELIHOOD approaches. The estimated parameters obtained either through the least squares error or the MAXIMUM LIKELIHOOD approaches are inefficient, while the error distributions are non-normal. In such cases, the mixed effects quantile regression can be used. Moreover, when the number of variables studied increases, the PENALIZED mixed effects quantile regression is one of the best methods to gain prediction accuracy and the model's interpretability. In this paper, under the assumption of an asymmetric Laplace distribution for random effects, we proposed a double PENALIZED model in which both the random and fixed effects are independently PENALIZED. Then, the performance of this new method is evaluated in the simulation studies, and a discussion of the results is presented along with a comparison with some competing models. In addition, its application is demonstrated by analyzing a real example.

When discussing non-Gaussian spatially correlated variables, generalized linear mixed models have enough flexibility for modeling various data types. However, the MAXIMUM LIKELIHOOD methods are plagued with substantial calculations for large data sets, resulting in long waiting times for estimating the model parameters. To alleviate this drawback, composite LIKELIHOOD functions obtained from the product of the LIKELIHOODs of subsets of observations are used. The current paper uses the pairwise LIKELIHOOD method to study the parameter ESTIMATIONs of spatial generalized linear mixed models. Then, we use the weighted pairwise and PENALIZED LIKELIHOOD functions to estimate the parameters of the mentioned models. The accuracy of estimates based on these LIKELIHOOD functions is evaluated and compared with full LIKELIHOOD function-based ESTIMATION using simulation studies. Based on our results, the PENALIZED LIKELIHOOD function improved parameter ESTIMATION. Prediction using PENALIZED LIKELIHOOD functions is applied. Ultimately, pairwise and PENALIZED pairwise LIKELIHOOD methods are applied to analyze count real data sets.

In this research, the generalized MAXIMUM LIKELIHOOD estimator (GMLE) is used to investigate the parameters ESTIMATION for weighted distributions. There exist situations where the random sample from the population of interest is not available due to the data having unequal probabilities of entering the sample. The method of weighted distributions models the certainty of the probabilities of the events as observed and recorded. It is shown that if the mechanism of sample selection is known up to one unknown parameter, the MAXIMUM LIKELIHOOD estimator (MLE) would be unidentifiable when the conjugate weight function is used. This problem is solved by addition of a prior distribution on model parameters yielding the GMLEs which are identifiable. We also propose the GMLEs for negative exponential, normal and Poisson weighted distributions when MLEs are unidentifiable.

Background: Cancer is the second leading cause of death globally, and it was responsible for almost 9. 6 million deaths in 2018. Breast cancer (BC) is the most common cancer among women with almost two million new cases worldwide in 2018. Thus, it is necessary to study new methods to estimate the survival predictive factors in BC patients. Objectives: This cohort study aimed to fit a Cox model to BC data using partial LIKELIHOOD (PL) and new MAXIMUM PENALIZED LIKELIHOOD (MPL) methods in order to determine the predictive factors of survival time and compare the accuracy of these two methods. Methods: This prospective cohort study used the data of 356 women with BC registered at the Cancer Research Center of Shahid Beheshti University of Medical Sciences in Tehran, Iran. The patients were identified from 1999 to 2015. The Cox model by new MPL and PL methods was used with variables such as the stage of cancer, tumor grade, estrogen receptor, and several other variables for univariate and multiple analyses. Results: The mean age  standard deviation (SD) of patients at diagnosis was about 48  11. 27 years ranging from 24 to 84 years. Using the new MPL method, in addition to lymphovascular invasion and recurrence variables, estrogen receptor (P = 0. 045) also had a statistically significant relationship with survival. The standard errors of most variables were smaller when using the MLP method than the PL method. The overall one-year, two-year, five-year, and 10-year survival rates based on the baseline hazard estimate were 96%, 92%, 70%, and 51%, respectively. Conclusions: In the analysis of BC data, new MPL method can help identify the factors that affect the survival of patients more accurately than usual methods do. This method decreases the standard error of most variables and can be applied for identifying predictive factors more accurately than previous methods.

This study presents a Pseudo noise sequence (PN) ESTIMATION algorithm using MAXIMUM LIKELIHOOD method in low signal to noise ratio. The received signal samples are divided into temporal segments. Then correlation matrix is computed for eigenvalue ESTIMATION. Eigenvector related to largest eigenvalue of this matrix is chosen and de-noised by stationary wavelet transform to find asynchronous of sequence and chip rate. The ESTIMATION of PN sequence, is found through a MAXIMUM LIKELIHOOD algorithm for delay ESTIMATION and interpolation filter. Simulation results are applied to evaluate the proposed method and compare with previous methods in terms of computational complexity and accuracy of the chip rate and the PN ESTIMATION. Furthermore, minimum number of required samples are investigated for true ESTIMATION accuracy measurement. The results indicated that, the proposed method presented 13% better accuracy of PN sequence ESTIMATION compared to other methods.