Abstract:

The models of time series often suffer from the problem of the existence of outliers ​​that accompany the data collection process for many reasons, their existence may have a significant impact on the estimation of the parameters of the studied model. Access to highly efficient estimators  is one of the most important stages of statistical analysis, And it is therefore important to choose the appropriate methods to obtain good  estimators. The aim of this research is to compare the ordinary estimators and the robust estimators of the estimation of the parameters of

Maximum likelihood estimation method, uniformly minimum variance unbiased estimation method and minimum mean square error estimation, as classical estimation procedures, are frequently used for parameter estimation in statistics, which assuming the parameter is constant , while Bayes method assuming the parameter is random variable and hence the Bayes estimator is an estimator which minimize the Bayes risk for each value the random observable and for square error lose function the Bayes estimator is the posterior mean. It is well known that the Bayesian estimation is hardly used as a parameter estimation technique due to some difficulties to finding a prior distribution.

The interest of this paper is that

Radiation therapy plays an important role in improving breast cancer cases, in order to obtain an appropriateestimate of radiation doses number given to the patient after tumor removal; some methods of nonparametric regression werecompared. The Kernel method was used by Nadaraya-Watson estimator to find the estimation regression function forsmoothing data based on the smoothing parameter h according to the Normal scale method (NSM), Least Squared CrossValidation method (LSCV) and Golden Rate Method (GRM). These methods were compared by simulation for samples ofthree sizes, the method (NSM) proved to be the best according to average of Mean Squares Error criterion and the method(LSCV) proved to be the best according to Average of Mean Absolu

Abstract

      In this study, we compare between the autoregressive approximations (Yule-Walker equations, Least Squares , Least Squares ( forward- backword ) and Burg’s (Geometric and Harmonic ) methods, to determine the optimal approximation to the time series generated from the first - order moving Average non-invertible process, and fractionally - integrated noise process, with several values for d (d=0.15,0.25,0.35,0.45) for different sample sizes (small,median,large)for two processes . We depend on figure of merit function which proposed by author Shibata in 1980, to determine the theoretical optimal order according to min

In this paper an estimator of reliability function for the pareto dist. Of the first kind has been derived and then a simulation approach by Monte-Calro method was made to compare the Bayers estimator of reliability function and the maximum likelihood estimator for this function. It has been found that the Bayes. estimator was better than maximum likelihood estimator for all sample sizes using Integral mean square error(IMSE).

Generally, statistical methods are used in various fields of science, especially in the research field, in which Statistical analysis is carried out by adopting several techniques, according to the nature of the study and its objectives. One of these techniques is building statistical models, which is done through regression models. This technique is considered one of the most important statistical methods for studying the relationship between a dependent variable, also called (the response variable) and the other variables, called covariate variables. This research describes the estimation of the partial linear regression model, as well as the estimation of the “missing at random” values (MAR). Regarding the

The logistic regression model is an important statistical model showing the relationship between the binary variable and the explanatory variables.                                                        The large number of explanations that are usually used to illustrate the response led to the emergence of the problem of linear multiplicity between the explanatory variables that make estimating the parameters of the model not accurate.    

Recently Genetic Algorithms (GAs) have frequently been used for optimizing the solution of estimation problems. One of the main advantages of using these techniques is that they require no knowledge or gradient information about the response surface. The poor behavior of genetic algorithms in some problems, sometimes attributed to design operators, has led to the development of other types of algorithms. One such class of these algorithms is compact Genetic Algorithm (cGA), it dramatically reduces the number of bits reqyuired to store the poulation and has a faster convergence speed. In this paper compact Genetic Algorithm is used to optimize the maximum likelihood estimator of the first order moving avergae model MA(1). Simulation results

Purpose: The research aims to estimate models representing phenomena that follow the logic of circular (angular) data, accounting for the 24-hour periodicity in measurement. Theoretical framework: The regression model is developed to account for the periodic nature of the circular scale, considering the periodicity in the dependent variable y, the explanatory variables x, or both. Design/methodology/approach: Two estimation methods were applied: a parametric model, represented by the Simple Circular Regression (SCR) model, and a nonparametric model, represented by the Nadaraya-Watson Circular Regression (NW) model. The analysis used real data from 50 patients at Al-Kindi Teaching Hospital in Baghdad. Findings: The Mean Circular Erro