The estimation of the parameters of linear regression is based on the usual Least Square method, as this method is based on the estimation of several basic assumptions. Therefore, the accuracy of estimating the parameters of the model depends on the validity of these hypotheses. The most successful technique was the robust estimation method which is minimizing maximum likelihood estimator (MM-estimator) that proved its efficiency in this purpose. However, the use of the model becomes unrealistic and one of these assumptions is the uniformity of the variance and the normal distribution of the error. These assumptions are not achievable in the case of studying a specific problem that may include complex data of more than one model. To

This Book is the second edition that intended to be textbook studied for undergraduate/ postgraduate course in mathematical statistics. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces events and probability review. Chapter Two devotes to random variables in their two types: discrete and continuous with definitions of probability mass function, probability density function and cumulative distribution function as well. Chapter Three discusses mathematical expectation with its special types such as: moments, moment generating function and other related topics. Chapter Four deals with some special discrete distributions: (Discrete Uniform, Bernoulli, Binomial, Poisson, Geometric, Neg

Intended for getting good estimates with more accurate results, we must choose the appropriate method of estimation. Most of the equations in classical methods are linear equations and finding analytical solutions to such equations is very difficult. Some estimators are inefficient because of problems in solving these equations. In this paper, we will estimate the survival function of censored data by using one of the most important artificial intelligence algorithms that is called the genetic algorithm to get optimal estimates for parameters Weibull distribution with two parameters. This leads to optimal estimates of the survival function. The genetic algorithm is employed in the method of moment, the least squares method and the weighted

The aim of this paper is to estimate a nonlinear regression function of the Export of the crude oil Saudi (in Million Barrels) as a function of the number of discovered fields.

 Through studying the behavior of the data we show that its behavior was not followed a linear pattern or can put it in a known form so far there was no possibility to see a general trend resulting from such exports.

We use different nonlinear estimators to estimate a regression function, Local linear estimator, Semi-parametric as well as an artificial neural network estimator (ANN).

The results proved that the (ANN) estimator is the best nonlinear estimator am

This paper is specifically a detailed review of the Spatial Quantile Autoregressive (SARQR) model that refers to the incorporation of quantile regression models into spatial autoregressive models to facilitate an improved analysis of the characteristics of spatially dependent data. The relevance of SARQR is emphasized in most applications, including but not limited to the fields that might need the study of spatial variation and dependencies. In particular, it looks at literature dated from 1971 and 2024 and shows the extent to which SARQR had already been applied previously in other disciplines such as economics, real estate, environmental science, and epidemiology. Accordingly, evidence indicates SARQR has numerous benefits compar

              The current paper proposes a new estimator for the linear regression model parameters under Big Data circumstances.  From the diversity of Big Data variables comes many challenges that  can be interesting to the  researchers who try their best to find new and novel methods to estimate the parameters of linear regression model. Data has been collected by Central Statistical Organization IRAQ, and the child labor in Iraq has been chosen as data. Child labor is the most vital phenomena that both society and education are suffering from and it affects the future of our next generation. Two methods have been selected to estimate the parameter

Factor analysis is distinguished by its ability to shorten and arrange many variables in a small number of linear components. In this research, we will study the essential variables that affect the Coronavirus disease 2019 (COVID-19), which is supposed to contribute to the diagnosis of each patient group based on linear measurements of the disease and determine the method of treatment with application data for (600) patients registered in General AL-KARAMA Hospital in Baghdad from 1/4/2020 to 15/7/2020. The explanation of the variances from the total variance of each factor separately was obtained with six elements, which together explained 69.266% of the measure's variability. The most important variable are cough, idleness, fever, headach

In this paper, we derived an estimators and parameters of Reliability and Hazard function of new mix distribution ( Rayleigh- Logarithmic) with two parameters and increasing failure rate using Bayes Method with Square Error Loss function and Jeffery and conditional probability random variable of observation. The main objective of this study is to find the efficiency of the derived of Bayesian estimator compared to the to the Maximum Likelihood of this function using Simulation technique by Monte Carlo method under different Rayleigh- Logarithmic parameter and sample sizes. The consequences have shown that Bayes estimator has been more efficient than the maximum likelihood estimator in all sample sizes with application

In this paper, previous studies about Fuzzy regression had been presented. The fuzzy regression is a generalization of the traditional regression model that formulates a fuzzy environment's relationship to independent and dependent variables. All this can be introduced by non-parametric model, as well as a semi-parametric model. Moreover, results obtained from the previous studies and their conclusions were put forward in this context. So, we suggest a novel method of estimation via new weights instead of the old weights and introduce

Paper Type: Review article.

another suggestion based on artificial neural networks.

يعتبر الخزين من الامور الهامة في العديد من الشركات حيث يمثل نسبة 50 % من رأس مال المستثمر الكلي مع شدة الضغط المتمثل الى خفض التكاليف الكلية المتمثلة مع انواع اخرى من حالات عدم التأكد (الضبابية) لذا سوف نقدم في هذا البحث نظام اقتصادي للكميات الكلية ( الانتاج الاقتصادي للكميات) للوصول حجم الدفعة المثلى المضببة (FEOQ) عندما تكون كل المعالم في حالة عدم التأكد حيث يتم تحويلها الى فترة واحدة وبعد ذلك الحصول على حجم الد

In this research , we study the inverse Gompertz distribution (IG) and estimate the  survival function of the distribution , and the survival function was evaluated using three methods (the Maximum likelihood, least squares, and percentiles estimators) and choosing the best method estimation ,as it was found that the best method for estimating the survival function is the squares-least method because it has the lowest IMSE and for all sample sizes

Abstract

       There are many uncertainty sources that may affect the statistical reasoning. However, traditional methods can not deal with all kinds of uncertainty sources, which has led many researchers to develop traditional methods. Studies still exist to this day, making hypotheses to create a common understanding for the purpose of reaching new solutions through the use of new methods that combine traditional and modern theories of sources of uncertainty

       The aim of current study was to develop the adaptive fuzzy linear regression model in the case of using inaccurate data as the source of uncertainty. Specifically, the

In this paper, the error distribution function is estimated for the single index model by the empirical distribution function and the kernel distribution function. Refined minimum average variance estimation (RMAVE) method is used for estimating single index model. We use simulation experiments to compare the two estimation methods for error distribution function with different sample sizes, the results show that the kernel distribution function is better than the empirical distribution function.

As the process of  estimate for model and variable selection significant is a crucial process in the semi-parametric modeling At the beginning of the modeling process often At there are many explanatory variables to Avoid the loss of any explanatory elements may be important as a result , the selection of significant variables become necessary , so the process of variable selection is not intended to simplifying  model complexity explanation , and also predicting. In this research was to use some of the semi-parametric methods (LASSO-MAVE , MAVE and The proposal method (Adaptive LASSO-MAVE) for variable selection and estimate semi-parametric single index model (SSIM) at the same time .

It is considered as one of the statistical methods used to describe and estimate the relationship between randomness (Y) and explanatory variables (X). The second is the homogeneity of the variance, in which the dependent variable is a binary response takes two values  (One when a specific event occurred and zero when that event did not happen) such as (injured and uninjured, married and unmarried) and that a large number of explanatory variables led to the emergence of the problem of linear multiplicity that makes the estimates inaccurate, and the method of greatest possibility and the method of declination of the letter was used in estimating A double-response logistic regression model by adopting the Jackna

It is often needed in demographic research to modern statistical tools are flexible and convenient to keep up with the type of data available in Iraq in terms of the passage of the country far from periods of war and economic sanctions and instability of the security for a period of time . So, This research aims to propose the use of style nonparametric splines as a substitute for some of the compounds of analysis within the model Lee-Carter your appreciation rate for fertility detailed variable response in Iraq than the period (1977 - 2011) , and then predict for the period (2012-2031). This goal was achieved using a style nonparametric decomposition of singular value vehicles using the main deltoid , and then estimate the effect of time-s

Recently, the financial mathematics has been emerged to interpret and predict the underlying mechanism that generates an incident of concern. A system of differential equations can reveal a dynamical development of financial mechanism across time. Multivariate wiener process represents the stochastic term in a system of stochastic differential equations (SDE). The standard wiener process follows a Markov chain, and hence it is a martingale (kind of Markov chain), which is a good integrator. Though, the fractional Wiener process does not follow a Markov chain, hence it is not a good integrator. This problem will produce an Arbitrage (non-equilibrium in the market) in the predicted series. It is undesired property that leads to erroneous conc

This paper deals with, Bayesian estimation of the parameters of Gamma distribution under Generalized Weighted loss function, based on Gamma and Exponential priors for the shape and scale parameters, respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared in terms of the mean squared errors (MSE’s).

Statistical methods of forecasting have applied with the intention of constructing a model to predict the number of the old aged people in retirement homes in Iraq. They were based on the monthly data of old aged people in Baghdad and the governorates except for the Kurdistan region from 2016 to 2019. Using BoxJenkins methodology, the stationarity of the series was examined. The appropriate model order was determined, the parameters were estimated, the significance was tested, adequacy of the model was checked, and then the best model of prediction was used. The best model for forecasting according to criteria of (Normalized BIC, MAPE, RMSE) is ARIMA (0, 1, 2)

In this paper has been building a statistical model of the Saudi financial market using GARCH models that take into account Volatility in prices during periods of circulation, were also study the effect of the type of random error distribution of the time series on the accuracy of the statistical model, as it were studied two types of statistical distributions are normal distribution and the T distribution. and found by application of a measured data that the best model for the Saudi market is GARCH (1,1) model when the random error distributed t. student's .

Nonparametric methods are used in the data that contain outliers values. The main importance in using Nonparametric methods is to locate the median in the multivariate regression model. It is difficult to locate the median due to the presence of more than one dimension and the dispersion of values and the increase of the studied phenomenon data.The genetic algorithms Minimum Weighted Covariance Determinant Estimator (MWCD), was applied and compared with the multilayer neural network Back propagation to find the estimate of the median location based on the minimum distance (Mahalanobis Distance) and smallest specified for the variance matrix. Joint Minimum Covariance Determinant (MCD) as one of the most nonparametric methods robust. The stud

Generalized Additive Model has been considered as a multivariate smoother that appeared recently in Nonparametric Regression Analysis. Thus, this research is devoted to study the mixed situation, i.e. for the phenomena that changes its behaviour from linear (with known functional form) represented in parametric part, to nonlinear (with unknown functional form: here, smoothing spline) represented in nonparametric part of the model. Furthermore, we propose robust semiparametric GAM estimator, which compared with two other existed techniques.

تم إستعراض تقدير معلمتي التوزيع اللوجستي بإستعمال طريقة ذات مقدرات مضبوطة وهي طريقة العزوم، ومقارنتها بمقدرات تقريبية مأخوذة بالأساس من أسلوب طريقة (وايت) في التقدير بأعتبار التوزيع اللوجستي من التوزيعات الأحتمالية الأسية، وهي كل من طريقة المربعات الصغرى الأعتيادية، وطريقة أنحدار الحرف، وأقتراح تطبيق طريقة أنحدار الحرف المعدلة على هذا التوزيع. وتم أستحصال النتائج بالأستناد الى تجارب محاكاة لتلك الطر

النموذج التجميعي المعمّم GAM من الممهدات متعددة المتغيرات حديثة الأستعمال في تحليل الأنحدار اللامعلمي، ولذا تم تكريس هذا البحث لدراسته ولكن بالصيغة الهجينة،أي عند للظاهرة التي تغير سلوكها من خطي ذات شكل دالي مسبق (معلمي)، ولاخطي بشكل غير معلوم (لامعلمي) والذي سيكون هنا الشريحة التمهيدية. هذا، بالأضافة الى تقديم مقترح لأيجاد مقدّر GAM شبه معلمي حصين ومقارنته بأسلوب تكراري وآخر غير تكراري.

ان الهدف من الدراسة هو بيان القدرة التنبؤية الافضل بين انموذج الانحدار اللوجستي والدالة المميزة الخطية باستعمال البيانات الاصليه اولا ثم المركبات الرئيسة لتقليص الابعاد بين المتغيرات لبيانات المسح الاجتماعي والاقتصادي للاسرة لمحافظة بغداد لعام 2012 وتضمنت عينة البحث 615 مفردة لـ13 متغير، 12منها متغير توضيحي والمتغير المعتمد شمل العاملين والعاطلين عن العمل، تم اجراء المقارنة بين الطريقتين اعلاه واتضح من خلال

فًي التحلٌيل اإلحصائ،ً حٌث تعتبر طرٌمة انحدار شرائح تلعب تمنٌات تحلٌل االنحدار الالمعلمً دوراً مركزٌاً لتمهٌد البٌانات، اذ ٌمكن من خاللها تمدٌر الدوال مباشرة من الجزاء واحدة من أكثر الطرائك المستعملة حالٌاً ( بدالً ة البٌانات الصاخبة)التً تحتوي على أخطاء( أو الملوثة )data noisy من االعتماد على نماذج معلمٌ محددة، وتعتمد طرٌمة التمدٌر المستعملة لمالئمه نموذج انحدار شرائح الجزاء فً الغالب على طرائك المربعات الصغر

In this paper, the Monte-Carlo simulation method was used to compare the robust circular S estimator with the circular Least squares method in the case of no outlier data and in the case of the presence of an outlier in the data through two trends, the first is contaminant with high inflection points that represents contaminant in the circular independent variable, and the second the contaminant in the vertical variable that represents the circular dependent variable using three comparison criteria, the median standard error (Median SE), the median of the mean squares of error (Median MSE), and the median of the mean cosines of the circular residuals (Median A(k)). It was concluded that the method of least squares is better than the

In this paper we proposed a new method for selecting a smoothing parameter in kernel estimator to estimate a nonparametric regression function in the presence of missing values. The proposed method is based on work on the golden ratio and Surah AL-E-Imran in the Qur'an. Simulation experiments were conducted to study a small sample behavior. The results proved the superiority the proposed on the competition method for selecting smoothing parameter.