مقارنة المقدرات اللا معلمية لتقدير دوال الكثافة الاحتمالية == Comparing Nonparametric Estimators For Probability Density Estimation
Author name:
مناف يوسف حمود
Supervisor name:
ظافر حسين رشيد النجار
General topic:
Administration and Economics
Specific topic:
Statistics
Degree:
Doctorate
University:
University of Baghdad - Faculty Of Administration And Economics - Department Of Statistics
Language:
Arabic
University location:
Baghdad
First pages:
07T447 - p.pdf
Abstract:
ان المسالة المهمة والرئيسة في التطبيقات الاحصائية تتمثل بمعرفة التوزيع الخاص بالمجتمع المطلوب دراسته ومعرفة خصائص ذلك المجتمع كي يتم تمثيل المجتمع تمثيلا سليما من خلال استعمال الاساليب الاحصائية الشائعة.في بعض مسائل الاستدلال الاحصائي المدروسة يتم افتراض | In some problems of statistical inference considered, we assumed that the distribution of random variable being sampled is known except, perhaps for some parameters.In practice, however, the functional form of the distribution is seldom, if ever, known. It is therefore desirable to devise some procedures that are free of or depending on few information or assumption concerning distribution.In this dissertation we demonstrate and study some procedures that are commonly referred to as nonparametric or distribution - free and also semiparametric methods.The term “Distribution - free” refers to to the fact that no assumption are made about the underlying distribution except that the distribution function is absolutely continuous.The term “Nonparametric” refers to the fact that there are no parameters involved in the traditional sense of term parameter used thus far.The term “Semiparametric” refers to combine the parametric term with nonparametric term, which there is few information or assumption about the distribution function.In chapter one we demonstrate an introduction to the problem, the main of the study and the historical review.In chapter two we demonstrate several nonparametric and semiparametric estimators for probability density function and these estimators are “fixed kernel which use fixed bandwidth or smoothing parameter, variable kernel which use variable bandwidth for each observation, semiparametric estimator which combine between two estimators {parametric by using of MLE and nonparametric estimator by using of fixed kernel}”.Beside these estimators we suggest four estimators like semiparametric estimator but the first suggestion combine MLE & variable kernel, the second suggestion combine two nonparametric estimators, the third suggestion combine robust estimator (for the mean & variance) with fixed kernel estimator, Finally we suggest estimator that combine robust estimator with variable kernel.Beside to above we demonstrate several estimators for smoothing parameter or bandwidth one of these estimators suggested from the author.Then we make a comparison between the parametric, nonparametric and semiparametric estimators with respect to bandwidth estimators by using simulation experiments, depending on different distributions (Normal, Lognormal and bimodal), different sample sizes and variances.We find that the best estimator for the density function is the first semiparametric estimator when we are using the 1st & 2nd distributions (Normal & Lognormal) except in few cases where we find the 1st suggested estimator is the best. And when we are using the 3rd distribution (Bimodal) we find that, the 2nd suggested estimator (Nonparametric estimator) are the best except in few cases where the other suggested estimators beside to 1st semiparametric estimator are the best.Also we find that the (BCV) estimator is the best estimator for the smoothing parameter when we are using the 1st distribution (Normal), except in few cases where the OS estimator is the best for h.For the 2nd distribution (Lognormal) we find the (LSCV) estimator is the best estimator for the smoothing parameter.Finally, For the 3rd distribution (Bimodal), We find that the (BCV) estimator is the best estimator for h except when the sample size equal to 100 (n=100), where the (DPI) estimator is the best.
