Kernel estimation of the conditional mode for fixed design models

Other Title(s)

تقدير النواة للمنوال الشرطي لنماذج التصميم الثابتة

Dissertant

al-Hartani, Dua Abd al-Rahman Khalil

Thesis advisor

Salihah, Raid Bashir Ibrahim

University

Islamic University

Faculty

Faculty of Science

Department

Department of Mathematics

University Country

Palestine (Gaza Strip)

Degree

Master

Degree Date

2017

English Abstract

We are interested in the area of nonparametric prediction, therefore, we study the relationship between a current observation and previous observations, where the conditional density function plays an important role.

In this thesis, we study the problem of estimating nonparametrically the conditional mode for fixed design models.

We suppose the error random variables are independent.

The joint asymptotic normality of the conditional mode estimator at different fixed design points is established under some regularity conditions.

We started our study by consider the mode of a sample of identically independent distributed (i.i.d.) data.

Also, we study some theoretical properties of the kernel estimator for the conditional density function.

Moreover we study some sufficient conditions under which the kernel estimation of the mode for random design models is asymptotically normally distributed.

After that we study the kernel estimation of the mode for fixed design models.

We assume that (x1, Y1),(x2, Y2), ...,(xn, Yn) are i.i.d.

random variables with conditional pdf f(y|x) where the variable Y depending upon a fixed design predictor x through a regression function m(x).

Finally, we used the proposed estimator in some applications using simulated and real data.

The results have indicated that the mode estimator has a good performance and efficiency estimator by MSE error and correlation coefficient.

Main Subjects

Mathematics

No. of Pages

84

Table of Contents

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Language

English

Data Type

Arab Theses

Record ID

BIM-901169