Non-uniform truncated power cubic spline density estimation on normal mixture distribution

Name: Arin Boonmeekham

LCSH: Kasetsart University -- Dissertations. Ph.D. (Statistics) 2023.

Classification :.LCCS: QA273.6

LCSH: Kasetsart University. -- Department of Statistics -- Dissertations.

LCSH: Distribution (Probability theory)

LCSH: Nonparametric statistics.

LCSH: Spline theory.

Abstract: The probability density function serves as a fundamental concept in probability theory and statistics. It plays a crucial role in various kinds of statistical research such as statistical inference, time series, decision-making, etc. The parametric density estimation assumes that the data are independent and identically distributed and follow a specific distribution with its parameter. The density is obtained by estimating the parameter. Nevertheless, when the underlying distribution is unknown, the proper method is nonparametric estimation which estimates the density directly from the sample. In this thesis, spline density estimation constructed by truncated power cubic spline basis is considered. The study aims to identify the number of knots and their locations in non-uniform space. The gradient descent algorithm for non-uniform knot placement of spline density estimation using truncated power cubic spline basis is proposed. The performance comparison of spline density estimation using non-uniform and uniform knots, and kernel density estimation with various bandwidth selections is evaluated using the average mean squared error obtained through Monte Carlo simulation. The result concludes that spline density estimation using non-uniform knots achieves better estimation results on normal mixture distribution. The analysis of the real dataset also illustrates that the truncated power cubic spline density estimation using non-uniform knots performs well.

Kasetsart University. Office of the University Library

Address: Bangkok

Email: tdckulib@ku.ac.th

Name: Thidaporn Supapakorn

Role: Thesis Advisor

Name: Juthaphorn Sinsomboonthong

Role: Thesis Co-Adviso

Created: 2023

Modified: 2025-06-25

Issued: 2025-06-25

วิทยานิพนธ์/Thesis

วิทยานิพนธ์/Thesis

application/pdf

URL: http://www.lib.ku.ac.th/KUthesis/2566/arin-boo-all.pdf

CallNumber: QA273.6.A75

eng

DegreeName: Doctor of Philosophy

Level: Doctoral Degree

Descipline: Statistics

Grantor: Kasetsart University

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