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Alternative Approaches to Significant Zero Crossings (SiZer) Method for Feature Detection in Non-Parametric Univariate Kernel Density Estimation

Title:

Alternative Approaches to Significant Zero Crossings (SiZer) Method for Feature Detection in Non-Parametric Univariate Kernel Density Estimation

Semerdjiev, Boyan (2014) Alternative Approaches to Significant Zero Crossings (SiZer) Method for Feature Detection in Non-Parametric Univariate Kernel Density Estimation. Masters thesis, Concordia University.

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Abstract

This work presents several methods for feature detection in density estimation of univariate data. Two versions of the original Significant Zero Crossings for Derivatives (SiZer) method and two other SiZer approaches for signal detection with Euler and Hadwiger characteristics are explored. The latter are based on approximating level-crossing probabilities by expected number of upcrossings. In addition, a method for two-sample density comparison is proposed, based on the discussed SiZer methodologies. Estimating a single best bandwidth parameter value is difficult. Therefore, all signal detection and comparison approaches utilize the concept of scale-space and color maps, allowing consideration of curve smoothing at multiple bandwidth levels simultaneously. Finally, the proposed methodologies do not compete and are therefore not compared. Instead, they complement each other and combining the observations from all of them together allows for better statistical inference of the data set.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Semerdjiev, Boyan
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:July 2014
Thesis Supervisor(s):Sen, Arusharka
ID Code:978804
Deposited By: BOYAN SEMERDJIEV
Deposited On:11 Nov 2014 15:31
Last Modified:18 Jan 2018 17:47
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