Wang, Qiyao
(2017)
TWO-SAMPLE INFERENCE AND CHANGE POINT DETECTION FOR SPARSE FUNCTIONAL DATA.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
With recent advances in technology, functional-type data is arising fast in a number of fields, including finance, physics, meteorology, public health, and information technology. Driven by explosive needs in real practice, statistical methods for functional data have bee developed quickly in recent decades. There are two typical types of functional data which possess different features and require different sets of techniques to model. One is called dense functional data, where for
each random subject there are a large number of regularly-spaced observations. Dense functional data has been relatively well studied in terms of modeling, estimation and inference. The second one is called sparse functional data, where only a few irregularly-spaced observations are attainable for each subject. Statistical methods for sparse functional data are of less development, despite the importance and demand for these methods. In this thesis, we focus on three topics within the field of sparse functional data inference: two-sample inference of mean functions of two independent groups of functional data, one-way functional ANOVA (FANOVA), and change point detection in mean functions for sparse functional time series.
For each of the three topics mentioned above, methods for dense functional data are firstly reviewed. It helps us to understand why or why not each of these methods is applicable to sparse functional data situations. For the two-sample mean function testing problem and one-way functional ANOVA, we develop asymptotic chi-square tests for detecting differences among mean functions when sparse and irregular observations are drawn from the underlying stochastic processes for each subject. For the change point detection in a sequence of functional samples, we create two test procedures whose asymptotic distributions are related to a summation of independent
Brownian Bridge squares. We provide theoretical arguments to justify the validity of the proposed tests. Numerical experiments, including simulation studies and applications to a CD4 count data set and two eBay online auction data sets, are presented to demonstrate the good performances of the proposed test procedures.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
28 September 2017 |
| Date Type: |
Publication |
| Defense Date: |
24 May 2017 |
| Approval Date: |
28 September 2017 |
| Submission Date: |
23 August 2017 |
| Access Restriction: |
2 year -- Restrict access to University of Pittsburgh for a period of 2 years. |
| Number of Pages: |
116 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Statistics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
mean function, shrinkage estimator, sparse design, functional time series, asymptotic distribution, CD4 count, eBay auction |
| Date Deposited: |
29 Sep 2017 01:08 |
| Last Modified: |
29 Sep 2019 05:15 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/33131 |
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