Modified Functional Principal Component Regression Öffentlichkeit

Abstract

Using simulated temperature data as a proof of concept, we present a novel approach to prediction via the development and application of Modified Functional Principal Component Regression (MFPCR). By employing bivariate splines over triangulations in a functional linear regression model, this study offers a proof of concept for the modified approach that include additional data to improve the Function Principal Component Regression (FPCR). The mock temperature prediction problem has few complexities and clear influencing factors. Our comparative analysis of MFPCR and FPCR reveals insights into predictive accuracy, uncertainty quantification, and the spatial distribution of functional data, setting the stage for more precise neighborhood-level forecasting in future investigations. 

Table of Contents

1 Abstract 2

2 Introduction and Background 2

3 Modified Functional Principal Component Regression 5

3.1 Autoregressive Process........................ 6

3.2 Computational Method Outline: .................. 8

4 Simulated Temperature Data 9

4.1 Constructing a Temperature Data Set ............... 10

4.2 Topological Features ......................... 10

4.3 North-South Effect.......................... 10

4.4 Hourly Variation ........................... 10

4.5 Seasonality .............................. 11

4.6 Adding Noise to the Signal ..................... 12

4.7 Combining the Features to Generate the Data. . . . . . . . . . . 12

5 Simulated Temperature Experiments 13

5.1 Fixed and Adjusted Attributes of the Simulations . . . . . . . . . 13

5.2 Principal Component Analysis ................... 14

5.3 Assessing the Prediction Function through MSE Comparison Amongst Adjusted Attributes ......................... 17

5.3.1 Base Case: Mountain Valley................. 18

5.3.2 Altered Input Function ................... 19

5.3.3 Weight Adjustments ..................... 19

5.3.4 Noise ............................. 19

5.3.5 Number of Eigenvalues.................... 20

5.3.6 Overall MSE Comparison .................. 20

6 Comparing the Predictions 21

6.1 MFPCR vs. FPCR.......................... 22

6.2 Comparing Prediction Functions with Updated Station Data . . 22

7 Conclusion and Extension to the Ground-Level Ozone Application 25 

About this Honors Thesis

Rights statement

• Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.

School	Emory College
Department	Mathematics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Applied Mathematics
Stichwort	Ground-Level Ozone Functional Data Analysis Principal Component Analysis
Committee Chair / Thesis Advisor	Bree Ettinger, Emory University
Committee Members	Shomu Banerjee, Emory University Talea Mayo, Emory University Julianne Chung, Emory University

Zuletzt geändert

Primary PDF

Thumbnail	Title	Date Uploaded	Actions
	Modified Functional Principal Component Regression ()	2024-04-14 14:26:19 -0400	Press to Select an action Download

Supplemental Files

Thumbnail	Title	Date Uploaded	Actions