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min/max algorithm for cubic splines over kpartitions
 Date Issued:
 2012
 Summary:
 The focus of this thesis is to statistically model violent crime rates against population over the years 19602009 for the United States. We approach this question as to be of interest since the trend of population for individual states follows different patterns. We propose here a method which employs cubic spline regression modeling. First we introduce a minimum/maximum algorithm that will identify potential knots. Then we employ least squares estimation to find potential regression coefficients based upon the cubic spline model and the knots chosen by the minimum/maximum algorithm. We then utilize the best subsets regression method to aid in model selection in which we find the minimum value of the Bayesian Information Criteria. Finally, we preent the R2adj as a measure of overall goodness of fit of our selected model. We have found among the fifty states and Washington D.C., 42 out of 51 showed an R2adj value that was greater than 90%. We also present an overall model of the United States. Also, we show additional applications our algorithm for data which show a non linear association. It is hoped that our method can serve as a unified model for violent crime rate over future years.
Title:  A min/max algorithm for cubic splines over kpartitions. 
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Name(s): 
Golinko, Eric David Charles E. Schmidt College of Science Department of Mathematical Sciences 

Type of Resource:  text  
Genre:  Electronic Thesis Or Dissertation  
Date Issued:  2012  
Publisher:  Florida Atlantic University  
Physical Form:  electronic  
Extent:  viii, 62 p. : ill. (some col.)  
Language(s):  English  
Summary:  The focus of this thesis is to statistically model violent crime rates against population over the years 19602009 for the United States. We approach this question as to be of interest since the trend of population for individual states follows different patterns. We propose here a method which employs cubic spline regression modeling. First we introduce a minimum/maximum algorithm that will identify potential knots. Then we employ least squares estimation to find potential regression coefficients based upon the cubic spline model and the knots chosen by the minimum/maximum algorithm. We then utilize the best subsets regression method to aid in model selection in which we find the minimum value of the Bayesian Information Criteria. Finally, we preent the R2adj as a measure of overall goodness of fit of our selected model. We have found among the fifty states and Washington D.C., 42 out of 51 showed an R2adj value that was greater than 90%. We also present an overall model of the United States. Also, we show additional applications our algorithm for data which show a non linear association. It is hoped that our method can serve as a unified model for violent crime rate over future years.  
Identifier:  794510485 (oclc), 3342107 (digitool), FADT3342107 (IID), fau:3861 (fedora)  
Note(s): 
by Eric David Golinko. Thesis (M.S.)Florida Atlantic University, 2012. Includes bibliography. Electronic reproduction. Boca Raton, Fla., 2012. Mode of access: World Wide Web. 

Subject(s): 
Spline theory  Data processing Bayesian statistical decision theory  Data processing Neural networks (Computer science) Mathematical statistics Uncertainty (Information theory) Probabilities Regression analysis 

Persistent Link to This Record:  http://purl.flvc.org/FAU/3342107  
Use and Reproduction:  http://rightsstatements.org/vocab/InC/1.0/  
Host Institution:  FAU 