A Min/Max Algorithm for Spline Based Modeling of Violent Crime Rates in USA

This paper focuses on modeling violent crime rates against population over the years 1960-2014 for the United States via cubic spline based method. We propose a new min/max algorithm on knots detection and estimation for cubic spline regression. We employ least squares estimation to find potential regression coefficients based upon the cubic spline model and the knots chosen by the min/max algorithm. Wethen 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 report the $R_{adj}^{2}$ as a measure of overall goodness-of-fit of our selected model. Among the fifty states and Washington D.C., we have found 42 out of 51 with $R_{adj}^{2}$ value that was greater than $90\%$. We also present an overall model for the United States as a whole. Our method can serve as a unified model for violent crime rate over future years.