I am a math lover. This is one of the research I kept working for the past three years. The essence of this work is to claim that the existing regression methods in analyzing a trunacted normal dependent variable all suffer from a critical methodological problem--boundary violations. This problem happens when a predicted value of the dependent variable falls outside the admissible range. For instance, our models predicts that a party has a vote share greater than 100% or less than 0% (a vote share should range from 0% to 100%). By applying the method of constrained optimization, I successully solve this problem for the trunacted regression model. My new method can always find the best admissible solution without suffering from boundary violations.
I realize that my claim is very provocative and some political methodologists might feel offended by this paper. Given the fact that I make no effort to earn academic credit, you can simply ignore my work if you feel offended or believe I am plainly wrong. On the other hand, I am very happy to discuss the detail of this work to whoever is interested and also welcome any feedback. My only purpose is to improve this work and spread out the idea if my claim is tenable.