This paper is to investigate the convergence rate of asymptotic normality of frequency polygon estimation for density function under mixing random fields, which include strongly mixing condition and some weaker mixing...This paper is to investigate the convergence rate of asymptotic normality of frequency polygon estimation for density function under mixing random fields, which include strongly mixing condition and some weaker mixing conditions. A Berry-Esseen bound of frequency polygon is established and the convergence rates of asymptotic normality are derived. In particularly, for the optimal bin width , it is showed that the convergence rate of asymptotic normality reaches to ?when mixing coefficient tends to zero exponentially fast.展开更多
This paper presents a new definition of the average normal to a polygon by introducing a cone bounded by the polygon, computing its normals and averaging the result. The equivalence of this new definition and that of ...This paper presents a new definition of the average normal to a polygon by introducing a cone bounded by the polygon, computing its normals and averaging the result. The equivalence of this new definition and that of Newell’s is given, and a simple calculation based on this new definition is obtained and 3 N additions and N subtractions are saved, where N is the number of the vertices of the polygon.展开更多
文摘This paper is to investigate the convergence rate of asymptotic normality of frequency polygon estimation for density function under mixing random fields, which include strongly mixing condition and some weaker mixing conditions. A Berry-Esseen bound of frequency polygon is established and the convergence rates of asymptotic normality are derived. In particularly, for the optimal bin width , it is showed that the convergence rate of asymptotic normality reaches to ?when mixing coefficient tends to zero exponentially fast.
文摘This paper presents a new definition of the average normal to a polygon by introducing a cone bounded by the polygon, computing its normals and averaging the result. The equivalence of this new definition and that of Newell’s is given, and a simple calculation based on this new definition is obtained and 3 N additions and N subtractions are saved, where N is the number of the vertices of the polygon.
