Kernel density estimation is one of the well-known technique in nonparametric density estima-tions. Kernel method is constructed by placing a kernel function disposed at each data point and it can obtain smooth estimations. We note that this method has cost of calculation increasing in proportion with the number of data. Its computational burden is relieved by the development of the computer, however, if we choose a continuous probability density function, then the calculation in-creases more. Therefore we suggest the trapezoid kernel function generated by the piecewise linear function, because we can reduce the cost of calculating the estimate by using trapezoid kernel. We show that it is easy to compute and has the better efficiency compared with other kernel functions. We discuss about the property of trapezoid kernel function focused on the calculational efficiency and show the numerical example, also.
View full abstract