Chebyshev Polynomial Approximations for Characteristic Function Estimation: Some Theoretical Supplements
本文通过傅里叶方法，用特征函数表达角度和余弦的密度，从而对具有闭式特征函数的分布参数进行最大似然估计，并讨论了非对称分布的可估性及方法不适用的情形。
SUMMARY Densities for the angle Θ = uX(mod 2π) and the cosine Y = cos(uX) can be expressed, through Fourier methods, in terms of the characteristic function of X. Thus, if X has a characteristic function of closed form, the parameters of its distribution may be estimated by maximum likelihood. The paper addresses the problems of estimability of asymmetric distributions and situations where the method may not apply.