Adaptive Smoothing Parameter in Kernel Density Estimation and Parameter Estimation in Normal Mixture Distributions

Kernel density estimation is a widely used tool in nonparametric density estimation procedures. Choice of a kernel function and a smoothing parameter are two important issues in implementing kernel density estimation procedures. In this paper, four different kernel functions are considered in implementing an adaptive selection procedure in choosing the smoothing parameter. In simulation, a skewed bimodal density which is a mixture of two normal distributions is considered along with the standard normal and the standard exponential densities. In skewed bimodal data, parameter estimation is also explored in the context of the parameter estimation in mixtures of normal distributions. Maximum likelihood estimation procedure is implemented in parameter estimation in mixtures of normal distributions.