Probability Density Function Estimation Using a New Series Nonparametric Estimator with Data Applications

In this paper, we studied a new nonparametric density estimation method.  We proposed this estimator in series univariate form that incorporates the kernel density estimator and kernel density differential estimator and derived its normality and variance.  We have also compared the asymptotic normality of the mean integrated squared error (AMISE) of the proposed estimator, kernel density estimator and bias reduced kernel estimator.  The results obtained have shown that the proposed estimator, Hermite series kernel density estimator one has better performance than the kernel density estimator and bias reduced kernel estimator when real data are applied.