Moment-type Nonparametric Estimation in Some Direct and Indirect Models

In this research, several approximation of the probability density function, cumulative distribution function in some direct and indirect models are proposed. They are based on the knowledge of the moments and the scaled Laplace transform of the target functions. The upper bounds for the uniform rate of approximations as well as the mean squared errors are established. Two cases when the support of underlying function is bounded and unbounded from above are studied. Proposed constructions provide new non-parametric estimates of the distribution and the density functions in right censored, current status, mean residual life time and length biased models. Simulation study justifies the consistency of the proposed estimates

Nonparametric density estimation based on the scaled Laplace transform inversion

New nonparametric procedure for estimating the probability density function of a positive random variable is suggested. Asymptotic expressions of the bias term and Mean Squared Error are derived. By means of graphical illustrations and evaluating the Average of L2-errors we conducted comparisons of the finite sample performance of proposed estimate with the one based on kernel density method