ESTIMATION OF CONDITIONAL DENSITIES AND SENSITIVITY MEASURES IN NONLINEAR DYNAMICAL-SYSTEMS

Using locally polynomial regression, we develop nonparametric estimato rs for the conditional density function and its square root, and their partial derivatives. Two measures of sensitivity to initial condition s in nonlinear stochastic dynamic systems are proposed, one of which r elates Fisher information with initial-value sensitivity in dynamical systems. We propose estimators for these, and show asymptotic normalit y for one of them. We further propose a simple method for choosing the bandwidth. The methods are illustrated by simulation of two well-know n models in dynamical systems.