Improving the Accuracy of the Probability Density Function Estimation

The paper considers the new approach to the reconstruction of the probability density function similarly the averaged shifted histogram method. An algorithm is used Richardson's extrapolation for increasing accuracy. We prove the estimates of the accuracy of the probability density function and its second derivative to choose the optimal settings for smoothing the histogram and kernel estimators and to consider the optimal choice problem of the bandwidth parameter. Presented the results of numerical experiments.