Estimation of a Probability Density Function of Very Many Variables

The problem of estimating an unknown probability density function from a sequence of samples is well known in pattern classification and many other problems. We approximate the unknown density function by a multivariable spline that is constructed from the histogram of samples. This spline function is expressed as a sum of combinatorially many terms. To assess these numerous terms, the technique of Monte Carlo sampling is exploited and a combined sampling is devised to reduce the standard error.