Density approximant based on noise multiplied data

Using noise multiplied data to protect confidential data has recently drawn some attention. Understanding the probability property of the underlying confidential data based on their masked data is of interest in confidential data analysis. This paper proposes the approach of sample-moment-based density approximant based on noise multiplied data and provides a new manner for approximating the density function of the underlying confidential data without accessing the original data. The approach of sample-moment-based density approximant is an extension of the approach of moment-based density approximant, which is mathematically equivalent to traditional orthogonal polynomials ap- proaches to the probability density function (Provost, 2005). This paper shows that, regardless of a negligible probability, a moment-based density approximant can be well approximated by its sample-moment-based approximant if the size of the sample used in the evaluation is reasonable large. Consequently, a density function can be reasonably approximated by its sample-moment-based density approximant. This paper focuses on the properties and the performance of the approach of the sample-moment-based density approximant based on noise multiplied data. Due to the restriction on the number of pages, some technical issues on implementing the approach proposed in practice will be discussed in another paper.