Abstract #301910

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JSM 2003 Abstract #301910
Activity Number: 331
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #301910
Title: Recovering the Probability Density from Percentiles
Author(s): Atsuyuki Kogure*+ and Masahiko Sagae
Companies: Keio University and Gifu University
Address: 5322 Endo, Fujisawa-shi, , 252-8520, Japan
Keywords: percentiles ; histogram ; large bias ; kernel method
Abstract:

Prior to the data analysis, datasets are often summarized in percentiles. Take, for example, the official statistics such as household income data, many of which are published in percentiles due to the sheer size of the data and/or because of the disclosure control for the individuals. With the data summarized in percentiles it may be a common practice to try to recover the original data distribution by constructing a histogram with percentiles. We show that the histogram method suffers large biases for many standard densities including the normal density. To alleviate the problem we propose a kernel method to estimate the density with percentiles. We present both analytical and simulation results to support our proposed method.

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