Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 1984, Volume 52, Issue 2

Interpolation from Grouped Data for Unimodal Densities<419:IFGDFU>2.0.CO;2-I
p. 419-426

Abba M. Krieger, Joseph L. Gastwirth

This paper considers the interpolation of percentiles when the value of the c.d.f. F(x) is specified at n points. Upper and lower bounds on the percentile are obtained assuming that data is generated by a unimodal density. Sharper bounds are derived when the average of the observations in each interval is given. In addition to improving the standard linear interpolation, our results indicate that much information can be gained by reporting group means as well as frequency counts.

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