Estimation of internet file-access/modification rates from indirect data

Consider an Internet file for which data on last time of access/modification (A/M) of the file are collected at periodic intervals, but for which direct A/M data are not available. Methodology is developed here that enables estimation of the A/M rates, in spite of having only indirect data of this nature. Both parametric and nonparametric methods are developed. Theoretical and empirical analyses are presented that indicate that the problem is indeed statistically tractable, and that the methods developed are of practical value. Behavior of the parametric estimators is examined when these assumptions are violated, and these estimators are found to be robust against some such violations.