The Effects of Rounding on Likelihood Procedures

Abstract

The aim of this paper is to investigate the robustness properties of likelihoodinference with respect to rounding effects. Attention is focused on exponentialfamilies and on inference about a scalar parameter of interest, also in the presenceof nuisance parameters. A summary value of the influence function of a givenstatistic, the local-shift sensitivity, is considered. It accounts for small fluctuations inthe observations. The main result is that the local-shift sensitivity is bounded for theusual likelihood-based statistics, i.e. the directed likelihood, the Wald and scorestatistics. It is also bounded for the modified directed likelihood, which is ahigher-order adjustment of the directed likelihood. The practical implication is thatlikelihood inference is expected to be robust with respect to rounding effects.Theoretical analysis is supplemented and confirmed by a number of Monte Carlostudies, performed to assess the coverage probabilities of confidence intervals basedon likelihood procedures when data are rounded. In addition, simulations indicatethat the directed likelihood is less sensitive to rounding effects than the Wald andscore statistics. This provides another criterion for choosing among first-orderequivalent likelihood procedures. The modified directed likelihood shows the samerobustness as the directed likelihood, so that its gain in inferential accuracy does notcome at the price of an increase in instability with respect to rounding.