986812401 Doubly truncated data appear in a number of applications, including astronomy and survival analysis. In this paper we review the existing methods to compute the NPMLE under double truncation, which has no explicit form and must be approximated numerically. We introduce the bootstrap as a method to estimate the finite sample distribution of the NPMLE under double truncation. The perfor...

For right censored data, Efron (1981) has shown that his “simple” and “obvious” methods of bootstrapping are equivalent. We explain why this equivalence no longer holds for truncated data. Wang (1991) generalized Efron’s “obvious” bootstrap method to data that are both left truncated and right censored, under the assumption that C ≥ T and C − T is independent of T , where T and C denote the (ge...

All data are digitized, and hence are essentially integers rather than true real numbers. Ordinarily this causes no difficulties since the truncation or rounding usually occurs below the noise level. However, in some instances, when the instruments or data delivery and storage systems are designed with less than optimal regard for the data or the subsequent data analysis, the effects of digitiz...

We detail the basic theory for regression models in which dependent variables are censored or underlying distributions are truncated. The model is extended to models for counts, sample selection models, and hazard models for duration data. Entry-level theory is presented for the practitioner. We then describe a few of the recent, frontier developments in theory and