Data available to an analyst might sometimes be censored, where only part of the actual series is observed. Consider the case in which only observations greater than some lower bound are recorded, as defined by the following process:

Running ordinary least squares estimation on data generated by the preceding process is not optimal because the estimates are likely to be biased and inefficient. One alternative to estimating models with censored data is the tobit estimator. This model is supported in the QLIM procedure in SAS/ETS and in the LIFEREG procedure in SAS/STAT. PROC ENTROPY provides another alternative which can make it very easy to estimate such a model correctly.
The following DATA step generates censored data in which any negative values of the dependent variable, y
, are set to a lower bound of 0.
data cens; do t = 1 to 100; x1 = 5 * ranuni(456); x2 = 10 * ranuni(456); y = 4.5*x1 + 2*x2 + 15 * rannor(456); if( y<0 ) then y = 0; output; end; run;
To illustrate the effect of the censored option in PROC ENTROPY, the model is initially estimated without accounting for censoring in the following statements:
title "Censored Data Estimation"; proc entropy data = cens gme primal; priors intercept 32 32 x1 15 15 x2 15 15; model y = x1 x2 / esupports = (25 1 25); run;
Output 13.3.1: GME Estimates
Censored Data Estimation 
GME Variable Estimates  

Variable  Estimate  Approx Std Err  t Value  Approx Pr > t 
x1  2.377609  0.000503  4725.98  <.0001 
x2  2.353014  0.000255  9244.87  <.0001 
intercept  5.478121  0.00188  2906.41  <.0001 
The previous model is reestimated by using the CENSORED option in the following statements:
proc entropy data = cens gme primal; priors intercept 32 32 x1 15 15 x2 15 15; model y = x1 x2 / esupports = (25 1 25) censored(lb = 0, esupports=(15 1 15) ); run;
Output 13.3.2: Entropy Estimates
Censored Data Estimation 
GME Variable Estimates  

Variable  Estimate  Approx Std Err  t Value  Approx Pr > t 
x1  4.429697  0.00690  641.85  <.0001 
x2  1.46858  0.00349  420.61  <.0001 
intercept  8.261412  0.0259  319.51  <.0001 
The second set of entropy estimates are much closer to the true parameter estimates of 4.5 and 2. Since another alternative available for fitting a model of censored data is a tobit model, PROC QLIM is used in the following statements to fit a tobit model to the data:
proc qlim data=cens; model y = x1 x2; endogenous y ~ censored(lb=0); run;
Output 13.3.3: QLIM Estimates
Censored Data Estimation 
Parameter Estimates  

Parameter  DF  Estimate  Standard Error  t Value  Approx Pr > t 
Intercept  1  2.979455  3.824252  0.78  0.4359 
x1  1  4.882284  1.019913  4.79  <.0001 
x2  1  1.374006  0.513000  2.68  0.0074 
_Sigma  1  13.723213  1.032911  13.29  <.0001 
For this data and code, PROC ENTROPY produces estimates that are closer to the true parameter values than those computed by PROC QLIM.