Statistical Modelling 7 (2007), 107–123
Tobit model estimation and sliced inverse regression
Lexin Li
North Carolina State University
USA
Jeffrey S Simonoff
Leonard N Stern School of Business,
New York University,
44 West 4th Street,
New York, NY 10012-1106
USA
eMail:
jsimonoff@stern.nyu.edu
Chih-Ling Tsai
Graduate School of Management,
University of California at Davis
USA
Abstract:
It is not unusual for the response variable in a regression model to
be subject to censoring or truncation. Tobit regression models are
specific examples of such a situation, where for some observations
the observed response is not the actual response, but the censoring
value (often zero), and an indicator that censoring (from below) has
occurred. It is well-known that the maximum likelihood estimator for
such a linear model assuming Gaussian errors is not consistent if
the error term is not homoscedastic and normally distributed. In
this paper, we consider estimation in the Tobit regression context
when homoscedasticity and normality of errors do not hold, as well
as when the true response is an unspecified nonlinear function of
linear terms, using sliced inverse regression (SIR). The properties
of SIR estimation for Tobit models are explored both theoretically
and based on extensive Monte Carlo simulations.We show that the SIR
estimator is a strong competitor to other Tobit regression estimators,
in that it has good properties when the usual linear model assumptions
hold, and can be much more effective than other Tobit model estimators
when those assumptions break down. An example related to household
charitable donations demonstrates the usefulness of the SIR estimator.
Keywords:
dimension reduction; heteroscedasticity; nonnormality;
single-index model
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