Abstract

This paper introduces a semi-parametric method for estimating regression co underlying parent population of errors in censored. The method is an example of the method of sieves; and it provides simultaneous estimates of the regression coefficients and the density of the underlying parent population. In the very simplest terms, the underlying unknown density is approximated by a spline with mesh size approaching zero with the sample size. The values of the density at the knots are then added to the list of the usual unknown parameters in a censored regression model, e.g., the regression coefficients and scale parameter. A quasi-likelihood function using the approximate spline density is then maximized over all the parameters mentioned above. The method is shown to result in strongly consistent parameter estimates.

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