4.31 The method of simulated scores for the estimation
of LDV models

The method of simulated scores (MSS) is presented for
estimating limited dependent variables models with
flexible correlation structure in the unobservables.
Simulators are proposed that are continuous in the
unknown parameter vectors, and hence standard
optimization methods can be used to compute the MSS
estimators that employ these simulators. The first
continuous method relies on a recursive conditioning
of the multivariate normal density through a Cholesky
triangularization of its variance-covariance matrix.
The 2nd method combines results about the conditionals
of the multivariate normal distribution with Gibbs
resampling techniques. Consistency and asymptotic
normality of the MSS estimators are established and
suitable rates at which the number of simulations must
rise if biased simulators are used are derived.