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About the article
Published Online: 2013-05-28
Published in Print: 2013-07-01
Horowitz (2001, theorem 2.2) averages gn (Xi); the STATA program on our website is sufficiently fast to apply the bootstrap to most survey datasets.
The Brent’s method combines the bisection method, the secant method and inverse quadratic interpolation. The idea is to use the secant method or inverse quadratic interpolation if possible, because they converge faster, but to fall back to the more robust bisection method if necessary. The secant method can be thought of as a finite difference approximation of the Newton-Raphson method. The Powell method extends the Brent method by searching in a specific direction, rather than changing one parameter at the time.
In the MLE for models with duration dependence, we do not need the standard identification restriction that the unobserved heterogeneity term has mean one because the baseline hazard is normalized to be equal to 1 in the first interval.
The Gâteaux derivative is a directional derivative; let
Our calculations were done in Gauss 6.0 on 3 parallel computers: a Pentium 2.1 PC, a Pentium 2.8 PC and a Pentium 2.0 laptop. The calculations took about 9 weeks of CPU time.
The LRE with a duration dependence on 10 intervals for a sample size of 500 did not converge in seven of the experiments. The average is therefore base on 93 experiments instead of 100.
The Doob-Meyer decomposition theorem is a theorem in stochastic calculus stating the conditions under which a submartingale may be decomposed in a unique way as the sum of a martingale and a continuous increasing process, see Meyer (1963) and Protter (2005).