arXiv subjects

Kim Hendrickx

Publications and source records attributed to Kim Hendrickx.

4 recordsLinked to original sources

arXiv2018

Score estimation in the monotone single index model

We consider estimation in the single index model where the link function is monotone. For this model a profile least squares estimator has been proposed to estimate the unknown link function and index. Although it is natural to propose this procedure, it is still unknown whether it produces index estimates which converge at the parametric rate. We show that this holds if we solve a score equation corresponding to this least squares problem. Using a Lagrangian formulation, we show how one can solve this score equation without any reparametrization. This makes it easy to solve the score equations in high dimensions. We also compare our method with the Effective Dimension Reduction (EDR) and the Penalized Least Squares Estimator (PLSE) methods, both available on CRAN as R packages, and compare with link-free methods, where the covariates are ellipticallly symmetric.

math.ST↗

arXiv2017

The nonparametric bootstrap for the current status model

It has been proved that direct bootstrapping of the nonparametric maximum likelihood estimator (MLE) of the distribution function in the current status model leads to inconsistent confidence intervals. We show that bootstrapping of functionals of the MLE can however be used to produce valid intervals. To this end, we prove that the bootstrapped MLE converges at the right rate in the $L_p$-distance. We also discuss applications of this result to the current status regression model.

stat.ME↗

arXiv2017

Current status linear regression

We construct $\sqrt{n}$-consistent and asymptotically normal estimates for the finite dimensional regression parameter in the current status linear regression model, which do not require any smoothing device and are based on maximum likelihood estimates (MLEs) of the infinite dimensional parameter. We also construct estimates, again only based on these MLEs, which are arbitrarily close to efficient estimates, if the generalized Fisher information is finite. This type of efficiency is also derived under minimal conditions for estimates based on smooth non-monotone plug-in estimates of the distribution function. Algorithms for computing the estimates and for selecting the bandwidth of the smooth estimates with a bootstrap method are provided. The connection with results in the econometric literature is also pointed out.

math.ST↗

arXiv2017

Confidence intervals for the current status model

We discuss a new way of constructing pointwise confidence intervals for the distribution function in the current status model. The confidence intervals are based on the smoothed maximum likelihood estimator (SMLE) and constructed using bootstrap methods. Other methods to construct confidence intervals, using the non-standard limit distribution of the (restricted) MLE, are compared to our approach via simulations and real data applications.

math.ST↗