We use U.S. hospital data from 2004 to 2011 to estimate a cost function using a Bayesisan semi-nonparametric method that allows for a heteroskedastic inefficiency. Moreover, we evaluate what is the impact of variables, such as region and hospital size, on cost estimating both the size and robustness of the variables in terms of reducing cost for hospitals.

This research overcomes both the decreased accuracy of Convex Adaptive Partitioning on real production survey datasets and the cross-validation performance challenges of CNLS to create a robust and scalable adaptive partitioning-based convex regression method.

We discover that real production datasets often contain local monotonicity violations, which affect CAP’s ability to propose feasible basis region splits. Moreover, we note that CNLS’s error minimization strategy within the observed dataset results in poor estimations on unobserved firms due to over-fitting. We create a hybrid of both methods that preserves their most favorable properties at a small computational time expense. The paper summarizing this research is available on Arxiv.

SCKLS (shape constrained kernel-weighted least squares) estimator integrates kernel-weighting to convex nonparametric least squares.

Kernel regression is one of the powerful nonparametric estimation methods. By imposing more weight to some closer points, kernel regression helps to avoid over-fitting although it requires the tuning parameter, bandwidth. By imposing some shape constraints such as monotonicity and concavity, we propose SCKLS estimator and apply it to estimate production function with simulated and real data. We also investigate the relationship with Convex Nonparametric Least Squares (CNLS) and we found that CNLS is minimum bias estimator in the class of SCKLS estimator. This is on-going research with Daisuke Yagi. This is the first chapter of his dissertation.

We propose a shape-constrained production function estimator starting from the method described in Kumbhakar, Park, Simar, Tsionas 2006 (KPST).

We maximize the loglikelihood of a local linear estimator at each observation. We estimate the parameters for the noise and inefficiency distributions that are potentially heteroscedasticity.

The challenge to imposing shape constraints, such as monotonicity and concavity, is we need to jointly esitmate the maximum likelihood function for all observations while imposing the constraints. This is on-going research with Kevin Layer.