Byeong U. Park

Abstract This article compares several promising data-driven methods for selecting the bandwidth of a kernel density estimator. The methods compared are least squares cross-validation, biased cross-validation, and a plug-in rule. The comparison is done by asymptotic rate of convergence to the optimum and a simulation study. It is seen that the plug-in bandwidth is usually most efficient when the underlying density is sufficiently smooth, but is less robust when there is not enough smoothness pre

Abstract This article compares several promising data-driven methods for selecting the bandwidth of a kernel density estimator. The methods compared are least squares cross-validation, biased cross-validation, and a plug-in rule. The comparison is done by asymptotic rate of convergence to the optimum and a simulation study. It is seen that the plug-in bandwidth is usually most efficient when the underlying density is sufficiently smooth, but is less robust when there is not enough smoothness pre

Summary Varying coefficient regression models are known to be very useful tools for analysing the relation between a response and a group of covariates. Their structure and interpretability are similar to those for the traditional linear regression model, but they are more flexible because of the infinite dimensionality of the corresponding parameter spaces. The aims of this paper are to give an overview on the existing methodological and theoretical developments for varying coefficient models a

Abstract This article considers the semiparametric stochastic frontier model with panel data that arises in the problem of measuring technical inefficiency in production processes. We assume a parametric form for the frontier function, which is linear in production inputs. The density of the individual firm-specific effects is considered to be unknown. We construct an efficient estimator of the slope parameters in the frontier function. We also give an estimator of the level of the frontier func

High-dimensional regression problems, which reveal dynamic behavior, are typically analyzed by time propagation of a few number of factors. The inference on the whole system is then based on the low-dimensional time series analysis. Such high-dimensional problems occur frequently in many different fields of science. In this article we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods. This more flexible modeling approach poses an import

Nonparametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are defined in terms of convex-hulls of the observed combinations of inputs×outputs in a sample of enterprises. The shape of the convex-hull relies on a hypothesis on the shape of the technology, defined as the boundary of the set of technically attainable points in the inputs × outputs space. So far, only the statistical properties of the smallest convex polyhed

We suggest two new, translation-based methods for estimating and correcting for bias when estimating the edge of a distribution. The first uses an empirical translation applied to the argument of the kernel, in order to remove the main effects of the asymmetries that are inherent when constructing estimators at boundaries. Placing the translation inside the kernel is in marked contrast to traditional approaches, such as the use of high-order kernels, which are related to the jackknife and, in ef

We propose and investigate additive density regression, a novel additive functional regression model for situations where the responses are random distributions that can be viewed as random densities and the predictors are vectors. Data in the form of samples of densities or distributions are increasingly encountered in statistical analysis and there is a need for flexible regression models that accommodate random densities as responses. Such models are of special interest for multivariate conti

The Free Disposal Hull (FDH) is a nonparametric estimator for the production set. In Productivity Analysis one derives the production frontier and eciency scores from the FDH. In the literature the method is considered to be deterministic. However, assuming that individuals are drawn independently from a distribution, where the support is the true production set, FDH eciency scores are random variables. The paper investigates its stochastic properties.