In nonparametric curve estimation, the smoothing parameter is critical for performance. In order to estimate the hazard rate, we compare nearest neighbor selectors that minimize the quadratic, the Kullback-Leibler, and the uniform loss. These measures result in a rule of thumb, a...

We provide Markov chain Monte Carlo (MCMC) algorithms for computing the bandwidth matrix for multivariate kernel density estimation. Our approach is based on treating the elements of the bandwidth matrix as parameters to be estimated, which we do by optimizing the likelihood cross-validation...

In nonparametric curve estimation, the smoothing parameter is critical for performance. In order to estimate the hazard rate, we compare nearest neighbor selectors that minimize the quadratic, the Kullback-Leibler, and the uniform loss. These measures result in a rule of thumb, a...

We consider a two-scaled diffusion system, when drift and diffusion parameters of the 'slow' component are contaminated by the ' fast' unobserved component. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the 'slow' component w.r.t. the...

In a single index Poisson regression model with unknown link function, the index parameter can be root-n consistently estimated by the method of pseudo maximumum likelihood. In this paper, we study, by simulation arguments, the practical validity of the asymptotic behavior of the pseudo maximum...

Optimal bandwidths for local polynomial regression usually involve functionals of the derivatives of the unknown regression function. In the multivariate case, estimates of these functionals are not readily available, primarily because estimating multivariate derivatives is complicated. In this...

Estimating equations have found wide popularity recently in parametric problems, yielding consistent estimators with asymptotically valid inferences obtained via the sandwich formula. Motivated by a problem in nutritional epidemiology, we use estimating equations to derive nonparametric...

In many regression applications both the independent and dependent variables are measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two different nonparametric techniques, regression splines and kernel...

We consider the problem of choosing two bandwidths simultaneously for estimating the difference of two functions at given points. When the asymptotic approximation of the mean squared error (AMSE) criterion is used, we show that minimisation problem is not well-defined when the sign of the...

Classical multivariate principal component analysis has been extended to functional data and termed functional principal componentanalysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal of this paper to develop two methods that do. In the ?rst...