We develop a specification test for the transition density of a discretely-sampled continuous-time diffusion process, based on a comparison of a nonparametric estimate of the transition density or distribution function to their corresponding parametric counterparts assumed by the null hypothesis. We provide a direct comparison of the two densities for an arbitrary specification of the null parametric model using three different discrepancy measures between the null and alternative transition density and distribution functions. We establish the asymptotic null distributions of proposed test statistics and compute their power functions. The finite sample properties are critically investigated via simulation studies and are compared with other tests. Our approaches are illustrated by applications to implied volatility data and Treasury bill data.

Local quasilikelihood estimation is a useful extension of local least squares methods, but its computational cost and algorithmic convergence problems make the procedure less appealing, particularly when it is iteratively used in methods such as the backfitting algorithm, crossvalidation and bootstrapping. A onestep local quasilikelihood estimator is introduced to overcome the computational drawbacks of the local quasilikelihood method. We demonstrate that as long as the initial estimators are reasonably good, the onestep estimator has the same asymptotic behaviour as the local quasilikelihood method. Our simulation shows that the onestep estimator performs at least as well as the local quasilikelihood method for a wide range of choices of bandwidths. A datadriven bandwidth selector is proposed for the onestep estimator based on the preasymptotic substitution method of Fan and Gijbels. It is

Error variance estimation plays an important role in statistical inference for high-dimensional regression models. This article concerns with error variance estimation in high-dimensional sparse additive model. We study the asymptotic behavior of the traditional mean squared errors, the naive estimate of error variance, and show that it may significantly underestimate the error variance due to spurious correlations that are even higher in nonparametric models than linear models. We further propose an accurate estimate for error variance in ultrahigh-dimensional sparse additive model by effectively integrating sure independence screening and refitted cross-validation techniques. The root <i>n</i> consistency and the asymptotic normality of the resulting estimate are established. We conduct Monte Carlo simulation study to examine the finite sample performance of the newly proposed estimate. A real data example is used to

The paper studies estimation of partially linear hazard regression models with varying coefficients for multivariate survival data. A profile pseudopartiallikelihood estimation method is proposed. The estimation of the parameters of the linear part is accomplished via maximization of the profile pseudopartiallikelihood, whereas the varyingcoefficient functions are considered as nuisance parameters that are profiled out of the likelihood. It is shown that the estimators of the parameters are root <i>n</i> consistent and the estimators of the nonparametric coefficient functions achieve optimal convergence rates. Asymptotic normality is obtained for the estimators of the finite parameters and varyingcoefficient functions. Consistent estimators of the asymptotic variances are derived and empirically tested, which facilitate inference for the model. We prove that the varyingcoefficient functions can be estimated as well as if the

Suppose that we have n observations from the convolution model Y = X+, where X and are the independent unobservable random variables, and is measurement error with a known distribution. We will discuss the asymptotic normality for deconvolving kernel density estimators of the unknown density f_{X}(.) of X by assuming either the tail of the characteristic function of behaves as f_{X}(.) (which is called supersmooth error), or the tail of the characteristic function is of order f_{X}(.) (called ordinary smooth error). Asymptotic normality of estimating the functional f_{X}(.) is also addressed.