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The likelihood ratio theory contributes tremendous success to para-metric inferences. Yet, there is no general applicable approach for non-parametric inferences based on function estimation. Maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting. Even if they exist, they are hard to find and can not be(More)
Time-homogeneous diffusion models have been widely used for describing the stochastic dynamics of the underlying economic variables. Recently, Stanton proposed drift and diffusion estimators based on a higher-order approximation scheme and kernel regression method. He claimed that " higher order approximations must outperform lower order approximations "(More)
In an effort to capture the time variation on the instantaneous return and volatility functions, a family of time-dependent diffusion processes is introduced to model the term structure dynamics. This allows one to examine how the instantaneous return and price volatility change over time and price level. Nonparametric techniques, based on kernel(More)
It is well known that the number of modes of a kernel density estimator is monotone nonincreasing in the bandwidth if the kernel is a Gaussian density. There is numerical evidence of nonmonotonic-ity in the case of some non-Gaussian kernels, but little additional information is available. The present paper provides theoretical and numerical descriptions of(More)
Many applications of nonparametric tests based on curve estimation involve selecting a smoothing parameter. The author proposes an adaptive test that combines several generalized likelihood ratio tests in order to get power performance nearly equal to whichever of the component tests is best. He derives the asymptotic joint distribution of the component(More)