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不规则设计下非线性小波回归的插值方法AI 解读

We introduce interpolation methods that enable nonlinear wavelet estimators to be employed with stochastic design, or nondyadic regular design, in problems of nonparametric regression. This approach allows relatively rapid computation, involving dyadic approximations to wavelet-after-interpolation techniques. New types of interpolation are described, enabling first-order variance reduction at the expense of second-order increases in bias. The effect of interpolation on…

依赖指数半参数估计量收敛速率的说明AI 解读

Considerable recent attention has been devoted to semiparametric estimation of the dependence index, or the Hurst constant, using methods based on information in either frequency or time domains. Convergence rates of estimators in the frequency domain have been derived, and in the present paper we obtain them for estimators in the time domain. It is shown that the latter can have superior performance for moderate-range time series, but are inferior in the context of…

非参数回归中适应稀疏设计的插值方法AI 解读

We suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing. These methods are based on simple rules, determined by the kernel and bandwidth, for deciding when and where pseudo-design points should be added to augment the original design sequence. New ordinates for the added design points are computed by simple interpolation, then local linear smoothing is applied directly to the expanded dataset. The method is competitive with…

摘要暂缺

非参数回归中适应稀疏设计的插值方法AI 解读

We suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing. These methods are based on simple rules, determined by the kernel and bandwidth, for deciding when and where pseudo-design points should be added to augment the original design sequence. New ordinates for the added design points are computed by simple interpolation, then local linear smoothing is applied directly to the expanded dataset. The method is competitive with…

基于含噪支持函数数据的凸集估计AI 解读

In problems of medical imaging and robotic vision, measurements of a convex set are sometimes obtained via the set's support function. The standard way in which the convex set is recovered from such data is to suppose that it is polygonal, model the errors as Normal random variables, and apply constrained maximum likelihood methods. Typically, the number of sides assumed of the polygon is equal to or a little less than the number of data points. However, from a statistical…

由含噪支持函数数据估计凸集AI 解读

In problems of medical imaging and robotic vision, measurements of a convex set are sometimes obtained via the set's support function. The standard way in which the convex set is recovered from such data is to suppose that it is polygonal, model the errors as Normal random variables, and apply constrained maximum likelihood methods. Typically, the number of sides assumed of the polygon is equal to or a little less than the number of data points. However, from a statistical…

改进非参数回归中的卷积与插值方法AI 解读

Following earlier work of Jones, Davies & Park (1994) we develop estimators based on convolution and interpolation methods, with the aim of reducing their variance and making them competitive with local linear smoothers. We argue that the classic convolution and interpolation approaches due to Gasser & Müller (1979) and Clark (1977) exhibit inflated variance on account of the relatively high variability of weights used in their construction. We show that, by convolving or…

含大量不连续点函数的小波方法表现AI 解读

Compared to traditional approaches to curve estimation, such as those based on kernels, wavelet methods are relatively unaffected by discontinuities and similar aberrations. In particular, the mean square convergence rate of a wavelet estimator of a fixed, piecewise-smooth curve is not influenced by discontinuities. Nevertheless, it is clear that as the estimation problem becomes more complex the limitations of wavelet methods must eventually be apparent. By allowing the…