日期精度：到日 5 篇 · 到月 2 篇 · 到年 0 篇
非参数自回归与非参数回归的渐近等价性
It is proved that nonparametric autoregression is asymptotically equivalent in the sense of Le Cam’s deficiency distance to nonparametric regression with random design as well as with regular nonrandom design.
用独立观测密度估计量强逼近弱依赖观测密度估计量
We derive an approximation of a density estimator based on weakly dependent random vectors by a density estimator built from independent random vectors. We construct, on a sufficiently rich probability space, such a pairing of the random variables of both experiments that the set of observations $X_1,\ldots,X_n}$ from the time series model is nearly the same as the set of observations $Y_1,\ldots,Y_n}$ from the i.i.d. model. With a high probability, all sets of the form $({X_1,\ldots,X_n}\\Delta{Y_1,\ldots,Y_n})\bigcap([a_1,b_1]\times\ldots\times[a_d,b_d])$…
非参数自回归中的回归式推断
We derive a strong approximation of a local polynomial estimator LPE in nonparametric autoregression by an (LPE) in a corresponding nonparametric regression model. This generally suggests the application of regression-typical tools for statistical inference in nonparametric autoregressive models. It provides an important simplification for the boot-strap method to be used: It is enough to mimic the structure of a nonparametric regression model rather than to imitate the more…
各向异性函数类中的小波阈值估计及演化谱自适应估计
We derive minimax rates for estimation in anisotropic smoothness classes. These rates are attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale parameter for every dimension. It is shown that this basis is superior to its one-scale multiresolution analog, if different degrees of smoothness in different directions are present. As an important application we introduce a new adaptive waveletestimator of the time-dependent…
非参数回归的自动带宽选择与置信区间
In the present paper we combine the issues of bandwidth choice and construction of confidence intervals in nonparametric regression. Main emphasis is put on fully data-driven methods. We modify the $\sqrt{n}$-consistent bandwidth selector of Härdle, Hall and Marron such that it is appropriate for heteroscedastic data, and we show how one can optimally choose the bandwidth g of the pilot estimator $\hat{m}_g$. Then we consider classical confidence intervals based on kernel…