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含测量误差的加性部分线性模型AI 解读

We consider statistical inference for additive partial linear models when the linear covariate is measured with error. We propose attenuation-to-correction and simulation-extrapolation, simex, estimators of the parameter of interest. It is shown that the first resulting estimator is asymptotically normal and requires no undersmoothing. This is an advantage of our estimator over existing backfitting-based estimators for semiparametric additive models which require…

惩罚样条的渐近性质AI 解读

We study the asymptotic behaviour of penalized spline estimators in the univariate case. We use B-splines and a penalty is placed on mth-order differences of the coefficients. The number of knots is assumed to converge to infinity as the sample size increases. We show that penalized splines behave similarly to Nadaraya--Watson kernel estimators with ‘equivalent’ kernels depending upon m. The equivalent kernels we obtain for penalized splines are the same as those found by…

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局部最小二乘回归的带宽选择方法AI 解读

Local least squares kernel regression provides an appealing solution to the nonparametric regression, or “scatterplot smoothing,” problem, as demonstrated by Fan, for example. The practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter. In this article we apply the ideas of plug-in bandwidth selection to develop strategies for choosing the smoothing parameter of local…

通过变换降低核密度估计的边界偏差AI 解读

SUMMARY We consider kernel estimation of a univariate density whose support is a compact interval. If the density is non-zero at either boundary, then the usual kernel estimator can be seriously biased. ‘Reflection’ at a boundary removes some bias, but unless the first derivative of the density is 0 at the boundary the estimator with reflection can still be much more severely biased at the boundary than in the interior. We propose to transform the data to a density that has…

多元局部加权最小二乘回归AI 解读

Nonparametric regression using locally weighted least squares was first discussed by Stone and by Cleveland. Recently, it was shown by Fan and by Fan and Gijbels that the local linear kernel-weighted least squares regression estimator has asymptotic properties making it superior, in certain senses, to the Nadaraya-Watson and Gasser-Muller kernel estimators. In this paper we extend their results on asymptotic bias and variance to the case of multivariate predictor variables.…

像素平均后错位图像的位移估计AI 解读

In problems where the recorded signal comprises two or more bands (i.e., wavelengths), it is often the case that the bands are not perfectly aligned in the focal plane. Such misregistration may be caused by atmospheric or oceanographic effects, which refract different bands to differing degrees, or it may result from features of the design of the recording equipment. This article develops two methods for estimating the lag, or the amount by which the bands are out of…

异方差回归模型的拟合AI 解读

In heteroscedastic regression models assumptions about the error distribution determine the method of consistent estimation of parameters. For example, consider the case where the model specifies the regression and dispersion functions for the data but robustness is of concern and one wishes to use least absolute error regressions. Except in certain special circumstances, parameter estimates obtained in this way are inconsistent. In this article we expand the heteroscedastic…

错位且经像素平均的图像中的位移估计AI 解读

In problems where the recorded signal comprises two or more bands (i.e., wavelengths), it is often the case that the bands are not perfectly aligned in the focal plane. Such misregistration may be caused by atmospheric or oceanographic effects, which refract different bands to differing degrees, or it may result from features of the design of the recording equipment. This article develops two methods for estimating the lag, or the amount by which the bands are out of…

异方差回归模型的拟合AI 解读

In heteroscedastic regression models assumptions about the error distribution determine the method of consistent estimation of parameters. For example, consider the case where the model specifies the regression and dispersion functions for the data but robustness is of concern and one wishes to use least absolute error regressions. Except in certain special circumstances, parameter estimates obtained in this way are inconsistent. In this article we expand the heteroscedastic…

线性回归中的一步 GM 估计与推断稳定性AI 解读

The folklore on one-step estimation is that it inherits the breakdown point of the preliminary estimator and yet has the same large sample distribution as the fully iterated version as long as the preliminary estimate converges faster than n –1/4, where n is the sample size. We investigate the extent to which this folklore is valid for one-step GM estimators and their associated standard errors in linear regression. We find that one-step GM estimates based on Newton-Raphson…

密度估计中的数据变换AI 解读

For the density estimation problem the global window width kernel density estimator does not perform well when the underlying density has features that require different amounts of smoothing at different locations. In this article we propose to transform the data with the intention that a global window width is more appropriate for the density of the transformed data. The density estimate of the original data is the “back-transform” by change of variables of the global…