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删失线性回归半参数估计中的带宽选择AI 解读

Quantile and semiparametric M estimation are methods for estimating a censored linear regression model without assuming that the distribution of the random component of the model belongs to a known parametric family. Both methods require estimating derivatives of the unknown cumulative distribution function of the random component. The derivatives can be estimated consistently using kernel estimators in the case of quantile estimation and finite difference quotients in the…

带宽选择器为何偏向较小带宽及其修正AI 解读

This note is concerned with the problem of automatic data-driven bandwidth selectors for nonparametric regression. Though some selectors were shown to be consistent and asymptotically unbiased by Rice (1984) and Hãrdle, Hall & Marron (1988), it is often observed in simulation studies that most selectors are biased toward undersmoothing. An explanation for this is given. The source of the large sample variation in the bandwidth estimates is also pointed out. This leads to the…

Wicksell 微粒问题中的核估计AI 解读

We consider the estimation of the probability density function of the radii of spheres in a medium, given the radii of their profiles in a random cross-section. This problem is known as Wicksell's corpuscle problem. We present a new estimator related to the classical kernel density estimator and discuss its properties. A comparison is made with other estimators related to the kernel estimator.

平滑样条的平均后验方差与平均平方误差的一致估计AI 解读

A smoothing spline estimator can be interpreted in two ways: either as the solution to a variational problem or as the posterior mean when a particular Gaussian prior is placed on the unknown regression function. In order to explain the remarkable performance of her Bayesian "confidence intervals" in a simulation study, Wahba conjectured that the average posterior variance of a spline estimate evaluated at the observation points will be close to the expected average squared…

二维拉普拉斯平滑的迭代方法及其图像修复应用AI 解读

Smoothing methods are increasingly important in modern graphically oriented data analysis. There are several fast and reliable univariate cross-validated smoothing algorithms, but comparable methods are not available in higher dimensions. This article develops an iterative approach to two-dimensional Laplacian spline smoothing based on tensor-product cubic B splines. Estimating equations are developed and solved iteratively using two-line symmetric successive over relaxation…

非参数平滑回归中无关联假设的随机化检验AI 解读

When a linear regression function is estimated by ordinary least squares, the null hypothesis of no relationship between the response and the design variable can be tested by the normal theory F test. This article describes a new test for use in the case in which a smooth regression function is estimated by a nonparametric procedure such as kernel estimation or local regression. The test is constructed as an approximation to an exact permutation test. The test statistic is…

数据驱动带宽选择方法的比较AI 解读

This paper provides a comparison. on three levels. of several promising data-driven methods for selecting the bandwidth of a kernel density estimator. The methods compared are: least squares cross-validation. biased cross-validation. partitioned cross-validation. and a plug-in rule. The levels of comparison are: asymptotic rate of convergence to the optimum, explici t calculation in the case of one target density. and a simulation study. It is seen that the plug-in bandwidth…

Wicksell 球体截面反演问题中的核估计AI 解读

We consider the estimation of the probability density function of the radii of spheres in a medium, given the radii of their profiles in a random cross-section. This problem is known as Wicksell's corpuscle problem. We present a new estimator related to the classical kernel density estimator and discuss its properties. A comparison is made with other estimators related to the kernel estimator.

带宽选择器为何倾向于选择较小带宽及其修正方法AI 解读

This note is concerned with the problem of automatic data-driven bandwidth selectors for nonparametric regression. Though some selectors were shown to be consistent and asymptotically unbiased by Rice (1984) and Hãrdle, Hall & Marron (1988), it is often observed in simulation studies that most selectors are biased toward undersmoothing. An explanation for this is given. The source of the large sample variation in the bandwidth estimates is also pointed out. This leads to the…

非参数核密度估计的可容许性与偏差改进AI 解读

The paper introduces the idea of inadmissible kernels and shows that an Epanechnikov type kernel is the only admissible kernel. An analysis of kernel density estimates leads to two new methods of bias reduction. We also discuss a general method of improving kernel density estimates in the sense of having smaller mean squared error. Finally we provide a theoretical framework for the operational method of using Abramson's square root law providing tangible and compact forms…

时间序列统计带宽的估计AI 解读

In many time series and signal processing applications such as spectral estimation, signal-to-noise estimation and frequency response estimation it is imperative to have a good estimate of the bandwidth of the time series. In many scientific applications deconvolution is carried out over the signal-dominated part of the spectrum resulting in a spectrum which is dominantly unimodal, and hence a technique like that used for smoothing windows can be used to define the…

截断数据的线性秩统计量AI 解读

Motivated by Prentice's (1978) generalization of linear rank statistics for censored data, we introduce a similar kernel for deriving linear rank statistics for truncated data. They take very similar forms to those of Prentice's statistics. Moreover, we also show that they can be expressed equivalently in weighted log rank-type forms, thus providing natural variance estimators. Explicit forms corresponding to Wilcoxon and log rank tests are obtained. Extensions to data…

可变带宽曲线估计量的偏差AI 解读

A major difficulty in understanding the properties of variable bandwidth methods (Breiman, Meisel & Purcell, 1977; Abramson, 1982) is that extremely lengthy and complex algebra is needed to assess the influence of bias. Indeed, the complexity is so great that it has forced investigators to use computer algebraic manipulation to determine formulae for bias. In this note we completely eliminate these algebraic obstacles by presenting a simple easy-to-use formula which gives…

核回归估计中的权重选择AI 解读

For kernel regression estimation a weighting scheme due to Nadaraya and Watson has been associated with random design, and a convolution type weighting scheme with fixed design. Based on integrated mean square error, none of the estimators is uniformly optimal in either design. However, the convolution type weights are minimax optimal. Further advantages of this estimator can be seen in the structure of the bias.

删失生存数据中风险率变化的非参数分析：变点模型的替代方案AI 解读

As a nonparametric estimator for the point of the most rapid change of a hazard rate we propose the location of an extremum of a nonparametric estimate of the derivative, or equivalently, of a zero of a nonparametric estimate of the second derivative. Using the kernel method for the nonparametric estimation of derivatives of the hazard rate, the asymptotic local limiting distribution and uniform consistency are applied to prove consistency and to find the limiting…

回归函数的非参数估计AI 解读

A data dependent method of estimating a regression function is proposed here. The model is allowed to be heteroscedastic. Applications to piecewise polynomial, spline, orthogonal series, kernel and nearest neighbor methods are discussed.

摘要暂缺

指标模型系数的半参数估计AI 解读

This paper gives a solution to the problem of estimating coefficients of index models, through the estimation of the density-weighted average derivative of a general regression function. A normalized version of the density-weighted average derivative can be estimated by certain linear instrumental variables coefficients. The estimators, based on sample analogies of the product moment representation of the average derivative, are constructed using nonparametric kernel…

回归中的方差函数估计：估计均值的影响AI 解读

SUMMARY We consider estimation of a variance function g in regression problems. Such estimation requires simultaneous estimation of the mean function f. We obtain clear results on the extent to which the smoothness of f influences best rates of convergence for estimating g. For example, in nonparametric regression with two derivatives on g, ‘classical' rates of convergence are possible if and only if the unknown f satisfies a Lipschitz condition of order 13 or more. If a…

空间点过程二阶强度加权积分的估计AI 解读

SUMMARY This paper considers the nonparametric estimation of the integral J=∫0Ttλ2(t)φ(t)dt where λ2(t) is the unknown second-order intensity function of a two-dimensional stationary isotropic point process observed in some region and φ(t) is known for t ϵ [0, T]. An unbiased estimator of J is derived, and a computationally fast approximation to it is proposed. The estimator is then used to obtain a kernel method for smoothing point process data, a new estimator of the…

依赖观测下的稳健非参数回归估计AI 解读

Robust nonparametric estimators for regression and autoregression are proposed for $\varphi$- and $\alpha$-mixing processes. Two families of $M$-type robust equivariant estimators are considered: (i) estimators based on kernel methods and (ii) estimators based on $k$-nearest neighbor kernel methods. Strong consistency of both families is proved under mild conditions. For the first class the result is true under no assumptions whatsoever on the distribution of the…

核条件 Kaplan–Meier 估计的一致收敛性AI 解读

We consider a class of nonparametric regression estimates introduced by Beran to estimate conditional survival functions in the presence of right censoring. An exponential probability bound for the tails of distributions of kernel estimates of conditional survival functions is derived. This inequality is next used to prove weak and strong uniform consistency results. The developments rest on sharp exponential bounds for the oscillation modulus of multivariate empirical…

极端次序统计量稳定性与极大似然核密度估计收敛的关系AI 解读

Let $f$ be a density on the real line and let $f_n$ be the kernel estimate of $f$ in which the smoothing factor is obtained by maximizing the cross-validated likelihood product according to the method of Duin and Habbema, Hermans and Vandenbroek. Under mild regularity conditions on the kernel and $f$, we show, among other things that $\int|f_n - f| \rightarrow 0$ almost surely if and only if the sample extremes of $f$ are strongly stable.

自适应非参数峰值估计AI 解读

It is shown that consistent estimates of the optimal bandwidths for kernel estimators of location and size of a peak of a regression function are available. Such estimates yield the same joint asymptotic distribution of location and size of a peak as the optimal bandwidths themselves. Therefore data-adaptive efficient estimation of peaks is possible. In order to prove this result, the weak convergence of a two-dimensional stochastic process with appropriately scaled…