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有序线性平滑器AI 解读

This paper deals with the following approach for estimating the mean $\mu$ of an $n$-dimensional random vector $Y$: first, a family $\mathbf{S}$ of $n \times n$ matrices is specified. Then, an element $\widehat{S} \in \mathbf{S}$ is selected by Mallows $C_L$, and $\widehat{\mu} = \widehat{S}\cdot Y$. The case is considered that $\mathbf{S}$ is an "ordered linear smoother" according to some easily interpretable, qualitative conditions. Examples include linear smoothing…

变点问题中的线性估计量AI 解读

Observations $X_i$ are uncorrelated with means $\theta_i, i = 1,\cdots, n$, and variances 1. The linear estimators $\widehat{\theta} = T\mathbf{X}$, for some $n \times n$ matrix $T$, are widely used in smoothing problems, where it is assumed that neighbouring parameter values are similar. The smoothness assumption is violated in change point problems, where neighbouring parameter values are equal, except at some unspecified change points where there are jumps of unknown size…

筛估计的收敛速度AI 解读

In this paper, we develop a general theory for the convergence rate of sieve estimates, maximum likelihood estimates (MLE's) and related estimates obtained by optimizing certain empirical criteria in general parameter spaces. In many cases, especially when the parameter space is infinite dimensional, maximization over the whole parameter space is undesirable. In such cases, one has to perform maximization over an approximating space (sieve) of the original parameter space…

相关曲线：回归局部解释方差的度量AI 解读

We call (a model for) an experiment heterocorrelatious if the strength of the relationship between a response variable Y and a covariate X is different in different regions of the covariate space. For such experiments we introduce a correlation curve that measures heter-ocorrelaticity in terms of the variance explained by regression locally at each covariate value. More precisely, the squared correlation curve is obtained by first expressing the usual linear model “variance…

删失回归：局部线性近似及其应用AI 解读

Various statistical tools are available for modeling the relationship between response and covariate if the data are fully observable. In the situation of censored data, however, those tools are no longer directly applicable. This article provides an easily implemented methodology for modeling the association, based on censored data. The form of the regression relationship will be completely determined by the data; no assumptions are made about this form. Basic ideas behind…

作为回归局部方差解释度量的相关曲线AI 解读

We call (a model for) an experiment heterocorrelatious if the strength of the relationship between a response variable Y and a covariate X is different in different regions of the covariate space. For such experiments we introduce a correlation curve that measures heter-ocorrelaticity in terms of the variance explained by regression locally at each covariate value. More precisely, the squared correlation curve is obtained by first expressing the usual linear model “variance…

摘要暂缺

基于核方法的参数密度拟合优度检验AI 解读

Let F denote a distribution function defined on the probability space (Ω, , P ), which is absolutely continuous with respect to the Lebesgue measure in R d with probability density function f . Let f 0 (·,β) be a parametric density function that depends on an unknown p × 1 vector β. In this paper, we consider tests of the goodness-of-fit of f 0 (·,β) for f (·) for some β based on (i) the integrated squared difference between a kernel estimate of f (·) and the quasimaximum…

部分均值的核估计与一般方差估计量AI 解读

Econometric applications of kernel estimators are proliferating, suggesting the need for convenient variance estimates and conditions for asymptotic normality. This paper develops a general “delta-method” variance estimator for functionals of kernel estimators. Also, regularity conditions for asymptotic normality are given, along with a guide to verify them for particular estimators. The general results are applied to partial means, which are averages of kernel estimators…

部分线性模型的数据驱动有效估计量AI 解读

Chen and Shiau showed that a two-stage spline smoothing method and the partial regression method lead to efficient estimators for the parametric component of a partially linear model when the smoothing parameter is a deterministic sequence tending to zero at an appropriate rate. This paper is concerned with the large-sample behavior of these estimators when the smoothing parameter is chosen by the generalized cross validation (GCV) method or Mallows' $C_L$. Under mild…

通过平滑经验变换降低核密度估计偏差AI 解读

A modification of kernel density estimation is proposed. The first step is ordinary kernel estimation of the density and its cdf. In the second step the data are transformed, using this estimated cdf, to an approximate uniform (or normal or other target) distribution. The density and cdf of the transformed data are then estimated by the kernel method and, by change of variable, converted to new estimates of the density and the cdf of the original data. This process is…

多元函数估计中的多项式样条及其张量积AI 解读

Let $X_1, \ldots, X_M, Y_1,\ldots, Y_N$ be random variables, and set $\mathbf{X} = (X_1, \ldots, X_M)$ and $\mathbf{Y} = (Y_1, \ldots, Y_N)$. Let $\varphi$ be the regression or logistic or Poisson regression function of $\mathbf{Y}$ on $\mathbf{X}(N = 1)$ or the logarithm of the density function of $\mathbf{Y}$ or the conditional density function of $\mathbf{Y}$ on $\mathbf{X}$. Consider the approximation $\varphi^\ast$ to $\varphi$ having a suitably defined form involving a…

多自变量单调函数的可行非参数估计AI 解读

This article presents a two-stage estimation procedure that uses an ad hoc but very easily implemented isotonization of a kernel estimator. This procedure yields an isotonic estimator with the convergence properties of the kernel estimator. Although the isotonization in the second stage does not satisfy the least squares condition, this hybrid estimator may be considered to be a multidimensional generalization of similar procedures for the one-dimensional case suggested by…

随机缺失数据下均值泛函的非参数估计AI 解读

This article considers a distribution-free estimation procedure for a basic pattern of missing data that often arises from the wellknown double sampling in survey methodology. Without parametric modeling of the missing mechanism or the joint distribution, kernel regression estimators are used to estimate mean functionals through empirical estimation of the missing pattern. A generalization of the method of Cheng and Wei is verified under the assumption of missing at random.…

稳健非参数回归的 L1 方法AI 解读

Consider the problem of estimating the regression function underlying a set of data that is contaminated by a heavy-tailed error distribution. The two standard approaches to such a problem are each flawed. Robust parametric least squares is appropriate only if there is good reason to believe that the underlying function has some particular form, whereas most nonparametric regression methods are asymptotically equivalent to kernel regression methods, which are not resistant…

多元密度估计：理论、实践与可视化AI 解读

Representation and Geometry of Multivariate Data. Nonparametric Estimation Criteria. Histograms: Theory and Practice. Frequency Polygons. Averaged Shifted Histograms. Kernel Density Estimators. The Curse of Dimensionality and Dimension Reduction. Nonparametric Regression and Additive Models. Special Topics. Appendices. Indexes.

含解释变量的计数过程非参数核估计AI 解读

SUMMARY Cox's proportional hazards model assumes that the duration hazard rate factors into a product of a baseline hazard rate and a nonnegative function of explanatory variables. An estimate of the baseline hazard rate, hence also of overall hazard rate, is proposed, based on a smoothing procedure using a kernel function. It is shown that the proposed estimator is uniformly consistent and converges weakly to a Gaussian process. Bandwidth selection issues are also discussed.

摘要暂缺

将疾病进展信息纳入生存分析的核方法AI 解读

This paper considers incorporating information on disease progression in the analysis of survival. A three-state model is assumed, with the distribution of each transition estimated separately. The distribution of survival following progression can depend on the time of progression. Kernel methods are used to give consistent estimators under general forms of dependence. The estimators for the individual transitions are then combined into an overall estimator of the survival…

图像数据离散薄板平滑样条的快速计算AI 解读

This paper describes a fast method of computation for a discretized version of the thin-plate spline for image data. This method uses the Discrete Cosine Transform and is contrasted with a similar approach based on the Discrete Fourier Transform. The two methods are similar from the point of view of speed, but the errors introduced near the edge of the image by use of the Discrete Fourier Transform are significantly reduced when the Discrete Cosine Transform is used. This is…

风险率估计中最小二乘交叉验证带宽的收敛速度AI 解读

It is known that the least squares cross-validation bandwidth is asymptotically optimal in the case of kernel-based density and hazard rate estimation in the settings of both complete and randomly right-censored samples. From a practical point of view, it is important to know at what rate the cross-validation bandwidth converges to the optimal. In this paper we answer this question in a general setup which unifies all four possible cases.

含变量测量误差的非参数回归AI 解读

The effect of errors in variables in nonparametric regression estimation is examined. To account for errors in covariates, deconvolution is involved in the construction of a new class of kernel estimators. It is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution. In fact, there are two types of rates of convergence according to whether the error…

反卷积、频带限制与四阶谱AI 解读

In the largest application area of time series analysis—geophysical exploration—the underlying innovations sequence is of primary interest and must be estimated. This sequence is estimated by deconvolving the non-Gaussian, noninvertible time series. This involves estimation of a phase-shift correction from the time series, which can be carried out by maximizing the kurtosis of the series. Unfortunately, the method is hampered by the fact that the time series is typically…

L1回归估计量分布的解析与自助法近似AI 解读

Edgeworth and bootstrap approximations to estimator distributions in L1 regression are described. Analytic approximations based on Edgeworth expansions that mix lattice and nonlattice components and allow for an intercept term in the regression are developed under mild conditions, which do not even require a density for the error distribution. Under stronger assumptions on the error distribution, the Edgeworth expansion assumes a simpler form. Bootstrap approximations are…