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Cox 模型中的回归样条：肝病协变量效应应用AI 解读

The Cox proportional hazards model restricts the log hazard ratio to be linear in the covariates. A smooth nonlinear covariate effect may go undetected in this model but can be well approximated by a spline function. A survival model based on data from a clinical trial of primary biliary cirrhosis is developed using regression splines, and the resulting log hazard ratio estimates are compared with those from nonparametric methods. We remove the linear restriction on the log…

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…

摘要暂缺

论非参数核密度估计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…

非平稳与不可逆时间序列模型渐近推断的 Fredholm 方法AI 解读

A unified approach which I call the Fredholm approach is suggested for the study of asymptotic behavior of estimators and" test statistics arising from nonstationary and/or noninvertible time series models. Some limit theorems are given concerning the distribution of (the ratio of) quadratic (plus linear) forms in random variables generated by a linear process that is not necessarily stationary. Especially, the limiting characteristic function is derived explicitly via the…

概率密度导数估计的带宽选择AI 解读

SUMMARY An adaptation of least squares cross-validation is proposed for bandwidth choice in the kernel estimation of the derivatives of a probability density. The practicality of the method is demonstrated by an example and a simulation study. Theoretical justification is provided by an asymptotic optimality result.

随机过程参数估计中广义交叉验证与修正最大似然的比较AI 解读

Wahba compared the performance of generalized cross validation (GCV) and modified maximum likelihood (MML) procedures for choosing the smoothing parameter of a smoothing spline. This work makes a more careful study of the two procedures when the stochastic model motivating the modified maximum likelihood estimate is correct. In particular, it is shown that in the case of the linear smoothing spline with equally spaced observations, both estimates are asymptotically normal…

条件分位数的核估计与近邻估计AI 解读

Let $(X_1, Z_1), (X_2, Z_2), \ldots, (X_n, Z_n)$ be iid as $(X, Z), Z$ taking values in $R^1$, and for $0 < p < 1$, let $\xi_p(x)$ denote the conditional $p$-quantile of $Z$ given $X = x,$ i.e., $P(Z \leq \xi_p(x)\mid X = x) = p$. In this paper, kernel and nearest-neighbor estimators of $\xi_p(x)$ are proposed. In order to study the asymptotics of these estimates, Bahadur-type representations of the sample conditional quantiles are obtained. These representations are used to…

相关误差数据的核平滑AI 解读

Kernel smoothing is a common method of estimating the mean function in the nonparametric regression model y = f(x) + ε, where f(x) is a smooth deterministic mean function and ε is an error process with mean zero. In this article, the mean squared error of kernel estimators is computed for processes with correlated errors, and the estimators are shown to be consistent when the sequence of error processes converges to a mixing sequence. The standard techniques for bandwidth…

非高斯回归模型中的自适应样条平滑AI 解读

A convenient and efficient algorithm for penalized likelihood smoothing spline regression is proposed and illustrated. The amount of smoothing is tuned adaptively via the generalized cross-validation method. Under certain conditions, the method is shown to approximately minimize the expected Kullback-Leibler discrepancy in modeling one-parameter exponential family observations through the canonical parameter. The algorithm is applied to fit logistic models using interaction…

摘要暂缺

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…

平稳经济时间序列的无模型渐近最优预测AI 解读

Given observations on a stationary economic vector time series process we show that the best h -step ahead forecast (best in the sense of having minimal mean square forecast error) of one of the variables can be consistently estimated by nonparametric regression on an ARMA memory index. Our approach is based on a combination of the ARMA memory index modeling approach of Bierens [7] with a modification to time series of the nonparametric kernel regression approach of Devroye…

N-kernel 软件评述AI 解读

Abstract The package performs estimation and prediction in the context of time‐series or cross‐section nonparametric models. It is menu‐driven and very easy to operate. The manual reads well. This version has some limitations, which can easily be corrected. Nevertheless it provides a useful pedagogical and research tool, even for people not familiar with nonparametric analysis.

回归函数的估计AI 解读

In this paper, an entropy approach is proposed to establish rates of convergence for estimators of a regression function. General regression problems are considered, with linear regression, splines and isotonic regression as special cases. The estimation methods studied are least squares, least absolute deviations and penalized least squares. Common features of these methods and various regression problems are highlighted.

混合过程下非参数模型稳健估计量的渐近分布AI 解读

In this paper we obtain the asymptotic distribution of robust nonparametric autoregression estimators for dependent observations. Weights based on kernel and nearest-neighbor methods are considered.

相依数据核密度估计的数据驱动带宽选择AI 解读

The bandwidth selection problem in kernel density estimation is investigated in situations where the observed data are dependent. The classical leave-out technique is extended, and thereby a class of cross-validated bandwidths is defined. These bandwidths are shown to be asymptotically optimal under a strong mixing condition. The leave-one out, or ordinary, form of cross-validation remains asymptotically optimal under the dependence model considered. However, a simulation…

估计混合密度与混合分布的傅里叶方法AI 解读

Let $X_1, X_2, \cdots$ be iid observations from a mixture density $f(x) = \int f(x \mid \theta)dG(\theta)$, where $f(x \mid \theta)$ is a known parametric family of density functions and $G$ is an unknown distribution function. This paper concerns estimating the mixing density $g = G'$ and the mixing distribution $G$. Fourier methods are used to derive kernel estimators, upper bounds for their rates of convergence and lower bounds for the optimal rate of convergence.…

ACE 类方法的一致性AI 解读

The ACE (alternating conditional expectations) algorithm developed by Breiman and Friedman is an iterative method for finding optimal transformations of variables in multiple regression. Recently, several authors have extended ACE to discriminant analysis, time series and principal components. The central idea of ACE and of each of these extensions is that an optimal transformation $\phi^\ast$ minimizes a squared error-related functional over a Hilbert space, subject to…

对数样条模型的大样本推断AI 解读

Let $f$ be a continuous and positive unknown density on a known compact interval $\mathscr{Y}$. Let $F$ denote the distribution function of $f$ and let $Q = F^{-1}$ denote its quantile function. A finite-parameter exponential family model based on $B$-splines is constructed. Maximum-likelihood estimation of the parameters of the model based on a random sample of size $n$ from $f$ yields estimates $\hat{f, F}$ and $\hat{Q}$ of $f, F$ and $Q$, respectively. Under mild…

密度估计中的最大平滑原则AI 解读

We propose a widely applicable method for choosing the smoothing parameters for nonparametric density estimators. It has come to be realized in recent years (e.g., see Hall and Marron 1987; Scott and Terrell 1987) that cross-validation methods for finding reasonable smoothing parameters from raw data are of very limited practical value. Their sampling variability is simply too large. The alternative discussed here, the maximal smoothing principle, suggests that we consider…

核分位数估计量AI 解读

For an estimator of quantiles, the efficiency of the sample quantile can be improved by considering linear combinations of order statistics, that is, L estimators. A variety of such methods have appeared in the literature; an important aspect of this article is that asymptotically several of these are shown to be kernel estimators with a Guassian kernel, and the bandwidths are identified. It is seen that some implicit choices of the smoothing parameter are asymptotically…

利用非参数回归检验线性模型的拟合优度AI 解读

This article investigates the use of nonparametric regression methodology to test the adequacy of a parametric linear model. The large-sample properties of parametric goodness-of-fit tests for linearity are considered. The inadequacies of such tests lead to the proposal of new tests that are constructed from nonparametric regression fits to the residuals from linear regression. Large-sample theory is derived for two variants of this type of statistic. The results demonstrate…

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.