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广义部分线性单指标模型AI 解读

The typical generalized linear model for a regression of a response Y on predictors (X, Z) has conditional mean function based on a linear combination of (X, Z). We generalize these models to have a nonparametric component, replacing the linear combination α T 0X + β T 0Z by η0(α T 0X) + β T 0Z, where η0(·) is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the “single-index” models, which have β0 = 0. Using…

非参数回归中适应稀疏设计的插值方法AI 解读

We suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing. These methods are based on simple rules, determined by the kernel and bandwidth, for deciding when and where pseudo-design points should be added to augment the original design sequence. New ordinates for the added design points are computed by simple interpolation, then local linear smoothing is applied directly to the expanded dataset. The method is competitive with…

密度导数核估计的根号 n 带宽选择方法AI 解读

Based on a random sample of size n from an unknown density f on the real line, the problem of adaptively selecting the bandwidth in kernel estimation of f (k) is investigated, where f (k) denotes the kth derivative of f. The estimates of density derivatives can be used to evaluate modes and inflection points of f and can be applied to the estimation of scores in certain additive models and to the empirical verification of the law of demand in econometrics. For all k, the…

协变量缺失回归中的加权半参数估计AI 解读

This article investigates estimation of the regression coefficients in an assumed mean function when covariates on some subjects are missing. We examine the performance of a Horvitz and Thompson (1952)-type weighted estimator by using different estimates of the selection probabilities, which may be treated as nuisance parameters (or a nuisance function). In particular, we investigate the properties of the estimate of the regression parameters when the selection probabilities…

适应非参数回归稀疏设计的插值方法：评论AI 解读

We suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing. These methods are based on simple rules, determined by the kernel and bandwidth, for deciding when and where pseudo-design points should be added to augment the original design sequence. New ordinates for the added design points are computed by simple interpolation, then local linear smoothing is applied directly to the expanded dataset. The method is competitive with…

非参数回归中适应稀疏设计的插值方法AI 解读

We suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing. These methods are based on simple rules, determined by the kernel and bandwidth, for deciding when and where pseudo-design points should be added to augment the original design sequence. New ordinates for the added design points are computed by simple interpolation, then local linear smoothing is applied directly to the expanded dataset. The method is competitive with…

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摘要暂缺

白噪声问题中的极小极大线性估计AI 解读

.Linear estimation of $f(x)$ at a point in a white noise model is considered. The exact linear minimax estimator of $f(0)$ is found for the family of $f(x)$ in which $f'(x)$ is Lip (M). The resulting estimator is then used to verify a conjecture of Sacks and Ylvisaker concerning the near optimality of the Epanechnikov kernel.

加性非线性 ARX 时间序列与投影估计AI 解读

We propose projections as means of identifying and estimating the components (endogenous and exogenous) of an additive nonlinear ARX model. The estimates are nonparametric in nature and involve averaging of kernel-type estimates. Such estimates have recently been treated informally in a univariate time series situation. Here we extend the scope to nonlinear ARX models and present a rigorous theory, including the derivation of asymptotic normality for the projection estimates…

摘要暂缺

多分类回归AI 解读

An automatic procedure that uses linear splines and their tensor products is proposed for fitting a regression model to data involving a polychotomous response variable and one or more predictors. The fitted model can be used for multiple classification. The automatic fitting procedure involves maximum likelihood estimation, stepwise addition, stepwise deletion, and model selection by the Akaike information criterion, cross-validation, or an independent test set. A modified…

混合自适应样条AI 解读

An adaptive spline method for smoothing is proposed that combines features from both regression spline and smoothing spline approaches. One of its advantages is the ability to vary the amount of smoothing in response to the inhomogeneous “curvature” of true functions at different locations. This method can be applied to many multivariate function estimation problems, which is illustrated by an application to smoothing temperature data on the globe. The method's performance…

分位数平滑样条的局部渐近理论AI 解读

Quantile smoothing splines were introduced by Koenker, Ng and Portnoy as natural and appealing estimates of conditional quantiles of response variables. The natural setting for the problem considers minimization of a weighted combination of a "fit" penalty and a "roughness" penalty over the space of functions whose derivatives have bounded variation. Although this space is not traditional, Shen has shown recently that the quantile smoothing splines do indeed converge at the…

局部自适应回归样条AI 解读

Least squares penalized regression estimates with total variation penalties are considered. It is shown that these estimators are least squares splines with locally data adaptive placed knot points. The definition of these variable knot splines as minimizers of global functionals can be used to study their asymptotic properties. In particular, these results imply that the estimates adapt well to spatially inhomogeneous smoothness. We show rates of convergence in bounded…

利用局部多项式回归拟合二元加性模型AI 解读

While the additive model is a popular nonparametric regression method, many of its theoretical properties are not well understood, especially when the backfitting algorithm is used for computation of the estimators. This article explores those properties when the additive model is fitted by local polynomial regression. Sufficient conditions guaranteeing the asymptotic existence of unique estimators for the bivariate additive model are given. Asymptotic approximations to the…

长程依赖的极限理论及相关模型的统计推断AI 解读

This paper provides limit theorems for multivariate, possibly non-Gaussian stationary processes whose spectral density matrices may have singularities not restricted at the origin, applying those limiting results to the asymptotic theory of parameter estimation and testing for statistical models of long-range dependent processes. The central limit theorems are proved based on the assumption that the innovations of the stationary processes satisfy certain mixing conditions…

基于预测的选择准则之最优性与估计量收敛速度AI 解读

Summary Several estimators of squared prediction error have been suggested for use in model and bandwidth selection problems. Among these are cross-validation, generalized cross-validation and a number of related techniques based on the residual sum of squares. For many situations with squared error loss, e.g. nonparametric smoothing, these estimators have been shown to be asymptotically optimal in the sense that in large samples the estimator minimizing the selection…

乘性误差平滑回归模型中的变量变换AI 解读

Summary We consider whether one should transform to estimate nonparametrically a regression curve sampled from data with a constant coefficient of variation, i.e. with multiplicative errors. Kernel-based smoothing methods are used to provide curve estimates from the data both in the original units and after transformation. Comparisons are based on the mean-squared error (MSE) or mean integrated squared error (MISE), calculated in the original units. Even when the data are…

考虑边界的密度导数乘积积分估计AI 解读

Summary Integrated squared density derivatives are important to the plug-in type of bandwidth selector for kernel density estimation. Conventional estimators of these quantities are inefficient when there is a non-smooth boundary in the support of the density. We introduce estimators that utilize density derivative estimators obtained from local polynomial fitting. They retain the rates of convergence in mean-squared error that are familiar from non-boundary cases, and the…

多变量非参数关系中因子数量的推断AI 解读

This paper considers the problem of determining the number of factors in a multivariate nonparametric relationship. The definition of factors given is broad enough to encompass a number of potential applications in econometrics, including inferring the rank of demand, consistent tests for lack of identification in linear instrumental variable models, and testing arbitrage pricing theory. The paper gives both series and kernel methods for testing hypotheses concerning, and…

改进非参数回归中的卷积与插值方法AI 解读

Following earlier work of Jones, Davies & Park (1994) we develop estimators based on convolution and interpolation methods, with the aim of reducing their variance and making them competitive with local linear smoothers. We argue that the classic convolution and interpolation approaches due to Gasser & Müller (1979) and Clark (1977) exhibit inflated variance on account of the relatively high variability of weights used in their construction. We show that, by convolving or…

不完全广义 L 统计量AI 解读

Given data $X_1, \dots, X_n$ and a kernel h with m arguments, Serfling introduced the class of generalized L-statistics (GL-statistics), which is defined by taking linear combinations of the ordered $h(X_{i_1}, \dots, X_{i_m})$ where $(i_1, \dots, i_m)$ ranges over all $n!/(n - m)!$ distinct m-tuples of $(1, \dots, n)$. In this paper we derive a class of incomplete generalized L-statistics (IGL-statistics) by taking linear combinations of the ordered elements from a subset…

核密度估计的一种普遍适用平滑参数AI 解读

We define a minimum distance estimate of the smoothing factor for kernel density estimates, based on a methodology first developed by Yatracos. It is shown that if $f_{nh}$ denotes the kernel density estimate on $\mathbb{R}^d$ for an i.i.d. sample of size n drawn from an unknown density f, where h is the smoothing factor, and if $f_n$ is the kernel estimate with the same kernel and with the proposed new data-based smoothing factor, then, under a regularity condition on the…