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片段式及相关类型函数型数据的协方差估计AI 解读

Aurore Delaiglea , Peter Halla, Wei Huanga* & Alois Kneipb a ACEMS and School of Mathematics and Statistics, University of Melbourne , Parkville , VIC , Australia;; b Department of Economics and Hausdorff Center for Mathematics, Universität Bonn , Bonn , Germany † This work was initiated with Peter Hall during a visit of Kneip to the University Melbourne. Peter died on January 9, 2016.Color versions of one or more of the figures in the article can be found online at…

动态非参数生产模型中的推断：Malmquist 指数的中心极限定理AI 解读

The Malmquist index gives a measure of productivity in dynamic settings and has been widely applied in empirical work. The index is typically estimated using envelopment estimators, particularly data envelopment analysis (DEA) estimators. Until now, inference about productivity change measured by Malmquist indices has been problematic, including both inference regarding productivity change experienced by particular firms as well as mean productivity change. This paper…

函数型预测变量非参数回归中影响点的超一致估计AI 解读

Summary Predicting scalar outcomes by using functional predictors is a classical problem in functional data analysis. In many applications, however, only specific locations or time points of the functional predictors have an influence on the outcome. Such ‘points of impact’ are typically unknown and must be estimated in addition to estimating the usual model components. We show that our points-of-impact estimator enjoys a superconsistent rate of convergence and does not…

We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression operators as a special case. We show the optimality of our reconstruction operator and demonstrate that the usually considered regression operators generally cannot be optimal reconstruction operators. Our estimation theory allows for…

非参数生产模型的假设检验AI 解读

Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiency of production. Practitioners use DEA estimators far more frequently than FDH estimators, implicitly assuming that production sets are convex. Moreover, use of the constant returns to scale (CRS) version of the DEA estimator requires an assumption of CRS. Although bootstrap methods have been developed for making inference about the efficiencies of individual units,…

具有影响点的函数型线性回归AI 解读

The paper considers functional linear regression, where scalar responses $Y_{1},\ldots,Y_{n}$ are modeled in dependence of i.i.d. random functions $X_{1},\ldots,X_{n}$. We study a generalization of the classical functional linear regression model. It is assumed that there exists an unknown number of “points of impact,” that is, discrete observation times where the corresponding functional values possess significant influences on the response variable. In addition to…

当偏差压倒方差：DEA 与 FDH 效率得分的中心极限定理AI 解读

Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiencies of production units. In applications, both efficiency scores for individual units as well as average efficiency scores are typically reported. While several bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods have existed for making inference about mean efficiency levels. This paper shows that…

未知测量误差方差下的生产前沿估计AI 解读

Frontier estimation appears in productivity analysis. Firm’s performance is measured by the distance between its output and an optimal production frontier. Frontier estimation becomes difficult if outputs are measured with noise and most approaches rely on restrictive parametric assumptions. This paper contributes to nonparametric approaches, with unknown frontier and unknown variance of a normally distributed error. We propose a nonparametric method identifying and…

异质人群的个体与总体需求收入弹性AI 解读

SUMMARY This paper deals with different concepts of income elasticities of demand for a heterogeneous population and the relationship between individual and aggregate elasticities. In general, the aggregate elasticity is not equal to the mean of individual elasticities. The difference depends on the heterogeneity of the population and is quantified by a covariance term. Sign and magnitude of this term are determined by an empirical analysis based on the UK Family Expenditure…

面板数据中时间趋势异质性的新估计方法AI 解读

This paper introduces a new estimation method for arbitrary temporal heterogeneity in panel data models. The paper provides a semiparametric method for estimating general patterns of cross-sectional specific time trends. The methods proposed in the paper are related to principal component analysis and estimate the time-varying trend effects using a small number of common functions calculated from the data. An important application for the new estimator is in the estimation…

高维回归分析中的因子模型与变量选择AI 解读

The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression by using a factor approach: it is assumed that the predictor vector can be decomposed into a sum of two uncorrelated random components reflecting common factors and specific variabilities of the explanatory variables. It is shown that the…

函数型线性回归的平滑样条估计AI 解读

The paper considers functional linear regression, where scalar responses Y1, …, Yn are modeled in dependence of random functions X1, …, Xn. We propose a smoothing splines estimator for the functional slope parameter based on a slight modification of the usual penalty. Theoretical analysis concentrates on the error in an out-of-sample prediction of the response for a new random function Xn+1. It is shown that rates of convergence of the prediction error depend on the…

共同函数主成分AI 解读

Functional principal component analysis (FPCA) based on the Karhunen–Loève decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal components for two sample problems. Our research is motivated not only by the theoretical challenge of this data situation, but also by the actual question of dynamics of implied volatility (IV) functions. For different maturities the log-returns of…

非参数前沿模型中 DEA 估计量的渐近理论与一致自助法AI 解读

Nonparametric data envelopment analysis (DEA) estimators based on linear programming methods have been widely applied in analyses of productive efficiency. The distributions of these estimators remain unknown except in the simple case of one input and one output, and previous bootstrap methods proposed for inference have not been proved consistent, making inference doubtful. This paper derives the asymptotic distribution of DEA estimators under variable returns to scale.…

摘要暂缺

生产效率得分的非参数 DEA 估计量收敛性札记AI 解读

Efficiency scores of production units are measured by their distance to an estimated production frontier. Nonparametric data envelopment analysis estimators are based on a finite sample of observed production units, and radial distances are considered. We investigate the consistency and the speed of convergence of these estimated efficiency scores (or of the radial distances) in the very general setup of a multi-output and multi-input case. It is shown that the speed of…

在曲线样本中寻找结构特征AI 解读

The shape of a regression curve can to a large extent be characterized by the succession of structural features like extrema, inflection points, and so on. When analyzing a sample of regression curves, it is often important to know at an early stage of data analysis which structural features are occurring consistently in each curve of the sample. Such a definition is usually not easy due to substantial interindividual variation both in the x and the y axis and due to the…

形状不变性下的非线性回归模型估计AI 解读

Given data from a sample of noisy curves, we consider a nonlinear parametric regression model with unknown model function. An iterative algorithm for estimating individual parameters as well as the model function is introduced under the assumption of a certain shape invariance: the individual regression curves are obtained from a common shape function by linear transformations of the axes. Our algorithm is based on least-squares methods for parameter estimation and on…

相似曲线数据中共同回归函数的非参数估计AI 解读

The paper is concerned with data from a collection of different, but related, regression curves $(m_j0_{j = 1}, \ldots, N, N \gg 1$. In statistical practice, analysis of such data is most frequently based on low-dimensional linear models. It is then assumed that each regression curve $m_j$ is a linear combination of a small number $L \ll N$ of common functions $g_1, \ldots, g_L$k. For example, if all $m_j$'s are straight lines, this holds with $L = 2, g_1 \equiv 1$ and $g_2(x) = x$…

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…

残差相关时核回归的带宽选择AI 解读

Standard techniques for selecting the bandwidth of a kernel estimator from the data in a nonparametric regression model perform badly when the errors are correlated. In this paper we propose a modified version of an existing plug-in bandwidth selector. The method is generalized to stationary error variables by estimating a functional of the residual covariance function. The proposed bandwidth selector shows good properties in asymptotic theory and in simulations without…

用于分析曲线样本数据的统计工具AI 解读

The paper is concerned with data representing a sample of smooth curves which can be considered as independent realizations of an underlying biological (chemical, $\ldots$) process. Such samples of curves often possess the following features: There is a typical structural pattern common to all curves of the sample. On the other hand, individual realizations of the typical shape show different dynamics and intensity. In particular, typical peaks are shifted from individual to…

残差相关时核回归的带宽选择AI 解读

Standard techniques for selecting the bandwidth of a kernel estimator from the data in a nonparametric regression model perform badly when the errors are correlated. In this paper we propose a modified version of an existing plug-in bandwidth selector. The method is generalized to stationary error variables by estimating a functional of the residual covariance function. The proposed bandwidth selector shows good properties in asymptotic theory and in simulations without…

灵活快速的自动平滑方法AI 解读

The choice of smoothing parameter or bandwidth is crucial when applying nonparametric regression estimators such as kernel estimators. The optimal choice depends on the data at hand. A data-driven bandwidth selection, close to the optimal one, would make these curve estimators objective, more reliable, and easier to use. Minimizing residual mean squared error criteria, such as cross-validation, have been frequently proposed to estimate the optimal smoothing parameter.…