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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…

非平稳时间序列的函数系数模型AI 解读

This paper studies functional coefficient regression models with nonstationary time series data, allowing also for stationary covariates. A local linear fitting scheme is developed to estimate the coefficient functions. The asymptotic distributions of the estimators are obtained, showing different convergence rates for the stationary and nonstationary covariates. A two-stage approach is proposed to achieve estimation optimality in the sense of minimizing the asymptotic mean…

谱均值及比率统计量的置信区间AI 解读

We propose a new method, to construct confidence intervals for spectral mean and related ratio statistics of a stationary process, that avoids direct estimation of their asymptotic variances. By introducing a bandwidth, a self-normalization procedure is adopted and the distribution of the new statistic is asymptotically nuisance-parameter free. The bandwidth is chosen using information criteria and a moving average sieve approximation. Through a simulation study, we…

存在不依从的随机试验中因果效应的高效非参数估计AI 解读

Causal approaches based on the potential outcome framework provide a useful tool for addressing noncompliance problems in randomized trials. We propose a new estimator of causal treatment effects in randomized clinical trials with noncompliance. We use the empirical likelihood approach to construct a profile random sieve likelihood and take into account the mixture structure in outcome distributions, so that our estimator is robust to parametric distribution assumptions and…

非参数单调函数估计的贝叶斯方法AI 解读

Summary The paper proposes two Bayesian approaches to non-parametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay that allows unconstrained estimation. The second approach uses a Bayesian regression spline model of Smith and Kohn with a mixture distribution of constrained normal distributions as the prior for the regression coefficients to ensure the monotonicity of…

含交互作用的半参数模型检验及基因—环境交互应用AI 解读

Summary Motivated from the problem of testing for genetic effects on complex traits in the presence of gene–environment interaction, we develop score tests in general semiparametric regression problems that involves Tukey style 1 degree-of-freedom form of interaction between parametrically and non-parametrically modelled covariates. We find that the score test in this type of model, as recently developed by Chatterjee and co-workers in the fully parametric setting, is biased…

样本选择模型的两步级数估计AI 解读

Sample selection models are important for correcting the effects of non-random sampling. This paper is about semiparametric estimation using a series approximation to the correction term. Regression spline and power series approximations are considered. Asymptotic normality and consistency of an asymptotic variance estimator are shown. Copyright (C) The Author(s). Journal compilation (C) Royal Economic Society 2009

结构非参数协整回归AI 解读

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel estimates, and frequently leads to ill-posed inverse problems. In functional…

动态光滑系数模型的非参数分位数估计AI 解读

We suggest quantile regression methods for a class of smooth coefficient time series models. We use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quantile framework. We establish the asymptotic properties of both the local polynomial and local constant estimators for α-mixing time series. We also suggest a bandwidth selector based on the nonparametric version of the Akaike information criterion, along with a consistent…

非参数核检验中的带宽选择AI 解读

We propose a sound approach to bandwidth selection in nonparametric kernel testing. The main idea is to find an Edgeworth expansion of the asymptotic distribution of the test concerned. Due to the involvement of a kernel bandwidth in the leading term of the Edgeworth expansion, we are able to establish closed-form expressions to explicitly represent the leading terms of both the size and power functions and then determine how the bandwidth should be chosen according to…

经济函数的动态演化：收益率曲线建模与预测AI 解读

The class of functional signal plus noise (FSN) models is introduced that provides a new, general method for modeling and forecasting time series of economic functions. The underlying, continuous economic function (or “signal”) is a natural cubic spline whose dynamic evolution is driven by a cointegrated vector autoregression for the ordinates (or “y-values”) at the knots of the spline. The natural cubic spline provides flexible cross-sectional fit and results in a linear…

通过子空间投影实现基于相关性的函数型聚类AI 解读

A correlation-based functional clustering method is proposed for grouping curves with similar shapes. A correlation between two random functions defined through the functional inner product is used as a similarity measure. Curves with similar shapes are embedded in the cluster subspace spanned by a mean shape function and eigenfunctions of the covariance kernel. The cluster membership prediction for each curve attempts to maximize the functional correlation between the…

弹性估计的推断方法AI 解读

Elasticities are often estimated from the results of demand analysis. However, drawing inferences from them may involve assumptions that could influence the outcome. In this paper we investigate one of the most common forms of elasticity which is defined as a ratio of estimated relationships and demonstrate how the Fieller method for the construction of confidence intervals can be used to draw inferences. We estimate the elasticities of expenditure from Engel curves using a…

半参数多指标模型的设定与估计AI 解读

We propose an easy to use derivative-based two-step estimation procedure for semiparametric index models, where the number of indexes is not known a priori. In the first step various functionals involving the derivatives of the unknown function are estimated using nonparametric kernel estimators, in particular the average outer product of the gradient (AOPG). By testing the rank of the AOPG we determine the required number of indexes. Subsequently, we estimate the index…

纵向数据边际回归样条的渐近性质AI 解读

There have been studies on how the asymptotic efficiency of a nonparametric function estimator depends on the handling of the within-cluster correlation when nonparametric regression models are used on longitudinal or cluster data. In particular, methods based on smoothing splines and local polynomial kernels exhibit different behaviour. We show that the generalized estimation equations based on weighted least squares regression splines for the nonparametric function have an…

广义混合效应模型中的半参数推断AI 解读

Summary The paper presents a study of the generalized partially linear model including random effects in its linear part. We propose an estimator that combines likelihood approaches for mixed effects models, with kernel methods. Following the methodology of Härdle and co-workers, we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model. The critical values are estimated by using a bootstrap…

条件风险价值与预期损失的非参数估计AI 解读

This paper considers a new nonparametric estimation of conditional value-at-risk and expected shortfall functions. Conditional value-at-risk is estimated by inverting the weighted double kernel local linear estimate of the conditional distribution function. The nonparametric estimator of conditional expected shortfall is constructed by a plugging-in method. Both the asymptotic normality and consistency of the proposed nonparametric estimators are established at both boundary…

离散化扩散模型的设定检验：理论与实践AI 解读

We propose two new tests for the specification of both the drift and the diffusion functions in a discretized version of a semiparametric continuous-time financial econometric model. Theoretically, we establish some asymptotic consistency results for the proposed tests. Practically, a simple selection procedure for the bandwidth parameter involved in each of the proposed tests is established based on the assessment of the power function of the test under study. To the best…

非参数密度估计量的渐近与形态表现：比较研究AI 解读

Motivated by finance applications, we assessed the performance of several univariate density estimation methods, focusing on their ability to deal with heavy-tailed target densities. Four approaches, a fixed bandwidth kernel estimator, an adaptive bandwidth kernel estimator, the Hermite series (SNP) estimator of Gallant and Nychka, and the logspline estimator of Kooperberg and Stone, are compared. We conclude that the logspline and adaptive kernel methods provide superior…

参数维数增长时的剖面核似然推断AI 解读

The generalized varying coefficient partially linear model with growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation and inference. When the number of parameters grows with sample size, the existence and asymptotic normality of the profile likelihood estimator are established under some regularity conditions. Profile likelihood ratio inference for the…

最近邻分类中的邻居阶数选择AI 解读

The kth-nearest neighbor rule is arguably the simplest and most intuitively appealing nonparametric classification procedure. However, application of this method is inhibited by lack of knowledge about its properties, in particular, about the manner in which it is influenced by the value of k; and by the absence of techniques for empirical choice of k. In the present paper we detail the way in which the value of k determines the misclassification error. We consider two…

局部多项式回归的方差分析、决定系数与 F 检验AI 解读

This paper provides ANOVA inference for nonparametric local polynomial regression (LPR) in analogy with ANOVA tools for the classical linear regression model. A surprisingly simple and exact local ANOVA decomposition is established, and a local R-squared quantity is defined to measure the proportion of local variation explained by fitting LPR. A global ANOVA decomposition is obtained by integrating local counterparts, and a global R-squared and a symmetric projection matrix…

再生核希尔伯特空间中的 Henderson 平滑器AI 解读

The Henderson smoother has been traditionally applied for trend-cycle estimation in the context of nonparametric seasonal adjustment software officially adopted by statistical agencies. This study introduces a Henderson third-order kernel representation by means of the reproducing kernel Hilbert space (RKHS) methodology. Two density functions and corresponding orthonormal polynomials have been calculated. Both are shown to give excellent representations for short- and…

混合类别与连续数据的条件分布函数和分位数函数非参数估计AI 解读

We propose a new nonparametric conditional cumulative distribution function kernel estimator that admits a mix of discrete and categorical data along with an associated nonparametric conditional quantile estimator. Bandwidth selection for kernel quantile regression remains an open topic of research. We employ a conditional probability density function-based bandwidth selector proposed by Hall, Racine, and Li that can automatically remove irrelevant variables and has…