基于局部多项式回归的模型校准抽样估计研究

在抽样估计中,当研究变量与辅助变量之间呈非线性关系时,传统的校准估计方法效果较差,基于非参数回归方法的模型校准估计量则可以很好地解决这一问题。首先,建立描述研究变量和辅助变量之间关系的超总体回归模型,使用非参数中的局部多项式方法得出模型参数的拟合值,并结合校准估计得出局部多项式模型校准估计量,同时给出其方差和方差估计量公式,证明了该估计量具有渐近无偏性、一致性和渐近正态性等优良的统计性质。然后,使用仿真模拟的方法证明在研究变量与研究变量之间呈非线性关系时,该估计量有良好的估计效果。最后,对该估计量在我国政府统计中的应用进行简单的介绍。     

Recursive Estimation of Regression Functions by Local Polynomial Fitting

The recursive estimation of the regression function m(x) = E(Y/X = x) and its derivatives is studied under dependence conditions. The examined method of nonparametric estimation is a recursive version of the estimator based on locally weighted polynomial fitting, that in recent articles has proved to be an attractive technique and has advantages over other popular estimation techniques. For strongly mixing processes, expressions for the bias and variance of these estimators are given and asymptotic normality is established. Finally, a simulation study illustrates the proposed estimation method.     

非参数局部多项式回归估计的最优子抽样算法

随着科学技术的发展,虽然人们提高了收集和处理数据的能力,但仍存在一些大数据集超出了现有计算机的计算能力.目前,抽取一部分样本来替代全样本进行建模计算是减轻计算负担的一种方法.大数据背景下线性模型的子抽样方法已经得到了相对成熟的研究,在减轻计算量方面获得了很大的优势.文章将线性模型下的子抽样方法推广到非参数回归模型,并推...     

Asymptotic Behavior of Bandwidth Selected by the Cross-Validation Method for Local Polynomial Fitting

In this paper, the asymptotic optimality of the cross validation bandwidth selector for the local polynomial fitting under strongly mixing dependence is obtained. The asymptotic normality of the bandwidth selected by the cross-validation method is derived, which is an extension of W. Härdle, P. Hall, and J. S. Marron (1988, J. Am. Statist. Assoc.83, 86–101).     

基于局部多项式展开的多元非参数模型贝叶斯带宽选择

在多元非参数模型中带宽和阶的选择对局部多项式估计量的表现十分重要。本文基于交叉验证准则提出一个自适应贝叶斯带宽选择方法。在给定的误差密度函数下,该方法可推导出对应的似然函数,并构造带宽参数的后验密度函数。随后,通过带宽的后验期望可同时获得阶和带宽的估计。数值模拟的结果表明,该方法不仅比大拇指准则方法精确,且比交叉验证方法耗时更少。与此同时,与Nadaraya-Watson估计相比,所提带宽选择方法对多元非参数模型的适应性要更好。最后,本文通过一组实际数据说明有限样本下所提贝叶斯带宽选择的表现很好。     

Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors

Local polynomial smoothing for the trend function and its derivatives in nonparametric regression with long-memory, short-memory and antipersistent errors is considered. We show that in the case of antipersistence, the convergence rate of a nonparametric regression estimator is faster than for uncorrelated or short-range dependent errors. Moreover, it is shown that unified asymptotic formulas for the optimal bandwidth and the MSE hold for all of the three dependence structures. Also, results on estimation at the boundary are included. A bandwidth selector for nonparametric regression with different types of dependent errors is proposed. Its asymptotic property is investigated. The practical performance of the proposal is illustrated by simulated and real data examples.     

基于协整分析和局部多项式回归的兵团经济增长实证分析

采用协整分析,实证分析了兵团的投资、消费与经济增长之间的关系,研究发现三者之间存在长期稳定的关系,但是由格兰杰因果检验发现投资和消费均不是兵团GDP增长的因。为进一步明确投资和消费对兵团经济的影响,采用岭回归的思想改进局部多项式方法,用当期投资,前一期投资和当期消费拟合兵团GDP,得到GDP对前述变量的偏导数值,进而利用这些偏导数来评价投资、消费对经济增长的影响。研究发现投资、消费对经济增长的作用呈现明显的非线性关系,有很强的时期性。     

一个半参数回归模型中Cramér渐近有效性的充要条件(英语)

本文考虑模型Y_i=X~Tβ g(T) ε,这里(X~T,T,Y,)是k 2-维随机向量,g是未知光滑函数,ε是均值为零方差有限的随机误差。本文证明了,的最小二乘估计是Cramer渐近有效的充要条件是误差6服从正态分布N(0,口’)。     

一个有效估计:半参数非时齐扩散模型的局部线性复合分位回归估计

主要研究半参数非时齐扩散模型的参数估计问题.基于非时齐扩散模型的离散观测样本,首先得到漂移参数的局部线性复合分位回归估计,并证明估计量的渐近偏差、渐近方差和渐近正态性.其次,讨论了带宽的选择和局部线性复合分位回归估计关于局部线性最小二乘估计的渐近相对效,所得到的局部估计较局部线性最小二乘估计更为有效.最后,通过模拟说明了局部线性复合分位回归估计比局部线性最小二乘估计的模拟效果更好.     

Minimum Disparity Estimation in Linear Regression Models: Distribution and Efficiency

This paper deals with the minimum disparity estimation in linear regression models. The estimators are defined as statistical quantities which minimize the blended weight Hellinger distance between a weighted kernel density estimator of errors and a smoothed model density of errors. It is shown that the estimators of the regression parameters are asymptotic normally distributed and efficient at the model if the weights of the density estimators are appropriately chosen.     

Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise

This paper deals with nonparametric estimation of a regression curve, where the estimation method should preserve possible jumps in the curve. At each point x at which one wants to estimate the regression function, the method chooses in an adaptive way among three estimates: a local linear estimate using only datapoints to the left of x, a local linear estimate based on only datapoints to the right of x, and finally a local linear estimate using data in a two-sided neighbourhood around x. The choice among these three estimates is made by looking at differences of the weighted residual mean squares of the three fits. The resulting estimate preserves the jumps well and in addition gives smooth estimates of the continuity parts of the curve. This property of compromise between local smoothing and jump-preserving is what distinguishes our method from most previously proposed methods, that mainly focused on local smoothing and consequently blurred possible jumps, or mainly focused on jump-preserving and hence led to rather noisy estimates in continuity regions of the underlying regression curve. Strong consistency of the estimator is established and its performance is tested via a simulation study. This study also compares the current method with some existing methods. The current method is illustrated in analyzing a real dataset.     

Estimation of a covariance matrix with location: Asymptotic formulas and optimal B-robust estimators

Applying the non-singular affine transformations AZ + μ to a spherically symmetrically distributed variate Z generates the covariance-location model, indexed by the parameters AA^T and μ, consisting of so-called elliptical distributions. We develop an algebraic machinery that simplifies the derivation of influence functions and asymptotic variance-covariance matrices for equivariant estimators of Σ and μ and reveals a natural structure of Σ. In addition, optimal B-robust estimators are derived.     

Robust Optimal Onboard Reentry Guidance of a Space Shuttle: Dynamic Game Approach and Guidance Synthesis via Neural Networks

Robust optimal control problems for dynamic systems must be solved ifmodeling inaccuracies cannot be avoided and/or unpredictable andunmeasurable influences are present. Here, the return of a future Europeanspace shuttle to Earth is considered. Four path constraints have to beobeyed to limit heating, dynamic pressure, load factor, and flight pathangle at high velocities. For the air density associated with theaerodynamic forces and the constraints, only an altitude-dependent rangecan be predicted. The worst-case air density is analyzed via an antagonisticnoncooperative two-person dynamic game. A closed-form solution of the gameprovides a robust optimal guidance scheme against all possible air densityfluctuations. The value function solves the Isaacs nonlinear first-orderpartial differential equation with suitable interior and boundaryconditions. The equation is solved with the method of characteristics in therelevant parts of the state space. A bundle of neighboring characteristictrajectories yields a large input/output data set and enables a guidancescheme synthesis with three-layer perceptrons. The difficult andcomputationally expensive perceptron training is done efficiently with thenew SQP-training method FAUN. Simulations show the real-time capability androbustness of the reentry guidance scheme finally chosen.