Quantile regression methods with varying-coefficient models for censored data

Considerable intellectual progress has been made to the development of various semiparametric varying-coefficient models over the past ten to fifteen years. An important advantage of these models is that they avoid much of the curse of dimensionality problem as the nonparametric functions are restricted only to some variables. More recently, varying-coefficient methods have been applied to quantile regression modeling, but all previous studies assume that the data are fully observed. The main purpose of this paper is to develop a varying-coefficient approach to the estimation of regression quantiles under random data censoring. We use a weighted inverse probability approach to account for censoring, and propose a majorize–minimize type algorithm to optimize the non-smooth objective function. The asymptotic properties of the proposed estimator of the nonparametric functions are studied, and a resampling method is developed for obtaining the estimator of the sampling variance. An important aspect of our method is that it allows the censoring time to depend on the covariates. Additionally, we show that this varying-coefficient procedure can be further improved when implemented within a composite quantile regression framework. Composite quantile regression has recently gained considerable attention due to its ability to combine information across different quantile functions. We assess the finite sample properties of the proposed procedures in simulated studies. A real data application is also considered.     

Distributed parametric and nonparametric regression with on-line performance bounds computation

In this paper we focus on collaborative multi-agent systems, where agents are distributed over a region of interest and collaborate to achieve a common estimation goal. In particular, we introduce two consensus-based distributed linear estimators. The first one is designed for a Bayesian scenario, where an unknown common finite-dimensional parameter vector has to be reconstructed, while the second one regards the nonparametric reconstruction of an unknown function sampled at different locations by the sensors. Both of the algorithms are characterized in terms of the trade-off between estimation performance, communication, computation and memory complexity. In the finite-dimensional setting, we derive mild sufficient conditions which ensure that a distributed estimator performs better than the local optimal ones in terms of estimation error variance. In the nonparametric setting, we introduce an on-line algorithm that allows the agents to simultaneously compute the function estimate with small computational, communication and data storage efforts, as well as to quantify its distance from the centralized estimate given by a Regularization Network, one of the most powerful regularized kernel methods. These results are obtained by deriving bounds on the estimation error that provide insights on how the uncertainty inherent in a sensor network, such as imperfect knowledge on the number of agents and the measurement models used by the sensors, can degrade the performance of the estimation process. Numerical experiments are included to support the theoretical findings.     

Small area estimation using a nonparametric model-based direct estimator

Nonparametric regression is widely used as a method of characterizing a non-linear relationship between a variable of interest and a set of covariates. Practical application of nonparametric regression methods in the field of small area estimation is fairly recent, and has so far focussed on the use of empirical best linear unbiased prediction under a model that combines a penalized spline (p-spline) fit and random area effects. The concept of model-based direct estimation is used to develop an alternative nonparametric approach to estimation of a small area mean. The suggested estimator is a weighted average of the sample values from the area, with weights derived from a linear regression model with random area effects extended to incorporate a smooth, nonparametrically specified trend. Estimation of the mean squared error of the proposed small area estimator is also discussed. Monte Carlo simulations based on both simulated and real datasets show that the proposed model-based direct estimator and its associated mean squared error estimator perform well. They are worth considering in small area estimation applications where the underlying population regression relationships are non-linear or have a complicated functional form.     

Valuation of American options via basis functions

After a brief review of recent developments in the pricing and hedging of American options, this paper modifies the basis function approach to adaptive control and neuro-dynamic programming, and applies it to develop: 1) nonparametric pricing formulas for actively traded American options and 2) simulation-based optimization strategies for complex over-the-counter options, whose optimal stopping problems are prohibitively difficult to solve numerically by standard backward induction algorithms because of the curse of dimensionality. An important issue in this approach is the choice of basis functions, for which some guidelines and their underlying theory are provided.     

Absolute penalty and shrinkage estimation in partially linear models

In the context of a partially linear regression model, shrinkage semiparametric estimation is considered based on the Stein-rule. In this framework, the coefficient vector is partitioned into two sub-vectors: the first sub-vector gives the coefficients of interest, i.e., main effects (for example, treatment effects), and the second sub-vector is for variables that may or may not need to be controlled. When estimating the first sub-vector, the best estimate may be obtained using either the full model that includes both sub-vectors, or the reduced model which leaves out the second sub-vector. It is demonstrated that shrinkage estimators which combine two semiparametric estimators computed for the full model and the reduced model outperform the semiparametric estimator for the full model. Using the semiparametric estimate for the reduced model is best when the second sub-vector is the null vector, but this estimator suffers seriously from bias otherwise. The relative dominance picture of suggested estimators is investigated. In particular, suitability of estimating the nonparametric component based on the B-spline basis function is explored. Further, the performance of the proposed estimators is compared with an absolute penalty estimator through Monte Carlo simulation. Lasso and adaptive lasso were implemented for simultaneous model selection and parameter estimation. A real data example is given to compare the proposed estimators with lasso and adaptive lasso estimators.     

Efficient estimation of a semiparametric dynamic copula model

A new semiparametric dynamic copula model is proposed where the marginals are specified as parametric GARCH-type processes, and the dependence parameter of the copula is allowed to change over time in a nonparametric way. A straightforward two-stage estimation method is given by local maximum likelihood for the dependence parameter, conditional on consistent first stage estimates of the marginals. First, the properties of the estimator are characterized in terms of bias and variance and the bandwidth selection problem is discussed. The proposed estimator attains the semiparametric efficiency bound and its superiority is demonstrated through simulations. Finally, the wide applicability of the model in financial time series is illustrated, and it is compared with traditional models based on conditional correlations.     

Semiparametric multivariate density estimation for positive data using copulas

The estimation of density functions for positive multivariate data is discussed. The proposed approach is semiparametric. The estimator combines gamma kernels or local linear kernels, also called boundary kernels, for the estimation of the marginal densities with parametric copulas to model the dependence. This semiparametric approach is robust both to the well-known boundary bias problem and the curse of dimensionality problem. Mean integrated squared error properties, including the rate of convergence, the uniform strong consistency and the asymptotic normality are derived. A simulation study investigates the finite sample performance of the estimator. The proposed estimator performs very well, also for data without boundary bias problems. For bandwidths choice in practice, the univariate least squares cross validation method for the bandwidth of the marginal density estimators is investigated. Applications in the field of finance are provided.     

A new method for solving the problem of the mean estimation when the underlying regression function is discontinuous

In the context of finite population survey sampling, we propose a new model-based mean estimator, when the function that links the variables is discontinuous. The available estimators of the mean based on nonparametric regression are derived under the assumption that the regression function is continuous. We propose a new approach to adjust for the effect of discontinuity on regression estimation of the mean. The performance of the proposed estimator is analysed through a simulation study because the theoretic study of asymptotics is not possible. In the literature, the new estimator requires more computational cost than others, but the simulation experiments indicate that the proposed method has higher efficiency than other traditional parametric and nonparametric regression methods.     

Neural networks for bandwidth selection in local linear regression of time series

The problem of automatic bandwidth selection in nonparametric regression is considered when a local linear estimator is used to derive nonparametrically the unknown regression function. A plug-in method for choosing the smoothing parameter based on the use of the neural networks is presented. The method applies to dependent data generating processes with nonlinear autoregressive time series representation. The consistency of the method is shown in the paper, and a simulation study is carried out to assess the empirical performance of the procedure.     

隐核最小二乘分类器在故障诊断中的应用

作为一种基于正定核的学习方法,传统支持向量机(Support Vector Machine,SVM)能较好地解决小样本、非线性、过学习、维数灾和局部极小等问题,从而广泛应用于模式识别、回归估计等领域。当前,核方法及其在故障诊断中的应用引起了人们的广泛重视并成为研究热点。为解决传统支持向量对核函数正定性的限制及求解速度不高的缺陷,通过引入最小二乘支持向量机分类算法提高学习速度,采用隐核特征映射技术实现核函数的进一步扩展,提出了一种新的隐核最小二乘分类器(HKLSC)算法。将其应用于实际工业过程的故障诊断中并根据采集的滚动轴承数据进行了仿真。结果表明,该隐核分类器具有很好的故障诊断性能,为故障诊断提供了一种新的有效途径。     

Multistage linear estimation using partitioning

The estimation algorithm described in this note solves the linear estimation problem as a two-stage estimator consisting of two consecutive Kalman filters. The interconnections between this estimator structure and the more familiar one-stage optimal Kalman filter are discussed. Applications to decentralized estimation, bias estimation, and parameter identification are described.     

Consistent identification of Wiener systems: A machine learning viewpoint

Wiener system identification has been recently performed by adopting a Bayesian semiparametric approach. In this framework, the linear system entering the first block is given a finite-dimensional parametrization, while nonparametric Gaussian regression is used to estimate the static nonlinearity in the second block. In this paper, we study the asymptotic behavior of this estimator when the number of noisy output samples tends to infinity without assuming the correctness of the Bayesian prior models. For this purpose, we interpret Wiener identification under a machine learning perspective. This allows us to extend recent results on function estimation in reproducing kernel Hilbert spaces to derive a condition guaranteeing the statistical consistency of the identification procedure. We also discuss how the violation of such a condition can lead to useless estimates of the Wiener structure.     

非线性主动悬架系统自适应最优控制

针对非线性主动悬架系统多性能指标综合优化问题,提出一类自适应最优控制方法.首先,通过引入一阶低通滤波操作,利用系统输入输出构建结构简单且调节参数少的一类未知非线性动态估计器,在线估计系统未知非线性动态;其次,构建包含乘驾舒适度、悬架行程空间及输入能耗的性能指标函数,采用单层神经网络对最优性能指标函数进行在线逼近,并得到新的哈密尔顿函数;为实现在线求解,构建一类新的基于参数估计误差信息的自适应律,在线更新神经网络权值并计算最优控制律;最后,理论分析闭环系统稳定性和收敛性,并通过专业软件Carsim与Matlab/Simulink搭建的联合仿真平台给出的对比仿真结果,验证所提出方法可有效解决主动悬架系统多目标性能优化控制问题,提升主动悬架系统综合性能.     

Local polynomial estimation in partial linear regression models under dependence

A regression model whose regression function is the sum of a linear and a nonparametric component is presented. The design is random and the response and explanatory variables satisfy mixing conditions. A new local polynomial type estimator for the nonparametric component of the model is proposed and its asymptotic normality is obtained. Specifically, this estimator works on a prewhitening transformation of the dependent variable, and the results show that it is asymptotically more efficient than the conventional estimator (which works on the original dependent variable) when the errors of the model are autocorrelated. A simulation study and an application to a real data set give promising results.     

A simulation-based two-stage scheduling methodology for controlling semiconductor wafer fabs

In this paper, we propose an efficient simulation-based two-stage scheduling methodology by integrating vector ordinal optimization (VOO) and response surface methodology (RSM) to make a good scheduling policy for fab operation. The suggested method combines local and global rules into a single rule, with the objective of simultaneously optimizing multiple performance indices. Our approach consists of 2 stages: rule combination selection, and parameter optimization. In the first stage, we apply the VOO techniques to effectively selecting good rule combination. Results show that 1 orders of computation time reduction over traditional simulations can be achieved. In the second stage, we adopt RSM and desirability function to tune the parameters associated to scheduling algorithm. The proposed approach is validated by means of a comparison with other scheduling policies. The results show that the proposed scheduling method is effective.     

On the optimality of two-stage state estimation in the presence ofrandom bias

Sufficient conditions for the optimality of a two-stage state estimator in the presence of random bias are derived. Under an algebraic constraint on the correlation between the state and bias process noises, the optimal estimate of the system state can be obtained as a linear combination of the output of the first stage (a bias-free filter) and the second stage (a bias filter). Because the algebraic constraint is restrictive in practice, the results indirectly indicate that for most practical systems the proposed solution to the two-stage estimation problem will be suboptimal     

Orthogonality-projection-based estimation for semi-varying coefficient models with heteroscedastic errors

This paper is concerned with the estimation in semi-varying coefficient models with heteroscedastic errors. An iterated two-stage orthogonality-projection-based estimation is proposed. This method can easily be used to estimate the model parametric and nonparametric parts, as well as the variance function, and in the estimators the parametric part and nonparametric part do not affect each other. Under some mild conditions, the consistency, conditional biases, conditional variances and asymptotic normality of the resulting estimators are studied explicitly. Moreover, some simulation studies are carried out to examine the finite sample performance of the proposed methods. Finally, the methodologies are illustrated by a real data set.     

Flexible estimation of wage distributions in the presence of covariates

An estimator of conditional wage distributions based on a piecewise-linear specification of the conditional hazard function is proposed. Under a minimal set of assumptions, the estimator is flexible enough to capture almost any underlying relationship, and is not affected by the curse of dimensionality. It also allows us to derive estimates of the conditional Lorenz curves and Gini indices. The methodology is used to investigate the wage trends in Spain in 1994-1999. The estimation results provide evidence that there has been strong decreases in both the returns to schooling and the inequality indices for workers with low levels of experience; these decreases may partly be explained by the “overeducation” phenomenon, which intensified in this period.     

有观测噪声的时变系统的参数估计

本文给出了有观测噪声、线性离散时变系统的参数估计新方法。它由两段互耦的自适应状态估计器和自适应参数估计器组成。通过引入虚拟时变噪声,我们结合在互耦算法中产生的模型误差到虚拟噪声统计,使模型误差得到有效地补偿和克服滤波发散。模拟例子说明了本文方法的有效性。     

Shrinkage estimation in general linear models

We propose a James-Stein-type shrinkage estimator for the parameter vector in a general linear model when it is suspected that some of the parameters may be restricted to a subspace. The James-Stein estimator is shown to demonstrate asymptotically superior risk performance relative to the conventional least squares estimator under quadratic loss. An extensive simulation study based on a multiple linear regression model and a logistic regression model further demonstrates the improved performance of this James-Stein estimator in finite samples. The application of this new estimator is illustrated using Ontario newborn infants data spanning four fiscal years.