ROBUST NONPARAMETRIC REGRESSION BASED ON L_1-NORM AND B-SPLINES

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B-Spline Method for Spatio-Temporal Inverse Model

Inverse models can be used to estimate surface fluxes in terms of the observed atmospheric concentration measurement data. This paper proposes a new nonparametric spatio-temporal inverse model and provides the global expressions for the estimates by employing the B-spline method. The authors establish the asymptotic normality of the estimators under mild conditions. The authors also conduct numerical studies to evaluate the finite sample performance of the proposed methodologies. Finally, the authors apply the method to anthropogenic carbon dioxide (CO₂) emission data from different provinces of Canada to illustrate the validity of the proposed techniques.

     

An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data

This paper proposes a flexible additive-multiplicative Cox-Aalen hazard model which allows time-varying covariate effects for the subdistribution in a competing risks study. Weighted estimating equation approaches under an covariates-dependent adjusted weight by fitting the Cox proportional hazard model for the censoring distribution are established for inference on the model parametric and nonparametric components. In addition, large number properties are presented and the finite sample behavior of the proposed estimators is evaluated through simulation studies, estimators from the proposed method perform satisfactorily on reduction of the bias. The authors apply our model to a competing risks data set from a tamoxifen trail for breast cancer study.     

Active Disturbance Rejection Control of Second-Order Nonlinear Uncertain Systems with Guaranteed Transient and Steady State Tracking Error Bounds

This paper presents an active disturbance rejection control (ADRC) method for a class of second-order nonlinear uncertain systems with guaranteed transient and steady state tracking error bounds. To deal with the tracking error constraint, an output error transformation and sliding surface technique are introduced to transform the constrained second-order system into an equivalent unconstrained first-order one. Then, an ADRC method is developed to achieve output tracking of the transformed uncertain system. The author proves that the closed-loop system is semi-globally uniformly bounded and it is sufficient to guarantee the tracking error constraint for the original system. Simulation results of a system of two inverted pendulums connected by a spring and a damper demonstrate the effectiveness of the proposed control method.

     

A Constrained Interval-Valued Linear Regression Model: A New Heteroscedasticity Estimation Method

Linear regression models for interval-valued data have been widely studied. Most literatures are to split an interval into two real numbers, i.e., the left- and right-endpoints or the center and radius of this interval, and fit two separate real-valued or two dimension linear regression models. This paper is focused on the bias-corrected and heteroscedasticity-adjusted modeling by imposing order constraint to the endpoints of the response interval and weighted linear least squares with estimated covariance matrix, based on a generalized linear model for interval-valued data. A three step estimation method is proposed. Theoretical conclusions and numerical evaluations show that the proposed estimator has higher efficiency than previous estimators.

     

Inference for repeated measures models under heteroscedasticity

This paper considers a widely used mixed effects model in repeated measures under heteroscedasticity. Hypotheses of the equality of the fixed effects and the simultaneous confidence intervals for all pair-wise differences are discussed.A generalized F-test has been proposed to test the equality of the fixed effects in the model,but simulation results for evaluating its performance have not been shown in the literature.Moreover,the generalized F-test cannot be used to deduce the simultaneous confidence intervals for all pair-wise differences of the fixed effects.The authors propose two new p-values to test the hypotheses of equality of the fixed effects and simultaneous confidence intervals of the differences of the effects based on the generalized pivotal quantities derived in this paper.The authors also compare the empirical performances of the proposed tests and the generalized F-test. The typeⅠerror rates and powers of these tests are evaluated using the Monte Carlo simulation.The simulation studies show that the generalized F-test does not perform well in terms of typeⅠerror rate under various sample size and parameter combinations.However,the typeⅠerror probabilities of the proposed tests are always close to the nominal value.It can also be seen that the simultaneous confidence intervals perform well.     

High Speed Machining for Linear Paths Blended with G3 Continuous Pythagorean-Hodograph Curves

Previously, many studies have illustrated corner blend problem with different parameter curves. Only a few of them take a Pythagorean-hodograph (PH) curve as the transition arc, let alone corresponding real-time interpolation methods. In this paper, an integrated corner-transition mixing-interpolation-based scheme (ICMS) is proposed, considering transition error and machine tool kinematics. Firstly, the ICMS smooths the sharp corners in a linear path through blending the linear path with G3 continuous PH transition curves. To obtain optimal PH transition curves globally, the problem of corner smoothing is formulated as an optimization problem with constraints. In order to improve optimization efficiency, the transition error constraint is deduced analytically, so is the curvature extreme of each transition curve. After being blended with PH transition curves, a linear path has become a blend curve. Secondly, the ICMS adopts a novel mixed interpolator to process this kind of blend curves by considering machine tool kinematics. The mixed interpolator can not only implement jerk-limited feedrate scheduling with critical points detection, but also realize self-switching of two interpolation modes. Finally, two patterns are machined with a carving platform based on ICMS. Experimental results show the effectiveness of ICMS.

     

Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models

This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END, for short) random variables. Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided. In particular, the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product. The results that the authors obtained generalize the corresponding ones for independent ra...     

Comparison of Covariate Balance Weighting Methods in Estimating Treatment Effects

Different covariate balance weighting methods have been proposed by researchers from different perspectives to estimate the treatment effects. This paper gives a brief review of the covariate balancing propensity score method by Imai and Ratkovic (2014), the stable balance weighting procedure by Zubizarreta (2015), the calibration balance weighting approach by Chan, et al. (2016), and the integrated propensity score technique by Sant’Anna, et al. (2020). Simulations are conducted to illustrate the finite sample performance of both the average treatment effect and quantile treatment effect estimators based on different weighting methods. Simulation results show that in general, the covariate balance weighting methods can outperform the conventional maximum likelihood estimation method while the performance of the four covariate balance weighting methods varies with the data generating processes. Finally, the four covariate balance weighting methods are applied to estimate the treatment effects of the college graduate on personal annual income.

     

The credibility models with equal correlation risks

In almost all credibility estimators considered previously, the claims are assumed to be independent over risks. However, from practical point of view, this paper investigates the credibility premium when risks are dependent on each other. The authors build the Bühlmann’s credibility models to account for an equal correlation structure over risks, and parameter estimations are also considered. Some desired results are derived.     

IMPROVED ROBUST H-INFINITY ESTIMATION FOR UNCERTAIN CONTINUOUS-TIME SYSTEMS

The design of full-order robust estimators is investigated for continuous-time polytopic uncertain systems. The main purpose is to obtain a stable linear estimator such that the estimation error system remains robustly stable with a prescribed H∞ attenuation level. Firstly, a simple alternative proof is given for an improved LMI representation of H∞ performance proposed recently. Based on the performance criterion which keeps the Lyapunov matrix out of the product of the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameterdependent Lyapunov functions and hence it is less conservative than the earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.     

Robust Estimation for Partial Functional Linear Regression Model Based on Modal Regression

This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression, which combines the common linear model with the functional linear regression model. The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error cases. The slope function is fitted by B-spline. Under suitable conditions, the authors obtain the convergence rates and asymptotic normality of the estimators. Finally, simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method. Both the simulation results and the real data analysis confirm that the newly proposed method works very well.     

动态空间自回归固定效应面板模型的估计与应用

文章首次探寻了在空间系统稳定以及n和T均为很大的情况下,DSAC固定效应面板模型的拟极大似然估计量的渐近性质.研究发现:运用转换法估计时,在一般情况下得到拟极大似然估计量存在O(1/T)阶的偏差,当(n-1)/T→0时,转换法得到的估计量以√(n-1)/T的速度一致地收敛于真值,当(n-1)/T→∞时,估计量以T的速度收敛至一个退化分布;用直接法估计时,在一般情况下得到的估计量会产生max(O(1/T),O(1/n))阶的偏差,当n/T→0和n/T→∞时,估计量分别以n和T的速度收敛至不同的退化分布;偏差修正估计量比拟极大似然估计量具有更好的有限样本性质:当n/T³→0时,转换法得到的偏差修正估计量以√(n-1)/T1的速度一致地收敛于真值,当n/T³和n³/T同时趋于0时,直接法得到的偏差修正估计量以√nT的速度一致地收敛于真值;直接法可以一致地估计个体效应和时间效应而转换法不能;当扰动项存在空间相关结构时DSAC固定效应面板模型的有限样本性质优于DSAR面板模型;最后用一个实证研究的例子表明了DSAC模型的应用价值.     

The Asymptotic Properties of Scad Penalized Generalized Linear Models with Adaptive Designs

This paper discusses the asymptotic properties of the SCAD (smoothing clipped absolute deviation) penalized quasi-likelihood estimator for generalized linear models with adaptive designs, which extend the related results for independent observations to dependent observations. Under certain conditions, the authors proved that the SCAD penalized method correctly selects covariates with non-zero coefficients with probability converging to one, and the penalized quasi-likelihood estimators of non-zero coefficients have the same asymptotic distribution they would have if the zero coefficients were known in advance. That is, the SCAD estimator has consistency and oracle properties. At last, the results are illustrated by some simulations.

     

基于AFSA的加速度计误差参数辨识

提出一种在无高精度测试转台的场合下,精确辨识加速度计误差参数的方法。所提方法以静态多位置加速度模方为观测量,以重力加速度模方误差的标准方差为指标,利用人工鱼群算法对加速度计误差进行辨识。对静态24位置进行仿真分析,在此基础上,对实验室自行研制的光纤捷联惯导系统进行加速度计参数辨识,并进行了24 h静态导航试验。仿真和试验均表明,所提方法是一种有效的加速度计参数辨识方法,具有一定的工程实用价值。     

异方差非参数回归模型均值与方差变点的小波估计与应用

金融市场中,受突发事件的影响反映资产平均收益的均值函数和反映资产收益波动的方差函数都有可能出现变点. 本文讨论了均值和方差都存在变点的异方差非参数回归模型的变点估计问题. 给出均值函数与方差函数的局部线性估计,利用函数小波系数的特性求得均值与方差变点位置的估计值并给出其收敛速度.在模拟实验中分析变点估计值的样本特性及均值变点估计与方差变点估计的相互影响.最后通过对两组股票数据的均值变点和方差变点进行估计,说明方法的有效性.     

Unbiased condition of the dispersion effects estimator in unreplicated two-level factorial experiments

This article presents a general form of the estimator for identifying dispersion effects from unreplicated two-level factorial experiments, and shows that the widely used estimators such as the BH, MH, and AMH estimators are all special cases of the proposed one, designated as the G estimator. The unbiased condition of the G estimator is proved, and a lower bound of variance of the G estimator is provided. A simulation based on a realistic design illustrates the variation of the variance and MSE (mean square error) of the G estimator on different coefficients. This estimator may be more flexible and has better performance than other methods such as the BH and MH estimators by appropriately selecting the coefficients.     

修正的KSS检验及其对中国通货膨胀率的应用

Kapetanios等^[1] 提出在指数平滑转换自回归（ESTAR）模型框架下进行单位根检验. 他们的检验是基于误差项为独立同分布的强假设下得到的,该假设在现实中很难成立. 当误差项为平稳弱相依时,该检验统计量的极限分布包含冗余参数. 通过构造修正的KSS检验,得到了不包含冗余参数的检验统计量. 蒙特卡罗模拟结果表明该修正的统计量大大减少了序列相关性带来的水平扭曲（size distortion）,且该检验统计量对于非线性平稳过程的检验功效高于PP检验. 将该检验用于中国的通货膨胀率,发现它存在着一个单位根,是非平稳过程.     

Test on Stochastic Block Model: Local Smoothing and Extreme Value Theory

In this paper, to obtain a consistent estimator of the number of communities, the authors present a new sequential testing procedure, based on the locally smoothed adjacency matrix and the extreme value theory. Under the null hypothesis, the test statistic converges to the type I extreme value distribution, and otherwise, it explodes fast and the divergence rate could even reach n in the strong signal case where n is the size of the network, guaranteeing high detection power. This method is simple to use and serves as an alternative approach to the novel one in Lei (2016) using random matrix theory. To detect the change of the community structure, the authors also propose a two-sample test for the stochastic block model with two observed adjacency matrices. Simulation studies justify the theory. The authors apply the proposed method to the political blog data set and find reasonable group structures.

     

The adaptive LASSO spline estimation of single-index model

In this paper, based on spline approximation, the authors propose a unified variable selection approach for single-index model via adaptive L ₁ penalty. The calculation methods of the proposed estimators are given on the basis of the known lars algorithm. Under some regular conditions, the authors demonstrate the asymptotic properties of the proposed estimators and the oracle properties of adaptive LASSO (aLASSO) variable selection. Simulations are used to investigate the performances of the proposed estimator and illustrate that it is effective for simultaneous variable selection as well as estimation of the single-index models.