In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.
Focusing on controlling the press-assembly quality of high-precision servo mechanism,an intelligent early warning method based on outlier data detection and linear regression is proposed.Linear regression is used to d...Focusing on controlling the press-assembly quality of high-precision servo mechanism,an intelligent early warning method based on outlier data detection and linear regression is proposed.Linear regression is used to deal with the relationship between assembly quality and press-assembly process,then the mathematical model of displacement-force in press-assembly process is established and a qualified press-assembly force range is defined for assembly quality control.To preprocess the raw dataset of displacement-force in the press-assembly process,an improved local outlier factor based on area density and P weight(LAOPW)is designed to eliminate the outliers which will result in inaccuracy of the mathematical model.A weighted distance based on information entropy is used to measure distance,and the reachable distance is replaced with P weight.Experiments show that the detection efficiency of the algorithm is improved by 5.6 ms compared with the traditional local outlier factor(LOF)algorithm,and the detection accuracy is improved by about 2%compared with the local outlier factor based on area density(LAOF)algorithm.The application of LAOPW algorithm and the linear regression model shows that it can effectively carry out intelligent early warning of press-assembly quality of high precision servo mechanism.展开更多
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
In linear regression model, the influence on the regression coefficients has beed paid great attention and other aspects such as the influence on confidence regions have also been studied. However, influence on F-test...In linear regression model, the influence on the regression coefficients has beed paid great attention and other aspects such as the influence on confidence regions have also been studied. However, influence on F-test in linear regression model received few consideration. This paper examines the local influence of small perturbations on Fstatistic. The diagnostic results permit one to check the sensitivity of F-statistic to the exact perturbations of error variance, explanatory variables and response variables. This method is applied to testing problem of transformation parameter in transformation model.Diagnostics are illustrated with two examples and compared with standard method.展开更多
In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the perfor...In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation （MSE） and mean absolute estimation （MAE） criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.展开更多
In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the ...In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.展开更多
In this paper, the invariance of the K-L distance and that of the infor-mation distance under some parameter transformations are derived; the equiva-lence of the local influence matrix corresponding to the K-L distanc...In this paper, the invariance of the K-L distance and that of the infor-mation distance under some parameter transformations are derived; the equiva-lence of the local influence matrix corresponding to the K-L distance, the informa-tion distance and the l展开更多
The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear sche...The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear scheme and the integrated method are used to obtain Focal quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.展开更多
鸡蛋新鲜度是反映鸡蛋内部品质的一个重要指标。为了能够实现鸡蛋新鲜度的快速无损检测,利用微型光纤光谱仪采集鸡蛋550～950nm的透射率光谱曲线,与鸡蛋的哈夫单位值进行了定量分析。通过不同的预处理方式分别结合偏最小二乘回归（parti...鸡蛋新鲜度是反映鸡蛋内部品质的一个重要指标。为了能够实现鸡蛋新鲜度的快速无损检测,利用微型光纤光谱仪采集鸡蛋550～950nm的透射率光谱曲线,与鸡蛋的哈夫单位值进行了定量分析。通过不同的预处理方式分别结合偏最小二乘回归（partial least squares regression,PLSR）与支持向量回归（support vector regression,SVR）建立模型,比较了不同模型的预测结果,发现一阶微分结合SVR能够实现较好地预测,且利用SVR建模要优于PLSR。为了提高运算效率,减少无用信息对建模的不良影响,分别利用线性降维主成分分析法（principal component analysis,PCA）与非线性降维局部线性嵌入（locally linear embedding,LLE）对一阶微分后的光谱数据降维,比较两种降维方法的预测效果,得出了LLE降维要优于PCA降维,其训练集和预测集的相关系数与均方根误差分别为92.2%,7.21和91.1%,8.80,训练集交叉验证的均方根误差相比减少了0.79。实验结果表明,利用局部线性嵌入结合支持向量回归进行非线性建模,能够提高鸡蛋新鲜度的预测能力,表明该方法对鸡蛋新鲜度的可见/近红外光谱检测可行。展开更多
文摘In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.
文摘Focusing on controlling the press-assembly quality of high-precision servo mechanism,an intelligent early warning method based on outlier data detection and linear regression is proposed.Linear regression is used to deal with the relationship between assembly quality and press-assembly process,then the mathematical model of displacement-force in press-assembly process is established and a qualified press-assembly force range is defined for assembly quality control.To preprocess the raw dataset of displacement-force in the press-assembly process,an improved local outlier factor based on area density and P weight(LAOPW)is designed to eliminate the outliers which will result in inaccuracy of the mathematical model.A weighted distance based on information entropy is used to measure distance,and the reachable distance is replaced with P weight.Experiments show that the detection efficiency of the algorithm is improved by 5.6 ms compared with the traditional local outlier factor(LOF)algorithm,and the detection accuracy is improved by about 2%compared with the local outlier factor based on area density(LAOF)algorithm.The application of LAOPW algorithm and the linear regression model shows that it can effectively carry out intelligent early warning of press-assembly quality of high precision servo mechanism.
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
文摘In linear regression model, the influence on the regression coefficients has beed paid great attention and other aspects such as the influence on confidence regions have also been studied. However, influence on F-test in linear regression model received few consideration. This paper examines the local influence of small perturbations on Fstatistic. The diagnostic results permit one to check the sensitivity of F-statistic to the exact perturbations of error variance, explanatory variables and response variables. This method is applied to testing problem of transformation parameter in transformation model.Diagnostics are illustrated with two examples and compared with standard method.
基金supported by the National Natural Science Foundation of China (No.10871201)the Major Project of Humanities Social Science Foundation of Ministry of Education (No. 08JJD910247)+2 种基金Key Project of Chinese Ministry of Education (No.108120)Beijing Natural Science Foundation (No. 1102021)Graduate Research Foundation of Ren Min University of China (Adaptive Composite Quantile Regression Model and Bootstrap Confidence Interval Theory and Applications (No.11XNH108))
文摘In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation （MSE） and mean absolute estimation （MAE） criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.
基金supported by National Institute on Drug Abuse grant R21 DA024260Yan Li issupported by National Science Foundation grant DMS 0348869 as a graduate research assistant
文摘In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.
文摘In this paper, the invariance of the K-L distance and that of the infor-mation distance under some parameter transformations are derived; the equiva-lence of the local influence matrix corresponding to the K-L distance, the informa-tion distance and the l
基金supported by the Zhejiang Provincial Natural Science Foundation of China (No. Y6110662)
文摘The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear scheme and the integrated method are used to obtain Focal quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.
文摘鸡蛋新鲜度是反映鸡蛋内部品质的一个重要指标。为了能够实现鸡蛋新鲜度的快速无损检测,利用微型光纤光谱仪采集鸡蛋550～950nm的透射率光谱曲线,与鸡蛋的哈夫单位值进行了定量分析。通过不同的预处理方式分别结合偏最小二乘回归（partial least squares regression,PLSR）与支持向量回归（support vector regression,SVR）建立模型,比较了不同模型的预测结果,发现一阶微分结合SVR能够实现较好地预测,且利用SVR建模要优于PLSR。为了提高运算效率,减少无用信息对建模的不良影响,分别利用线性降维主成分分析法（principal component analysis,PCA）与非线性降维局部线性嵌入（locally linear embedding,LLE）对一阶微分后的光谱数据降维,比较两种降维方法的预测效果,得出了LLE降维要优于PCA降维,其训练集和预测集的相关系数与均方根误差分别为92.2%,7.21和91.1%,8.80,训练集交叉验证的均方根误差相比减少了0.79。实验结果表明,利用局部线性嵌入结合支持向量回归进行非线性建模,能够提高鸡蛋新鲜度的预测能力,表明该方法对鸡蛋新鲜度的可见/近红外光谱检测可行。
