A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of r...A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of leastsquares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the onestep local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.展开更多
The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov spaceB 3 p,q is proved under quite general assumpation...The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov spaceB 3 p,q is proved under quite general assumpations. The adaptive nonlinear wavelet estimator with near-optimal convergence rate in a wide range of smoothness function classes is also constructed. The properties of the nonlinear wavelet estimator given for random design regression and only with bounded third order moment of the error can be compared with those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error.展开更多
The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic ...The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial correlation.Some MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) teststatistic.Simulation results confirm that the proposed test performs satisfactorily in estimated sizeand power.展开更多
This paper investigates the problem of collecting multidimensional data throughout time(i.e.,longitudinal studies)for the fundamental task of frequency estimation under Local Differential Privacy(LDP)guarantees.Contra...This paper investigates the problem of collecting multidimensional data throughout time(i.e.,longitudinal studies)for the fundamental task of frequency estimation under Local Differential Privacy(LDP)guarantees.Contrary to frequency estimation of a single attribute,the multidimensional aspect demands particular attention to the privacy budget.Besides,when collecting user statistics longitudinally,privacy progressively degrades.Indeed,the“multiple”settings in combination(i.e.,many attributes and several collections throughout time)impose several challenges,for which this paper proposes the first solution for frequency estimates under LDP.To tackle these issues,we extend the analysis of three state-of-the-art LDP protocols(Generalized Randomized Response–GRR,Optimized Unary Encoding–OUE,and Symmetric Unary Encoding–SUE)for both longitudinal and multidimensional data collections.While the known literature uses OUE and SUE for two rounds of sanitization(a.k.a.memoization),i.e.,L-OUE and L-SUE,respectively,we analytically and experimentally show that starting with OUE and then with SUE provides higher data utility(i.e.,L-OSUE).Also,for attributes with small domain sizes,we propose Longitudinal GRR(L-GRR),which provides higher utility than the other protocols based on unary encoding.Last,we also propose a new solution named Adaptive LDP for LOngitudinal and Multidimensional FREquency Estimates(ALLOMFREE),which randomly samples a single attribute to be sent with the whole privacy budget and adaptively selects the optimal protocol,i.e.,either L-GRR or L-OSUE.As shown in the results,ALLOMFREE consistently and considerably outperforms the state-of-the-art L-SUE and L-OUE protocols in the quality of the frequency estimates.展开更多
In recent years,the research field of data collection under local differential privacy(LDP)has expanded its focus fromelementary data types to includemore complex structural data,such as set-value and graph data.Howev...In recent years,the research field of data collection under local differential privacy(LDP)has expanded its focus fromelementary data types to includemore complex structural data,such as set-value and graph data.However,our comprehensive review of existing literature reveals that there needs to be more studies that engage with key-value data collection.Such studies would simultaneously collect the frequencies of keys and the mean of values associated with each key.Additionally,the allocation of the privacy budget between the frequencies of keys and the means of values for each key does not yield an optimal utility tradeoff.Recognizing the importance of obtaining accurate key frequencies and mean estimations for key-value data collection,this paper presents a novel framework:the Key-Strategy Framework forKey-ValueDataCollection under LDP.Initially,theKey-StrategyUnary Encoding(KS-UE)strategy is proposed within non-interactive frameworks for the purpose of privacy budget allocation to achieve precise key frequencies;subsequently,the Key-Strategy Generalized Randomized Response(KS-GRR)strategy is introduced for interactive frameworks to enhance the efficiency of collecting frequent keys through group-anditeration methods.Both strategies are adapted for scenarios in which users possess either a single or multiple key-value pairs.Theoretically,we demonstrate that the variance of KS-UE is lower than that of existing methods.These claims are substantiated through extensive experimental evaluation on real-world datasets,confirming the effectiveness and efficiency of the KS-UE and KS-GRR strategies.展开更多
In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to ...In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients. Moreover, a local estimation method is introduced to adjust the weights of the quadratic polynomial regression function to improve the model accuracy. Finally, the proposed method is applied to predict the SVI values in a real wastewater treatment process(WWTP). The experimental results demonstrate that the proposed MLQPR method has faster testing speed and more accurate results than some existing methods.展开更多
In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion model.We establish strong consistency and ...In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion model.We establish strong consistency and asymptotic normality for the estimate of the second infinitesimal moment of continuous time models using the reweighted Nadaraya-Watson estimator to the true function.展开更多
针对微型飞行器(Micro air vehicle,MAV)在室内飞行过程中无法获得GPS信号,而微型惯性单元(Inertial measurement unit,IMU)的陀螺仪和加速度计随机漂移误差较大,提出一种利用单目视觉估计微型飞行器位姿并构建室内环境的方法。在机载...针对微型飞行器(Micro air vehicle,MAV)在室内飞行过程中无法获得GPS信号,而微型惯性单元(Inertial measurement unit,IMU)的陀螺仪和加速度计随机漂移误差较大,提出一种利用单目视觉估计微型飞行器位姿并构建室内环境的方法。在机载单目摄像机拍摄的序列图像中引入一种基于生物视觉的方法获得匹配特征点,并由五点算法获得帧间摄像机运动参数和特征点位置参数的初始解;利用平面关系将特征点的位置信息由三维降低到二维,给出一种局部优化方法求解摄像机运动参数和特征点位置参数的最大似然估计,提高位姿估计和环境构建的精度。最后通过扩展卡尔曼滤波方法融合IMU传感器和单目视觉测量信息解算出微型飞行器的位姿。实验结果表明,该方法能够实时可靠地估计微型飞行器的位置和姿态,构建的环境信息满足导航需求,适用于微型飞行器室内环境中的导航控制。展开更多
文摘A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of leastsquares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the onestep local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.
基金Project supported by Doctoral Programme Foundationthe National Natural Science Foundation of China (Grant No. 19871003)Natural Science Fundation of Heilongjiang Province, China.
文摘The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov spaceB 3 p,q is proved under quite general assumpations. The adaptive nonlinear wavelet estimator with near-optimal convergence rate in a wide range of smoothness function classes is also constructed. The properties of the nonlinear wavelet estimator given for random design regression and only with bounded third order moment of the error can be compared with those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error.
基金supported by the National Natural Science Foundation of China under Grant Nos. 10871217 and 40574003the Science and Technology Project of Chongqing Education Committee under Grant No. KJ080609+1 种基金the Doctor's Start-up Research Fund under Grant No. 08-52204the Youth Science Research Fund of Chongging Technology and Business University under Grant No. 0852008
文摘The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial correlation.Some MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) teststatistic.Simulation results confirm that the proposed test performs satisfactorily in estimated sizeand power.
基金supported by the Agence Nationale de la Recherche(ANR)(contract“ANR-17-EURE-0002”)by the Region of Bourgogne Franche-ComtéCADRAN Projectsupported by the European Research Council(ERC)project HYPATIA under the European Union's Horizon 2020 research and innovation programme.Grant agreement n.835294。
文摘This paper investigates the problem of collecting multidimensional data throughout time(i.e.,longitudinal studies)for the fundamental task of frequency estimation under Local Differential Privacy(LDP)guarantees.Contrary to frequency estimation of a single attribute,the multidimensional aspect demands particular attention to the privacy budget.Besides,when collecting user statistics longitudinally,privacy progressively degrades.Indeed,the“multiple”settings in combination(i.e.,many attributes and several collections throughout time)impose several challenges,for which this paper proposes the first solution for frequency estimates under LDP.To tackle these issues,we extend the analysis of three state-of-the-art LDP protocols(Generalized Randomized Response–GRR,Optimized Unary Encoding–OUE,and Symmetric Unary Encoding–SUE)for both longitudinal and multidimensional data collections.While the known literature uses OUE and SUE for two rounds of sanitization(a.k.a.memoization),i.e.,L-OUE and L-SUE,respectively,we analytically and experimentally show that starting with OUE and then with SUE provides higher data utility(i.e.,L-OSUE).Also,for attributes with small domain sizes,we propose Longitudinal GRR(L-GRR),which provides higher utility than the other protocols based on unary encoding.Last,we also propose a new solution named Adaptive LDP for LOngitudinal and Multidimensional FREquency Estimates(ALLOMFREE),which randomly samples a single attribute to be sent with the whole privacy budget and adaptively selects the optimal protocol,i.e.,either L-GRR or L-OSUE.As shown in the results,ALLOMFREE consistently and considerably outperforms the state-of-the-art L-SUE and L-OUE protocols in the quality of the frequency estimates.
基金supported by a grant fromthe National Key R&DProgram of China.
文摘In recent years,the research field of data collection under local differential privacy(LDP)has expanded its focus fromelementary data types to includemore complex structural data,such as set-value and graph data.However,our comprehensive review of existing literature reveals that there needs to be more studies that engage with key-value data collection.Such studies would simultaneously collect the frequencies of keys and the mean of values associated with each key.Additionally,the allocation of the privacy budget between the frequencies of keys and the means of values for each key does not yield an optimal utility tradeoff.Recognizing the importance of obtaining accurate key frequencies and mean estimations for key-value data collection,this paper presents a novel framework:the Key-Strategy Framework forKey-ValueDataCollection under LDP.Initially,theKey-StrategyUnary Encoding(KS-UE)strategy is proposed within non-interactive frameworks for the purpose of privacy budget allocation to achieve precise key frequencies;subsequently,the Key-Strategy Generalized Randomized Response(KS-GRR)strategy is introduced for interactive frameworks to enhance the efficiency of collecting frequent keys through group-anditeration methods.Both strategies are adapted for scenarios in which users possess either a single or multiple key-value pairs.Theoretically,we demonstrate that the variance of KS-UE is lower than that of existing methods.These claims are substantiated through extensive experimental evaluation on real-world datasets,confirming the effectiveness and efficiency of the KS-UE and KS-GRR strategies.
文摘In this study, a multivariate local quadratic polynomial regression(MLQPR) method is proposed to design a model for the sludge volume index(SVI). In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients. Moreover, a local estimation method is introduced to adjust the weights of the quadratic polynomial regression function to improve the model accuracy. Finally, the proposed method is applied to predict the SVI values in a real wastewater treatment process(WWTP). The experimental results demonstrate that the proposed MLQPR method has faster testing speed and more accurate results than some existing methods.
基金supported by National Natural Science Foundation of China (Grant Nos.10871177,11071213)Research Fund for the Doctor Program of Higher Education of China (Grant No.20090101110020)
文摘In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion model.We establish strong consistency and asymptotic normality for the estimate of the second infinitesimal moment of continuous time models using the reweighted Nadaraya-Watson estimator to the true function.
文摘针对微型飞行器(Micro air vehicle,MAV)在室内飞行过程中无法获得GPS信号,而微型惯性单元(Inertial measurement unit,IMU)的陀螺仪和加速度计随机漂移误差较大,提出一种利用单目视觉估计微型飞行器位姿并构建室内环境的方法。在机载单目摄像机拍摄的序列图像中引入一种基于生物视觉的方法获得匹配特征点,并由五点算法获得帧间摄像机运动参数和特征点位置参数的初始解;利用平面关系将特征点的位置信息由三维降低到二维,给出一种局部优化方法求解摄像机运动参数和特征点位置参数的最大似然估计,提高位姿估计和环境构建的精度。最后通过扩展卡尔曼滤波方法融合IMU传感器和单目视觉测量信息解算出微型飞行器的位姿。实验结果表明,该方法能够实时可靠地估计微型飞行器的位置和姿态,构建的环境信息满足导航需求,适用于微型飞行器室内环境中的导航控制。
