In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; ...In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences.展开更多
In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete co...In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.展开更多
The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-depend...The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-dependent finite populations means. The asymptotic properties (unbiasedness and consistency) of the proposed estimator are investigated. Comparisons between different parametric and nonparametric estimators are performed based on the bootstrap standard deviation, mean square error and percentage relative bias. A simulation study is carried out to determine the best performing estimator of the time-dependent finite population means. The simulation results show that local linear regression estimator yields good properties.展开更多
We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math...We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math.Inequal.,2019,13(1):251–260].As an application of the main results,we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.展开更多
Consider the nonparametric regression model Y=go（T）+u,where Y is real-valued,u is a random error,T ranges over a nondegenerate compact interval,say[0,1],and go（·）is anunknown regression function,which is m（m...Consider the nonparametric regression model Y=go（T）+u,where Y is real-valued,u is a random error,T ranges over a nondegenerate compact interval,say[0,1],and go（·）is anunknown regression function,which is m（m≥0）times continuously differentiable and its ruthderivative,g<sub>0</sub><sup>（m）</sup>,satisfies a H■lder condition of order γ（m +γ】1/2）.A piecewise polynomial L<sub>1</sub>-norm estimator of go is proposed.Under some regularity conditions including that the randomerrors are independent but not necessarily have a common distribution,it is proved that therates of convergence of the piecewise polynomial L<sub>1</sub>-norm estimator are o(n<sup>-2（m+γ）+1/m+γ-1/δ</sup>almostsurely and o(n<sup>-2（m+γ）+1/m+γ-δ</sup>)in probability,which can arbitrarily approach the optimal rates ofconvergence for nonparametric regression,where δ is any number in （0, min（（m+γ-1/2）/3,γ））.展开更多
We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warp...We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warped wavelet basis. We investigate the properties of this new basis and evaluate its asymptotic performance by determining an upper bound of the mean integrated squared error under different dependence structures. We prove that it attains a sharp rate of convergence for a wide class of unknown regression functions.展开更多
In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by ...In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.展开更多
Transient stability assessment(TSA) is of great importance in power systems. For a given contingency, one of the most widely-used transient stability indices is the critical clearing time(CCT), which is a function of ...Transient stability assessment(TSA) is of great importance in power systems. For a given contingency, one of the most widely-used transient stability indices is the critical clearing time(CCT), which is a function of the pre-fault power flow.TSA can be regarded as the fitting of this function with the prefault power flow as the input and the CCT as the output. In this paper, a data-driven TSA model is proposed to estimate the CCT. The model is based on Mahalanobis-kernel regression,which employs the Mahalanobis distance in the kernel regression method to formulate a better regressor. A distance metric learning approach is developed to determine the problem-specific distance for TSA, which describes the dissimilarity between two power flow scenarios. The proposed model is more accurate compared to other data-driven methods, and its accuracy can be further improved by supplementing more training samples.Moreover, the model provides the probability density function of the CCT, and different estimations of CCT at different conservativeness levels. Test results verify the validity and the merits of the method.展开更多
We consider the estimation of causal treatment effect using nonparametric regression orinverse propensity weighting together with sufficient dimension reduction for searching lowdimensional covariate subsets. A specia...We consider the estimation of causal treatment effect using nonparametric regression orinverse propensity weighting together with sufficient dimension reduction for searching lowdimensional covariate subsets. A special case of this problem is the estimation of a responseeffect with data having ignorable missing response values. An issue that is not well addressedin the literature is whether the estimation of the low-dimensional covariate subsets by sufficient dimension reduction has an impact on the asymptotic variance of the resulting causaleffect estimator. With some incorrect or inaccurate statements, many researchers believe thatthe estimation of the low-dimensional covariate subsets by sufficient dimension reduction doesnot affect the asymptotic variance. We rigorously establish a result showing that this is nottrue unless the low-dimensional covariate subsets include some covariates superfluous for estimation, and including such covariates loses efficiency. Our theory is supplemented by somesimulation results.展开更多
基金Supported by the Science Development Foundation of HFUT(041002F)
文摘In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences.
基金Supported by the Research Teaching Model Curriculum of Anhui University(xjyjkc1407)Supported by the Students Innovative Training Project of Anhui University(201310357004,201410357117,201410357249)Supported by the Quality Improvement Projects for Undergraduate Education of Anhui University(ZLTS2015035)
文摘In this paper, by using some inequalities of negatively orthant dependent(NOD,in short) random variables and the truncated method of random variables, we investigate the nonparametric regression model. The complete consistency result for the estimator of g(x) is presented.
文摘The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-dependent finite populations means. The asymptotic properties (unbiasedness and consistency) of the proposed estimator are investigated. Comparisons between different parametric and nonparametric estimators are performed based on the bootstrap standard deviation, mean square error and percentage relative bias. A simulation study is carried out to determine the best performing estimator of the time-dependent finite population means. The simulation results show that local linear regression estimator yields good properties.
基金China(Grant Nos.11671012,11871072)the Natural Science Foundation of Anhui Province(1808085QA03,1908085QA01,1908085QA07)+1 种基金the Provincial Natural Science Research Project of Anhui Colleges(KJ2019A0001,KJ2019A0003)the Students Innovative Training Project of Anhui University(S201910357342).
文摘We establish some results on the complete moment convergence for weighted sums of widely orthant-dependent(WOD)random variables,which improve and extend the corresponding results of Y.F.Wu,M.G.Zhai,and J.Y.Peng[J.Math.Inequal.,2019,13(1):251–260].As an application of the main results,we investigate the complete consistency for the estimator in a nonparametric regression model based on WOD errors and provide some simulations to verify our theoretical results.
基金Supported by the National Natural Science Foundation of China.
文摘Consider the nonparametric regression model Y=go（T）+u,where Y is real-valued,u is a random error,T ranges over a nondegenerate compact interval,say[0,1],and go（·）is anunknown regression function,which is m（m≥0）times continuously differentiable and its ruthderivative,g<sub>0</sub><sup>（m）</sup>,satisfies a H■lder condition of order γ（m +γ】1/2）.A piecewise polynomial L<sub>1</sub>-norm estimator of go is proposed.Under some regularity conditions including that the randomerrors are independent but not necessarily have a common distribution,it is proved that therates of convergence of the piecewise polynomial L<sub>1</sub>-norm estimator are o(n<sup>-2（m+γ）+1/m+γ-1/δ</sup>almostsurely and o(n<sup>-2（m+γ）+1/m+γ-δ</sup>)in probability,which can arbitrarily approach the optimal rates ofconvergence for nonparametric regression,where δ is any number in （0, min（（m+γ-1/2）/3,γ））.
文摘We consider the problem of estimating an unknown density and its derivatives in a regression setting with random design. Instead of expanding the function on a regular wavelet basis, we expand it on the basis , a warped wavelet basis. We investigate the properties of this new basis and evaluate its asymptotic performance by determining an upper bound of the mean integrated squared error under different dependence structures. We prove that it attains a sharp rate of convergence for a wide class of unknown regression functions.
文摘In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.
基金supported by National Key R&D Program of China (No.2018YFB0904500)State Grid Corporation of China。
文摘Transient stability assessment(TSA) is of great importance in power systems. For a given contingency, one of the most widely-used transient stability indices is the critical clearing time(CCT), which is a function of the pre-fault power flow.TSA can be regarded as the fitting of this function with the prefault power flow as the input and the CCT as the output. In this paper, a data-driven TSA model is proposed to estimate the CCT. The model is based on Mahalanobis-kernel regression,which employs the Mahalanobis distance in the kernel regression method to formulate a better regressor. A distance metric learning approach is developed to determine the problem-specific distance for TSA, which describes the dissimilarity between two power flow scenarios. The proposed model is more accurate compared to other data-driven methods, and its accuracy can be further improved by supplementing more training samples.Moreover, the model provides the probability density function of the CCT, and different estimations of CCT at different conservativeness levels. Test results verify the validity and the merits of the method.
基金This research was partially supported through a PatientCentered Outcomes Research Institute(PCORI)Award(ME-1409-21219)This research was also supported by the National Natural Science Foundation of China(11501208)+2 种基金Fundamental Research Funds for the Central Universities,National Social Science Foundation(13BTJ009)the Chinese 111 Project grant(B14019)the U.S.National Science Foundation(DMS-1305474 and DMS-1612873).
文摘We consider the estimation of causal treatment effect using nonparametric regression orinverse propensity weighting together with sufficient dimension reduction for searching lowdimensional covariate subsets. A special case of this problem is the estimation of a responseeffect with data having ignorable missing response values. An issue that is not well addressedin the literature is whether the estimation of the low-dimensional covariate subsets by sufficient dimension reduction has an impact on the asymptotic variance of the resulting causaleffect estimator. With some incorrect or inaccurate statements, many researchers believe thatthe estimation of the low-dimensional covariate subsets by sufficient dimension reduction doesnot affect the asymptotic variance. We rigorously establish a result showing that this is nottrue unless the low-dimensional covariate subsets include some covariates superfluous for estimation, and including such covariates loses efficiency. Our theory is supplemented by somesimulation results.
