LetX 1,…,X n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+1,q ? 1. Let $f_n (x) = n^{ - 1} c(h)\sum\nolimits_{i = 1}^n {K[(1 - x'X_i )...LetX 1,…,X n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+1,q ? 1. Let $f_n (x) = n^{ - 1} c(h)\sum\nolimits_{i = 1}^n {K[(1 - x'X_i )/h^2 ]} $ be a kernel estimator off(x). In this paper we establish a central limit theorem for integrated square error off n under some mild conditions.展开更多
The problem of hazard rate estimation under right-censored assumption has been investigated extensively.Integrated square error(ISE)of estimation is one of the most widely accepted measurements of the global performan...The problem of hazard rate estimation under right-censored assumption has been investigated extensively.Integrated square error(ISE)of estimation is one of the most widely accepted measurements of the global performance for nonparametric kernel estimation.But there are no results available for ISE of hazard rate estimation under right-censored model with censoring indicators missing at random(MAR)so far.This paper constructs an imputation estimator of the hazard rate function and establish asymptotic normality of the ISE for the kernel hazard rate estimator with censoring indicators MAR.At the same time,an asymptotic representation of the mean integrated square error(MISE)is also presented.The finite sample behavior of the estimator is investigated via one simple simulation.展开更多
This paper explores pole placement techniques for the 4th order C1 DC-to-DC Buck converter focusing on optimizing various performance metrics. Refinements were made to existing ITAE (Integral of Time-weighted Absolute...This paper explores pole placement techniques for the 4th order C1 DC-to-DC Buck converter focusing on optimizing various performance metrics. Refinements were made to existing ITAE (Integral of Time-weighted Absolute Error) polynomials. Additionally, metrics such as IAE (Integral Absolute Error), ISE (Integral of Square Error), ITSE (Integral of Time Squared Error), a MaxMin metric as well as LQR (Linear Quadratic Regulator) were evaluated. PSO (Particle Swarm Optimization) was employed for metric optimization. Time domain response to a step disturbance input was evaluated. The design which optimized the ISE metric proved to be the best performing, followed by IAE and MaxMin (with equivalent results) and then LQR.展开更多
Histogram and kernel estimators are usually regarded as the two main classical data-based nonparametric tools to estimate the underlying density functions for some given data sets. In this paper we will integrate them...Histogram and kernel estimators are usually regarded as the two main classical data-based nonparametric tools to estimate the underlying density functions for some given data sets. In this paper we will integrate them and define a histogram-kernel error based on the integrated square error between histogram and binned kernel density estimator, and then exploit its asymptotic properties. 3ust as indicated in this paper, the histogram-kernel error only depends on the choice of bin width and the data for the given prior kernel densities. The asymptotic optimal bin width is derived by minimizing the mean histogram-kernel error. By comparing with Scott＇s optimal bin width formula for a histogram, a new method is proposed to construct the data-based histogram without knowledge of the underlying density function. Monte Carlo study is used to verify the usefulness of our method for different kinds of density functions and sample sizes.展开更多
This paper presents an adaptive neuro fuzzy interference system （ANFIS） based approach to tune the parameters of the static synchronous compensator （STAT- COM） with frequent disturbances in load model and power in...This paper presents an adaptive neuro fuzzy interference system （ANFIS） based approach to tune the parameters of the static synchronous compensator （STAT- COM） with frequent disturbances in load model and power input of a wind-diesel based isolated hybrid power system （IHPS）. In literature, proportional integral （PI） based controller constants are optimized for voltage stability in hybrid systems due to the interaction of load disturbances and input power disturbances. These conventional controlling techniques use the integral square error （ISE） criterion with an open loop load model. An ANFIS tuned constants of a STATCOM controller for controlling the reactive power requirement to stabilize the voltage variation is proposed in the paper. Moreover, the interaction between the load and the isolated power system is developed in terms of closed loop load interaction with the system. Furthermore, a comparison of transient responses of IHPS is also presented when the system has only the STATCOM and the static compensation requirement of the induction generator is fulfilled by the fixed capacitor, dynamic compensation requirement, meanwhile, is fulfilled by STATCOM. The model is tested for a 1% step increase in reactive power load demand at t = 0 s and then a sudden change of 3% from the 1% at t = 0.01 s for a 1% step increase in power input at variable wind speed model.展开更多
In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present.The outstanding advantage of non-linea...In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present.The outstanding advantage of non-linear wavelet method is estimating the unsoothed functions,however,the classical kernel estimation cannot do this work.At the same time,we study the larger sample properties of the ISE for hazard rate estimator.展开更多
文摘LetX 1,…,X n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+1,q ? 1. Let $f_n (x) = n^{ - 1} c(h)\sum\nolimits_{i = 1}^n {K[(1 - x'X_i )/h^2 ]} $ be a kernel estimator off(x). In this paper we establish a central limit theorem for integrated square error off n under some mild conditions.
基金the China Postdoctoral Science Foundation under Grant No.2019M651422the National Natural Science Foundation of China under Grant Nos.71701127,11831008 and 11971171+3 种基金the National Social Science Foundation Key Program under Grant No.17ZDA091the 111 Project of China under Grant No.B14019the Natural Science Foundation of Shanghai under Grant Nos.17ZR1409000 and 20ZR1423000the Project of Humanities and Social Science Foundation of Ministry of Education under Grant No.20YJC910003。
文摘The problem of hazard rate estimation under right-censored assumption has been investigated extensively.Integrated square error(ISE)of estimation is one of the most widely accepted measurements of the global performance for nonparametric kernel estimation.But there are no results available for ISE of hazard rate estimation under right-censored model with censoring indicators missing at random(MAR)so far.This paper constructs an imputation estimator of the hazard rate function and establish asymptotic normality of the ISE for the kernel hazard rate estimator with censoring indicators MAR.At the same time,an asymptotic representation of the mean integrated square error(MISE)is also presented.The finite sample behavior of the estimator is investigated via one simple simulation.
文摘This paper explores pole placement techniques for the 4th order C1 DC-to-DC Buck converter focusing on optimizing various performance metrics. Refinements were made to existing ITAE (Integral of Time-weighted Absolute Error) polynomials. Additionally, metrics such as IAE (Integral Absolute Error), ISE (Integral of Square Error), ITSE (Integral of Time Squared Error), a MaxMin metric as well as LQR (Linear Quadratic Regulator) were evaluated. PSO (Particle Swarm Optimization) was employed for metric optimization. Time domain response to a step disturbance input was evaluated. The design which optimized the ISE metric proved to be the best performing, followed by IAE and MaxMin (with equivalent results) and then LQR.
基金Supported by the National Natural Science Foundation of China (No. 70371018, 70572074)
文摘Histogram and kernel estimators are usually regarded as the two main classical data-based nonparametric tools to estimate the underlying density functions for some given data sets. In this paper we will integrate them and define a histogram-kernel error based on the integrated square error between histogram and binned kernel density estimator, and then exploit its asymptotic properties. 3ust as indicated in this paper, the histogram-kernel error only depends on the choice of bin width and the data for the given prior kernel densities. The asymptotic optimal bin width is derived by minimizing the mean histogram-kernel error. By comparing with Scott＇s optimal bin width formula for a histogram, a new method is proposed to construct the data-based histogram without knowledge of the underlying density function. Monte Carlo study is used to verify the usefulness of our method for different kinds of density functions and sample sizes.
文摘This paper presents an adaptive neuro fuzzy interference system （ANFIS） based approach to tune the parameters of the static synchronous compensator （STAT- COM） with frequent disturbances in load model and power input of a wind-diesel based isolated hybrid power system （IHPS）. In literature, proportional integral （PI） based controller constants are optimized for voltage stability in hybrid systems due to the interaction of load disturbances and input power disturbances. These conventional controlling techniques use the integral square error （ISE） criterion with an open loop load model. An ANFIS tuned constants of a STATCOM controller for controlling the reactive power requirement to stabilize the voltage variation is proposed in the paper. Moreover, the interaction between the load and the isolated power system is developed in terms of closed loop load interaction with the system. Furthermore, a comparison of transient responses of IHPS is also presented when the system has only the STATCOM and the static compensation requirement of the induction generator is fulfilled by the fixed capacitor, dynamic compensation requirement, meanwhile, is fulfilled by STATCOM. The model is tested for a 1% step increase in reactive power load demand at t = 0 s and then a sudden change of 3% from the 1% at t = 0.01 s for a 1% step increase in power input at variable wind speed model.
文摘In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present.The outstanding advantage of non-linear wavelet method is estimating the unsoothed functions,however,the classical kernel estimation cannot do this work.At the same time,we study the larger sample properties of the ISE for hazard rate estimator.
