Conventional Akaike’s Information Criterion (AIC) for normal error models uses the maximum-likelihood estimator of error variance. Other estimators of error variance, however, can be employed for defining AIC for nor...Conventional Akaike’s Information Criterion (AIC) for normal error models uses the maximum-likelihood estimator of error variance. Other estimators of error variance, however, can be employed for defining AIC for normal error models. The maximization of the log-likelihood using an adjustable error variance in light of future data yields a revised version of AIC for normal error models. It also gives a new estimator of error variance, which will be called the “third variance”. If the model is described as a constant plus normal error, which is equivalent to fitting a normal distribution to one-dimensional data, the approximated value of the third variance is obtained by replacing (n-1) (n is the number of data) of the unbiased estimator of error variance with (n-4). The existence of the third variance is confirmed by a simple numerical simulation.展开更多
This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol （NRGS） for an errors- in-variables （EIV） system corrupted with bounded noise. Following an identification framewo...This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol （NRGS） for an errors- in-variables （EIV） system corrupted with bounded noise. Following an identification framework for estimation of a perturbation model set, a worst-case v-gap error bound for the estimated nominal NRGS can be first determined from a priori and a posteriori information on the underlying EIV system. Then, an NRGS perturbation model set can be derived from a close relation between the v-gap metric of two models and H∞-norm of their NRGSs＇ difference. The obtained NRGS perturbation model set paves the way for robust controller design using an H∞ loop-shaping method because it is a standard form of the well-known NCF （normalized coprime factor） perturbation model set. Finally, a numerical simulation is used to demonstrate the effectiveness of the proposed identification method.展开更多
In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original...In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error （MM） and the asymptotic bias （MB）, respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.展开更多
Runoff observation uncertainty is a key unsolved issue in the hydrology community.Existing studies mainly focused on observation uncertainty sources and their impacts on simulation performance,but the impacts on chang...Runoff observation uncertainty is a key unsolved issue in the hydrology community.Existing studies mainly focused on observation uncertainty sources and their impacts on simulation performance,but the impacts on changes of flow regime characteristics remained rare.This study detects temporal changes in 16 flow regime metrics from five main components(i.e.,magnitude,frequency of events,variability,duration,and timing),and evaluates the effects of observation uncertainty on trends of flow regime metrics by adopting a normal distribution error model and using uncertainty width,significant change rate of slopes,coefficient of variation,and degree of deviation.The daily runoff series from 1971 to 2020 at five hydrological stations(i.e.,Huangheyan,Tangnaihai,and Lanzhou in the Yellow River Source Region,Xianyang in the Weihe River Catchment,and Heishiguan in the Yiluo River Catchment)in the water conservation zone of Yellow River are collected for our study.Results showed that:(1)Flow regimes showed significant increases in the low flow magnitude,and significant decreases in the high and average flow magnitude,variability and duration at all the five stations.The magnitude,variability and duration metrics decreased significantly,and the frequency metrics increased significantly at Heishiguan.The low flow magnitude and timing metrics increased significantly,while the high flow magnitude,frequency and variability metrics decreased significantly at Xianyang.The low flow magnitude and high flow timing metrics increased significantly,while the low flow frequency,high flow magnitude and variability metrics decreased significantly in the Yellow River Source Region.(2)Observation uncertainty remarkably impacted the changes of 28.75% of total flow regime metrics at all the stations.The trends of 11.25% of total metrics changed from significance to insignificance,while those of 17.5% of total metrics changed from insignificance to significance.For the rest metrics,the trends remained the same,i.e.,significant(18.75%)and insignificant(52.50%)trends.(3)Observation uncertainty had the greatest impacts on the frequency metrics,especially at Xianyang,followed by duration,variability,timing and magnitude metrics.展开更多
This paper based on the essay [1], studies in case that replicated observations are available in some experimental points., the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptot...This paper based on the essay [1], studies in case that replicated observations are available in some experimental points., the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptotic normality is established.展开更多
To guarantee the accuracy of error analysis and evaluate the manufacturing tolerance s influence,anumerical error analysis method for parallel kinematic machines (PKMs) is presented in this paper.Quasi-Newton method a...To guarantee the accuracy of error analysis and evaluate the manufacturing tolerance s influence,anumerical error analysis method for parallel kinematic machines (PKMs) is presented in this paper.Quasi-Newton method and genetic algorithm are introduced for the forward kinematic solution.Based onthe inverse and forward kinematic solutions,the end-effector s error calculation procedure is developed.To solve the accuracy problem caused by the length and angular parameters' different units,a normalizationmethod is proposed based on the manufacturing tolerance.Comparison between the error analysis resultscalculated by the traditional method and the numerical method for a 4RRR PKM shows that,this numericalerror analysis method is more accurate,simpler,and can evaluate the machine s real error basedon the manufacturing tolerance.展开更多
The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown f...The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.展开更多
文摘Conventional Akaike’s Information Criterion (AIC) for normal error models uses the maximum-likelihood estimator of error variance. Other estimators of error variance, however, can be employed for defining AIC for normal error models. The maximization of the log-likelihood using an adjustable error variance in light of future data yields a revised version of AIC for normal error models. It also gives a new estimator of error variance, which will be called the “third variance”. If the model is described as a constant plus normal error, which is equivalent to fitting a normal distribution to one-dimensional data, the approximated value of the third variance is obtained by replacing (n-1) (n is the number of data) of the unbiased estimator of error variance with (n-4). The existence of the third variance is confirmed by a simple numerical simulation.
基金supported in part by the National Natural Science Foundation of China(Nos.61203119,61304153)the Key Program of Tianjin Natural Science Foundation,China(No.14JCZDJC36300)the Tianjin University of Technology and Education funded project(No.RC14-48)
文摘This paper proposes a novel method to quantify the error of a nominal normalized right graph symbol （NRGS） for an errors- in-variables （EIV） system corrupted with bounded noise. Following an identification framework for estimation of a perturbation model set, a worst-case v-gap error bound for the estimated nominal NRGS can be first determined from a priori and a posteriori information on the underlying EIV system. Then, an NRGS perturbation model set can be derived from a close relation between the v-gap metric of two models and H∞-norm of their NRGSs＇ difference. The obtained NRGS perturbation model set paves the way for robust controller design using an H∞ loop-shaping method because it is a standard form of the well-known NCF （normalized coprime factor） perturbation model set. Finally, a numerical simulation is used to demonstrate the effectiveness of the proposed identification method.
基金The NSF(11271155) of ChinaResearch Fund(20070183023) for the Doctoral Program of Higher Education
文摘In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error （MM） and the asymptotic bias （MB）, respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.
基金National Key Research and Development Program of China,No.2021YFC3201102National Natural Science Foundation of China,No.42071041,No.42171047。
文摘Runoff observation uncertainty is a key unsolved issue in the hydrology community.Existing studies mainly focused on observation uncertainty sources and their impacts on simulation performance,but the impacts on changes of flow regime characteristics remained rare.This study detects temporal changes in 16 flow regime metrics from five main components(i.e.,magnitude,frequency of events,variability,duration,and timing),and evaluates the effects of observation uncertainty on trends of flow regime metrics by adopting a normal distribution error model and using uncertainty width,significant change rate of slopes,coefficient of variation,and degree of deviation.The daily runoff series from 1971 to 2020 at five hydrological stations(i.e.,Huangheyan,Tangnaihai,and Lanzhou in the Yellow River Source Region,Xianyang in the Weihe River Catchment,and Heishiguan in the Yiluo River Catchment)in the water conservation zone of Yellow River are collected for our study.Results showed that:(1)Flow regimes showed significant increases in the low flow magnitude,and significant decreases in the high and average flow magnitude,variability and duration at all the five stations.The magnitude,variability and duration metrics decreased significantly,and the frequency metrics increased significantly at Heishiguan.The low flow magnitude and timing metrics increased significantly,while the high flow magnitude,frequency and variability metrics decreased significantly at Xianyang.The low flow magnitude and high flow timing metrics increased significantly,while the low flow frequency,high flow magnitude and variability metrics decreased significantly in the Yellow River Source Region.(2)Observation uncertainty remarkably impacted the changes of 28.75% of total flow regime metrics at all the stations.The trends of 11.25% of total metrics changed from significance to insignificance,while those of 17.5% of total metrics changed from insignificance to significance.For the rest metrics,the trends remained the same,i.e.,significant(18.75%)and insignificant(52.50%)trends.(3)Observation uncertainty had the greatest impacts on the frequency metrics,especially at Xianyang,followed by duration,variability,timing and magnitude metrics.
基金the National Natural Science Foundation of China (Grant No. 19631040)
文摘This paper based on the essay [1], studies in case that replicated observations are available in some experimental points., the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptotic normality is established.
基金Supported by the National High Technology Research and Development Programme of China ( No. 2007AA041901 )the National Natural Science Foundation of China ( No. 50775117 )+1 种基金the National S&T Major Project ( No. 2009XZ04001-025 )the Technology Innovation Fund of AVIC ( No.2009E 13224 )
文摘To guarantee the accuracy of error analysis and evaluate the manufacturing tolerance s influence,anumerical error analysis method for parallel kinematic machines (PKMs) is presented in this paper.Quasi-Newton method and genetic algorithm are introduced for the forward kinematic solution.Based onthe inverse and forward kinematic solutions,the end-effector s error calculation procedure is developed.To solve the accuracy problem caused by the length and angular parameters' different units,a normalizationmethod is proposed based on the manufacturing tolerance.Comparison between the error analysis resultscalculated by the traditional method and the numerical method for a 4RRR PKM shows that,this numericalerror analysis method is more accurate,simpler,and can evaluate the machine s real error basedon the manufacturing tolerance.
基金Partially supported by the National Natural Science Foundation of China(10571136)
文摘The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.
