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
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
[ Objective] The study aimed to correct error of lightning location data with small amplitude. [ Method] Using the curve fitting toolbox of matlab mathematical software, the distribution of lightning location data in ...[ Objective] The study aimed to correct error of lightning location data with small amplitude. [ Method] Using the curve fitting toolbox of matlab mathematical software, the distribution of lightning location data in Chongqing during 1999 -2008 was fitted based on logarithmic normal distribution function, and the specific characters of lightning data with current amplitude from -10 to 10 kA were analyzed. [ Result] During 1999 - 2008, the frequency of lightning with current amplitude from -10 to 10 kA in Chongqing City accounted for 4.93% of total frequency, while the fre- quency of lightning with current amplitude from -5 to 5 kA accounted for only 1.27%, lower than 2%, according with the conventional deletion proportion in China. Lightning data with current amplitude from -5 to 5 kA caused a great disturbance to the fitting effect, so the fitting effect was the best after these lightning data was deleted. After the lightning location system of Chongqing City was upgraded in 2005, the frequency of lightning with current amplitude from -10 to 10 kA decreased, and there were obvious changes in the frequency of lightning with current amplitude from -10 to -5 kA and from 5 to 10 kA, while the frequency of lightning with current amplitude from -5 to 5 kA was small and stable, so these data could be deleted. [Conclusion] The research could provide theoretical references for error correction of lightning location data with small amplitude in Chongqing City.展开更多
In this paper, the estimation of the parameters in partial functional linear models with ARCH(p) errors is discussed. With employing the functional principle component, a hybrid estimating method is suggested. The asy...In this paper, the estimation of the parameters in partial functional linear models with ARCH(p) errors is discussed. With employing the functional principle component, a hybrid estimating method is suggested. The asymptotic normality of the proposed estimators for both the linear parameter in the mean model and the parameter in the ARCH error model is obtained, and the convergence rate of the slope function estimate is established. Besides, some simulations and a real data analysis are conducted for illustration, and it is shown that the proposed method performs well with a finite sample.展开更多
The aim of this paper is to present a generalization of the Shapiro-Wilk W-test or Shapiro-Francia W'-test for application to two or more variables. It consists of calculating all the unweighted linear combination...The aim of this paper is to present a generalization of the Shapiro-Wilk W-test or Shapiro-Francia W'-test for application to two or more variables. It consists of calculating all the unweighted linear combinations of the variables and their W- or W'-statistics with the Royston’s log-transformation and standardization, z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub>. Because the calculation of the probability of z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub> is to the right tail, negative values are truncated to 0 before doing their sum of squares. Independence in the sequence of these half-normally distributed values is required for the test statistic to follow a chi-square distribution. This assumption is checked using the robust Ljung-Box test. One degree of freedom is lost for each cancelled value. Defined the new test with its two variants (Q-test or Q'-test), 50 random samples with 4 variables and 20 participants were generated, 20% following a multivariate normal distribution and 80% deviating from this distribution. The new test was compared with Mardia’s, runs, and Royston’s tests. Central tendency differences in type II error and statistical power were tested using the Friedman’s test and pairwise comparisons using the Wilcoxon’s test. Differences in the frequency of successes in statistical decision making were compared using the Cochran’s Q test and pairwise comparisons using the McNemar’s test. Sensitivity, specificity and efficiency proportions were compared using the McNemar’s Z test. The generated 50 samples were classified into five ordered categories of deviation from multivariate normality, the correlation between this variable and p-value of each test was calculated using the Spearman’s coefficient and these correlations were compared. Family-wise error rate corrections were applied. The new test and the Royston’s test were the best choices, with a very slight advantage Q-test over Q'-test. Based on these promising results, further study and use of this new sensitive, specific and effective test are suggested.展开更多
<span style="font-family:Verdana;">This paper represents</span> <span style="font-family:Verdana;">a continuation of</span><span style="color:#C45911;"> <...<span style="font-family:Verdana;">This paper represents</span> <span style="font-family:Verdana;">a continuation of</span><span style="color:#C45911;"> </span><span><span style="white-space:nowrap;"><a href="#ref1" target="_blank">[1]</a></span><span style="font-family:Verdana;"> and</span> <span style="white-space:nowrap;"><a href="#ref2" target="_blank">[2]</a></span></span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.</span>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.
基金the Special Project for Public Welfare Industry(GYHY200806014)
文摘[ Objective] The study aimed to correct error of lightning location data with small amplitude. [ Method] Using the curve fitting toolbox of matlab mathematical software, the distribution of lightning location data in Chongqing during 1999 -2008 was fitted based on logarithmic normal distribution function, and the specific characters of lightning data with current amplitude from -10 to 10 kA were analyzed. [ Result] During 1999 - 2008, the frequency of lightning with current amplitude from -10 to 10 kA in Chongqing City accounted for 4.93% of total frequency, while the fre- quency of lightning with current amplitude from -5 to 5 kA accounted for only 1.27%, lower than 2%, according with the conventional deletion proportion in China. Lightning data with current amplitude from -5 to 5 kA caused a great disturbance to the fitting effect, so the fitting effect was the best after these lightning data was deleted. After the lightning location system of Chongqing City was upgraded in 2005, the frequency of lightning with current amplitude from -10 to 10 kA decreased, and there were obvious changes in the frequency of lightning with current amplitude from -10 to -5 kA and from 5 to 10 kA, while the frequency of lightning with current amplitude from -5 to 5 kA was small and stable, so these data could be deleted. [Conclusion] The research could provide theoretical references for error correction of lightning location data with small amplitude in Chongqing City.
文摘In this paper, the estimation of the parameters in partial functional linear models with ARCH(p) errors is discussed. With employing the functional principle component, a hybrid estimating method is suggested. The asymptotic normality of the proposed estimators for both the linear parameter in the mean model and the parameter in the ARCH error model is obtained, and the convergence rate of the slope function estimate is established. Besides, some simulations and a real data analysis are conducted for illustration, and it is shown that the proposed method performs well with a finite sample.
文摘The aim of this paper is to present a generalization of the Shapiro-Wilk W-test or Shapiro-Francia W'-test for application to two or more variables. It consists of calculating all the unweighted linear combinations of the variables and their W- or W'-statistics with the Royston’s log-transformation and standardization, z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub>. Because the calculation of the probability of z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub> is to the right tail, negative values are truncated to 0 before doing their sum of squares. Independence in the sequence of these half-normally distributed values is required for the test statistic to follow a chi-square distribution. This assumption is checked using the robust Ljung-Box test. One degree of freedom is lost for each cancelled value. Defined the new test with its two variants (Q-test or Q'-test), 50 random samples with 4 variables and 20 participants were generated, 20% following a multivariate normal distribution and 80% deviating from this distribution. The new test was compared with Mardia’s, runs, and Royston’s tests. Central tendency differences in type II error and statistical power were tested using the Friedman’s test and pairwise comparisons using the Wilcoxon’s test. Differences in the frequency of successes in statistical decision making were compared using the Cochran’s Q test and pairwise comparisons using the McNemar’s test. Sensitivity, specificity and efficiency proportions were compared using the McNemar’s Z test. The generated 50 samples were classified into five ordered categories of deviation from multivariate normality, the correlation between this variable and p-value of each test was calculated using the Spearman’s coefficient and these correlations were compared. Family-wise error rate corrections were applied. The new test and the Royston’s test were the best choices, with a very slight advantage Q-test over Q'-test. Based on these promising results, further study and use of this new sensitive, specific and effective test are suggested.
文摘<span style="font-family:Verdana;">This paper represents</span> <span style="font-family:Verdana;">a continuation of</span><span style="color:#C45911;"> </span><span><span style="white-space:nowrap;"><a href="#ref1" target="_blank">[1]</a></span><span style="font-family:Verdana;"> and</span> <span style="white-space:nowrap;"><a href="#ref2" target="_blank">[2]</a></span></span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.</span>
