Let{Xk,i;k≥1,i≥1}be an array of random variables,{Xk;k≥1}be a strictly stationaryα-mixing sequence,where Xk=(Xk,1,Xk,2,...).Let{pn;n≥1}be a sequence of positive integers such that c1≤p n n≤c2,where c1,c2>0.I...Let{Xk,i;k≥1,i≥1}be an array of random variables,{Xk;k≥1}be a strictly stationaryα-mixing sequence,where Xk=(Xk,1,Xk,2,...).Let{pn;n≥1}be a sequence of positive integers such that c1≤p n n≤c2,where c1,c2>0.In this paper,we obtain the asymptotic distributions of the largest entries Ln=max1≤i<j≤pn|ρ(n)ij|of the sample correlation matrices,whereρ(n)ij denotes the Pearson correlation coefficient between X(i)and X(j),X(i)=(X1,i,X2,i,...).The asymptotic distributions of Ln is derived by using the Chen–Stein Poisson approximation method.展开更多
In this paper, we study the strong consistency and convergence partitioning estimate of nonparametric regression function under the sample that is α sequence taking values in R^d × R^1 with identical distributio...In this paper, we study the strong consistency and convergence partitioning estimate of nonparametric regression function under the sample that is α sequence taking values in R^d × R^1 with identical distribution. rate of modified ((Xi,Yi),i 〉 1} .展开更多
Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing d...Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.展开更多
Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MS...Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.展开更多
1 Main resultsSINCE the concept of complete convergence was raised by Hsu and Robbins (1947), it has at- tracted much attention. The general results were proved by Baum and Katz (1965): if{X<sub>n</sub>...1 Main resultsSINCE the concept of complete convergence was raised by Hsu and Robbins (1947), it has at- tracted much attention. The general results were proved by Baum and Katz (1965): if{X<sub>n</sub>,n≥1} is a sequence of i. i. d. random variables with EX<sub>n</sub>=0 E|X<sub>1</sub>|<sup>p</sup>【∞, p≥1, 1≥α】展开更多
In this paper,the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered.With the help of stochastic approximation algorithms with expanding...In this paper,the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered.With the help of stochastic approximation algorithms with expanding truncations,the authors give the recursive estimates for the parameters of both the linear system and the binary sensor.Under reasonable conditions,all constructed estimates are proved to be convergent to the true values with probability one,and the convergence rates are also established.A simulation example is provided to justify the theoretical results.展开更多
Value-at-Risk(VaR)and expected shortfall(ES)are two key risk measures in financial risk management.Comparing these two measures has been a hot debate,and most discussions focus on risk measure properties.This paper us...Value-at-Risk(VaR)and expected shortfall(ES)are two key risk measures in financial risk management.Comparing these two measures has been a hot debate,and most discussions focus on risk measure properties.This paper uses independent data and autoregressive models with normal or t-distribution to examine the effect of the heavy tail and dependence on comparing the nonparametric inference uncertainty of these two risk measures.Theoretical and numerical analyses suggest that VaR at 99%level is better than ES at 97.5%level for distributions with heavier tails.展开更多
This paper concerns the identification problem of scalar errors-in-variables(EIV)systems with general nonlinear output observations and ARMA observation noises.Under independent and identically distributed(i.i.d.)Gaus...This paper concerns the identification problem of scalar errors-in-variables(EIV)systems with general nonlinear output observations and ARMA observation noises.Under independent and identically distributed(i.i.d.)Gaussian inputs with unknown variance,recursive algorithms for estimating the parameters of the EIV systems are presented.For general nonlinear observations,conditions on the system are imposed to guarantee the almost sure convergence of the estimates.A simulation example is included to justify the theoretical results.展开更多
In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models (GLMs), when designs are fixed points and random variables respect...In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models (GLMs), when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the (conditional) variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the (conditional) variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.展开更多
When addressing various financial problems,such as estimating stock portfolio risk,it is necessary to derive the distribution of the sum of the dependent random variables.Although deriving this distribution requires i...When addressing various financial problems,such as estimating stock portfolio risk,it is necessary to derive the distribution of the sum of the dependent random variables.Although deriving this distribution requires identifying the joint distribution of these random variables,exact estimation of the joint distribution of dependent random variables is difficult.Therefore,in recent years,studies have been conducted on the bound of the sum of dependent random variables with dependence uncertainty.In this study,we obtain an improved Hoeffding inequality for dependent bounded variables.Further,we expand the above result to the case of sub-Gaussian random variables.展开更多
基金National Natural Science Foundation of China(Grant Nos.11771178 and 12171198)the Science and Technology Development Program of Jilin Province(Grant No.20210101467JC)+1 种基金Science and Technology Program of Jilin Educational Department during the“13th Five-Year”Plan Period(Grant No.JJKH20200951KJ)Fundamental Research Funds for the Central Universities。
文摘Let{Xk,i;k≥1,i≥1}be an array of random variables,{Xk;k≥1}be a strictly stationaryα-mixing sequence,where Xk=(Xk,1,Xk,2,...).Let{pn;n≥1}be a sequence of positive integers such that c1≤p n n≤c2,where c1,c2>0.In this paper,we obtain the asymptotic distributions of the largest entries Ln=max1≤i<j≤pn|ρ(n)ij|of the sample correlation matrices,whereρ(n)ij denotes the Pearson correlation coefficient between X(i)and X(j),X(i)=(X1,i,X2,i,...).The asymptotic distributions of Ln is derived by using the Chen–Stein Poisson approximation method.
文摘In this paper, we study the strong consistency and convergence partitioning estimate of nonparametric regression function under the sample that is α sequence taking values in R^d × R^1 with identical distribution. rate of modified ((Xi,Yi),i 〉 1} .
文摘Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.
文摘Asymptotic results are obtained using an approach based on limit theorem results obtained for α-mixing sequences for the class of general spacings (GSP) methods which include the maximum spacings (MSP) method. The MSP method has been shown to be very useful for estimating parameters for univariate continuous models with a shift at the origin which are often encountered in loss models of actuarial science and extreme models. The MSP estimators have also been shown to be as efficient as maximum likelihood estimators in general and can be used as an alternative method when ML method might have numerical difficulties for some parametric models. Asymptotic properties are presented in a unified way. Robustness results for estimation and parameter testing results which facilitate the applications of the GSP methods are also included and related to quasi-likelihood results.
文摘1 Main resultsSINCE the concept of complete convergence was raised by Hsu and Robbins (1947), it has at- tracted much attention. The general results were proved by Baum and Katz (1965): if{X<sub>n</sub>,n≥1} is a sequence of i. i. d. random variables with EX<sub>n</sub>=0 E|X<sub>1</sub>|<sup>p</sup>【∞, p≥1, 1≥α】
文摘In this paper,the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered.With the help of stochastic approximation algorithms with expanding truncations,the authors give the recursive estimates for the parameters of both the linear system and the binary sensor.Under reasonable conditions,all constructed estimates are proved to be convergent to the true values with probability one,and the convergence rates are also established.A simulation example is provided to justify the theoretical results.
文摘Value-at-Risk(VaR)and expected shortfall(ES)are two key risk measures in financial risk management.Comparing these two measures has been a hot debate,and most discussions focus on risk measure properties.This paper uses independent data and autoregressive models with normal or t-distribution to examine the effect of the heavy tail and dependence on comparing the nonparametric inference uncertainty of these two risk measures.Theoretical and numerical analyses suggest that VaR at 99%level is better than ES at 97.5%level for distributions with heavier tails.
基金supported by the National Natural Science Foundation of China under Grant No.11571362.
文摘This paper concerns the identification problem of scalar errors-in-variables(EIV)systems with general nonlinear output observations and ARMA observation noises.Under independent and identically distributed(i.i.d.)Gaussian inputs with unknown variance,recursive algorithms for estimating the parameters of the EIV systems are presented.For general nonlinear observations,conditions on the system are imposed to guarantee the almost sure convergence of the estimates.A simulation example is included to justify the theoretical results.
基金Supported by the National Natural Science Foundation of China (No.10471140).
文摘In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models (GLMs), when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the (conditional) variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the (conditional) variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.
基金This work was supported by JSPS Grant-in-Aid for Young Scientists(Grant No.18K12873)Waseda University Grants for Special Research Projects(“Tokutei Kadai”)(Grant No.2019C-688).
文摘When addressing various financial problems,such as estimating stock portfolio risk,it is necessary to derive the distribution of the sum of the dependent random variables.Although deriving this distribution requires identifying the joint distribution of these random variables,exact estimation of the joint distribution of dependent random variables is difficult.Therefore,in recent years,studies have been conducted on the bound of the sum of dependent random variables with dependence uncertainty.In this study,we obtain an improved Hoeffding inequality for dependent bounded variables.Further,we expand the above result to the case of sub-Gaussian random variables.