In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to...In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .展开更多
Under the assumption of strictly stationary process, this paper proposes a nonparametric model to test the kurtosis and conditional kurtosis for risk time series. We apply this method to the daily returns of S&P500 i...Under the assumption of strictly stationary process, this paper proposes a nonparametric model to test the kurtosis and conditional kurtosis for risk time series. We apply this method to the daily returns of S&P500 index and the Shanghai Composite Index, and simulate GARCH data for verifying the efficiency of the presented model. Our results indicate that the risk series distribution is heavily tailed, but the historical information can make its future distribution light-tailed. However the far future distribution's tails are little affected by the historical data.展开更多
We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ^τX, where the unit vector θ is selected such that the average Kullback-Leib...We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ^τX, where the unit vector θ is selected such that the average Kullback-Leibler discrepancy distance between the two conditional density functions obtains the minimum. Our approach is nonparametric as far as the estimation of the conditional density functions is concerned. We have shown that this nonparametric estimator is asymptotically adaptive to the unknown index θ in the sense that the first order asymptotic mean squared error of the estimator is the same as that when θ was known. The proposed method is illustrated using both simulated and real-data examples.展开更多
This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index ...This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index model,and this approach represents a good compromise between nonparametric and parametric models.Then we give under general conditions and when the variables are independent,the quadratic error and asymptotic normality of estimator by local linear method,based on the single-index structure.Finally,wecomplete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area.展开更多
In order to avoid the discussion of equation (1.1), this paper employs the proof method of Liang (2012) to consider the re-weighted Nadaraya-Watson estimation of conditional density. The established results genera...In order to avoid the discussion of equation (1.1), this paper employs the proof method of Liang (2012) to consider the re-weighted Nadaraya-Watson estimation of conditional density. The established results generalize those of De Gooijer and Zerom (2003). In addition, this paper improves the bandwidth condition of Liang (2012).展开更多
Let S be a periodic set in R and L2(S) be a subspace of L2(R). This paper investigates the density problem for multiwindow Gabor systems in L2(S) for the case that the product of time- frequency shift parameters...Let S be a periodic set in R and L2(S) be a subspace of L2(R). This paper investigates the density problem for multiwindow Gabor systems in L2(S) for the case that the product of time- frequency shift parameters is a rational number. We derive the density conditions for a multiwindow Gabor system to be complete (a frame) in L2(S). Under such conditions, we construct a multiwindow tight Gabor frame for L2 (S) with window functions being characteristic functions. We also provide a characterization of a multiwindow Gabor frame to be a Riesz basis for L2(S), and obtain the density condition for a multiwindow Gabor Riesz basis for L2 (S).展开更多
In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class o...In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class of its equivalent forms.Based on this property,some strong limit theorems including conditional entropy density are studied for the tree-indexed Markov chains in random environment.展开更多
基金Supported by Natural Science Foundation of Beijing City and National Natural Science Foundation ofChina(2 2 30 4 1 0 0 1 30 1
文摘In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .
基金supported by the National Natural Science Foundation of China (Grant No.60773081)the Key Project of Shanghai Municipality (Grant No.S30104)
文摘Under the assumption of strictly stationary process, this paper proposes a nonparametric model to test the kurtosis and conditional kurtosis for risk time series. We apply this method to the daily returns of S&P500 index and the Shanghai Composite Index, and simulate GARCH data for verifying the efficiency of the presented model. Our results indicate that the risk series distribution is heavily tailed, but the historical information can make its future distribution light-tailed. However the far future distribution's tails are little affected by the historical data.
基金supported by US National Science Foundation grant DMS-0704337 National Natural Science Foundation of China(No.10628104)supported by an EPSRC research grant EP/C549058/1
文摘We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ^τX, where the unit vector θ is selected such that the average Kullback-Leibler discrepancy distance between the two conditional density functions obtains the minimum. Our approach is nonparametric as far as the estimation of the conditional density functions is concerned. We have shown that this nonparametric estimator is asymptotically adaptive to the unknown index θ in the sense that the first order asymptotic mean squared error of the estimator is the same as that when θ was known. The proposed method is illustrated using both simulated and real-data examples.
文摘This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index model,and this approach represents a good compromise between nonparametric and parametric models.Then we give under general conditions and when the variables are independent,the quadratic error and asymptotic normality of estimator by local linear method,based on the single-index structure.Finally,wecomplete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area.
基金supported by National Natural Science Foundation of China(No.11301084)Natural Science Foundation of Fujian Province(No.2014J01010)
文摘In order to avoid the discussion of equation (1.1), this paper employs the proof method of Liang (2012) to consider the re-weighted Nadaraya-Watson estimation of conditional density. The established results generalize those of De Gooijer and Zerom (2003). In addition, this paper improves the bandwidth condition of Liang (2012).
基金Supported by National Natural Science Foundation of China(Grant Nos.10901013and11271037)Beijing Natural Science Foundation(Grant No.1122008)Fundamental Research Funds for the Central Universities(Grant No.2011JBM299)
文摘Let S be a periodic set in R and L2(S) be a subspace of L2(R). This paper investigates the density problem for multiwindow Gabor systems in L2(S) for the case that the product of time- frequency shift parameters is a rational number. We derive the density conditions for a multiwindow Gabor system to be complete (a frame) in L2(S). Under such conditions, we construct a multiwindow tight Gabor frame for L2 (S) with window functions being characteristic functions. We also provide a characterization of a multiwindow Gabor frame to be a Riesz basis for L2(S), and obtain the density condition for a multiwindow Gabor Riesz basis for L2 (S).
基金supported by the National Natural Science Foundation of China(Nos.11571142,11971197,11601191)。
文摘In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class of its equivalent forms.Based on this property,some strong limit theorems including conditional entropy density are studied for the tree-indexed Markov chains in random environment.