We study tile local linear estimator for tile drift coefficient of stochastic differential equations driven by α-stable Levy motions observed at discrete instants. Under regular conditions, we derive the weak consis-...We study tile local linear estimator for tile drift coefficient of stochastic differential equations driven by α-stable Levy motions observed at discrete instants. Under regular conditions, we derive the weak consis- tency and central limit theorem of the estimator. Compared with Nadaraya-Watson estimator, the local linear estimator has a bias reduction whether the kernel function is symmetric or not under different schemes. A silnu- lation study demonstrates that the local linear estimator performs better than Nadaraya-Watson estimator, especially on the boundary.展开更多
In this paper, we consider the empirical likelihood inference for the jump-diffusion model. We construct the confidence intervals based on the empirical likelihood for the infinitesimal moments in the jump-diffusion m...In this paper, we consider the empirical likelihood inference for the jump-diffusion model. We construct the confidence intervals based on the empirical likelihood for the infinitesimal moments in the jump-diffusion models. They are better than the confidence intervals which are based on the asymptotic normality of point estimates.展开更多
In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion model.We establish strong consistency and ...In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion model.We establish strong consistency and asymptotic normality for the estimate of the second infinitesimal moment of continuous time models using the reweighted Nadaraya-Watson estimator to the true function.展开更多
Using the blocking techniques and m-dependent methods,the asymptotic behavior of kernel density estimators for a class of stationary processes,which includes some nonlinear time series models,is investigated.First,the...Using the blocking techniques and m-dependent methods,the asymptotic behavior of kernel density estimators for a class of stationary processes,which includes some nonlinear time series models,is investigated.First,the pointwise and uniformly weak convergence rates of the deviation of kernel density estimator with respect to its mean(and the true density function)are derived.Secondly,the corresponding strong convergence rates are investigated.It is showed,under mild conditions on the kernel functions and bandwidths,that the optimal rates for the i.i.d.density models are also optimal for these processes.展开更多
We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-depen...We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-dependent approximation. Our results can be used in the study of the estimation of value-at-risk(Va R) and applied to many time series which have important applications in econometrics.展开更多
In this paper, we show the invariance principle for the partial sum processes of fractionally integrated processes, otherwise known as I(d + m) processes, where |d| < 1/2 and m is a nonnegative integer, with strong...In this paper, we show the invariance principle for the partial sum processes of fractionally integrated processes, otherwise known as I(d + m) processes, where |d| < 1/2 and m is a nonnegative integer, with strong near-epoch dependent innovations. The results are applied to the test of unit root. The conditions given improve previous results in the literature concerning fractionally integrated processes.展开更多
Let{X k(t),t≥0},k=1,2,…,be a sequence of independent Gaussian processes withσk 2(h)=E(X k(t+h)-X k(t))2.Putσ(p,h)=(∑∞k=1σk p(h))1/p,p≥1.The author establishes the large increment results for boundedσ(p,h).
Let{X n}be a sequence of random variables and X n1X n2…X nn their order statistics.In this paper a central limit theorem and a strong law of large numbers for randomly trimmed sums T n=βn i=αn+1 X ni are establishe...Let{X n}be a sequence of random variables and X n1X n2…X nn their order statistics.In this paper a central limit theorem and a strong law of large numbers for randomly trimmed sums T n=βn i=αn+1 X ni are established in the case thatαn andβn are positive integer-valued random variables such thatαn/n andβn/n converge to random variablesαandβrespectively with 0α<β1 in certain sense,and{X n}is aφ-mixing sequence.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11171303 and 11071213)the Specialized Research Fund for the Doctor Program of Higher Education(Grant No.20090101110020)
文摘We study tile local linear estimator for tile drift coefficient of stochastic differential equations driven by α-stable Levy motions observed at discrete instants. Under regular conditions, we derive the weak consis- tency and central limit theorem of the estimator. Compared with Nadaraya-Watson estimator, the local linear estimator has a bias reduction whether the kernel function is symmetric or not under different schemes. A silnu- lation study demonstrates that the local linear estimator performs better than Nadaraya-Watson estimator, especially on the boundary.
基金supported by National Natural Science Foundation of China(Grant No. 10771095)Natural Science Foundation of Jiangsu Province of China
文摘In this paper, we consider the empirical likelihood inference for the jump-diffusion model. We construct the confidence intervals based on the empirical likelihood for the infinitesimal moments in the jump-diffusion models. They are better than the confidence intervals which are based on the asymptotic normality of point estimates.
基金supported by National Natural Science Foundation of China (Grant Nos.10871177,11071213)Research Fund for the Doctor Program of Higher Education of China (Grant No.20090101110020)
文摘In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion model.We establish strong consistency and asymptotic normality for the estimate of the second infinitesimal moment of continuous time models using the reweighted Nadaraya-Watson estimator to the true function.
基金supported by National Natural Science Foundation of China(Grant Nos.11171303 and 61273093)the Specialized Research Fund for the Doctor Program of Higher Education(Grant No.20090101110020)
文摘Using the blocking techniques and m-dependent methods,the asymptotic behavior of kernel density estimators for a class of stationary processes,which includes some nonlinear time series models,is investigated.First,the pointwise and uniformly weak convergence rates of the deviation of kernel density estimator with respect to its mean(and the true density function)are derived.Secondly,the corresponding strong convergence rates are investigated.It is showed,under mild conditions on the kernel functions and bandwidths,that the optimal rates for the i.i.d.density models are also optimal for these processes.
文摘We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-dependent approximation. Our results can be used in the study of the estimation of value-at-risk(Va R) and applied to many time series which have important applications in econometrics.
基金supported by National Social Science Foundation of China (Grant No.07CTJ001)National Research Project for Statistics (Grant No. 2009LY056)National Natural Science Foundation of China (Grant Nos. 10901136, 71072113)
文摘In this paper, we show the invariance principle for the partial sum processes of fractionally integrated processes, otherwise known as I(d + m) processes, where |d| < 1/2 and m is a nonnegative integer, with strong near-epoch dependent innovations. The results are applied to the test of unit root. The conditions given improve previous results in the literature concerning fractionally integrated processes.
文摘Let{X k(t),t≥0},k=1,2,…,be a sequence of independent Gaussian processes withσk 2(h)=E(X k(t+h)-X k(t))2.Putσ(p,h)=(∑∞k=1σk p(h))1/p,p≥1.The author establishes the large increment results for boundedσ(p,h).
文摘Let{X n}be a sequence of random variables and X n1X n2…X nn their order statistics.In this paper a central limit theorem and a strong law of large numbers for randomly trimmed sums T n=βn i=αn+1 X ni are established in the case thatαn andβn are positive integer-valued random variables such thatαn/n andβn/n converge to random variablesαandβrespectively with 0α<β1 in certain sense,and{X n}is aφ-mixing sequence.