Suppose that the time series Xt satisfieswhere α0≥δ＞0,αi≥0 for i=1,2,…,q;βi,i=1,…,p, are real numbers; p and q are the order of the model. The sequence {ξt};（0,1） and is independent of {hs,s≤t} for fixed ...Suppose that the time series Xt satisfieswhere α0≥δ＞0,αi≥0 for i=1,2,…,q;βi,i=1,…,p, are real numbers; p and q are the order of the model. The sequence {ξt};（0,1） and is independent of {hs,s≤t} for fixed t. The above model is usually written as AR（p）-ARCH（q）.We consider stationary series AR（p）-ARCH（q） model and assume the stationary field is θ0. We express this statement asH1:α1≥α2…≥αq,β1≥β2≥…≥βp and we consider an order restricted testing problem, which is to testH0:α1=α2=…=αq,β1=β2=…=βpagainst H1-H0. We derive the likelihood ratio （LR） test statistic and its asymptotic distri-展开更多
In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction...In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order： α1≥α2≥…≥αq and β1≥β2≥…≥βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio （LR） test statistic for the testing problem and derive its asymptotic null distribution.展开更多
Deals with the determination of the nearly best linear estimates of location and scale parameters of a logistic population, when both parameters are unknown, by introducing Blom’s semi empirical ’α,β correction’ ...Deals with the determination of the nearly best linear estimates of location and scale parameters of a logistic population, when both parameters are unknown, by introducing Blom’s semi empirical ’α,β correction’ into the asymptotic mean and covariance formulae with complete and ordered samples taken into consideration and various nearly best linear estimates established and points out the high efficiency of these estimators relative to the best linear unbiased estimators (BLUEs) and other linear estimators makes them useful in practice.展开更多
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solution...Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.展开更多
In this paper, we study Robin boundary vlaue problem for third order equation εx'' = f(t, x, x', ω(ε)x', ε), x(0) = A, a1x'(0) - a2x'(0) = B, b1x'(1) +b2x'(1) = C. By means of upper...In this paper, we study Robin boundary vlaue problem for third order equation εx'' = f(t, x, x', ω(ε)x', ε), x(0) = A, a1x'(0) - a2x'(0) = B, b1x'(1) +b2x'(1) = C. By means of upper and lower solutions method, and the existenceand asymptotic estimation of solution are established.展开更多
We develop higher order accurate estimators of integrated volatility in a stochastic volatility models by using kernel smoothing method and using different weights to kernels. The weights have some relationship to mom...We develop higher order accurate estimators of integrated volatility in a stochastic volatility models by using kernel smoothing method and using different weights to kernels. The weights have some relationship to moment problem. As the bandwidth of the kernel vanishes, an estimator of the instantaneous stochastic volatility is obtained. We also develop some new estimators based on smoothing splines.展开更多
Let m be a positive integer, g(m) be the number of integers t for which 1≤t≤m and there does not exist a positive integer n satisfying (t=t(n))t~ n+1 ≡t(modm).For a number x≥3, letG(x)=∑m≤xg(m).In this paper, we...Let m be a positive integer, g(m) be the number of integers t for which 1≤t≤m and there does not exist a positive integer n satisfying (t=t(n))t~ n+1 ≡t(modm).For a number x≥3, letG(x)=∑m≤xg(m).In this paper, we obtain the asymptotic formula:G(x)=αx^2+O(xlogx),as x→∞. Our result improves the corresponding result with an error term O(xlog^2x) of Yang Zhaohua obtained in 1986.展开更多
The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social netwo...The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social networks). In this paper, the authors study the asymptotic property of the moment estimator based on the degrees of vertices in ordered networks whose edges are ordered random variables. In particular, the authors establish the uniform consistency and the asymptotic normality of the moment estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.展开更多
When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are func...When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .展开更多
When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are func...When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .展开更多
文摘Suppose that the time series Xt satisfieswhere α0≥δ＞0,αi≥0 for i=1,2,…,q;βi,i=1,…,p, are real numbers; p and q are the order of the model. The sequence {ξt};（0,1） and is independent of {hs,s≤t} for fixed t. The above model is usually written as AR（p）-ARCH（q）.We consider stationary series AR（p）-ARCH（q） model and assume the stationary field is θ0. We express this statement asH1:α1≥α2…≥αq,β1≥β2≥…≥βp and we consider an order restricted testing problem, which is to testH0:α1=α2=…=αq,β1=β2=…=βpagainst H1-H0. We derive the likelihood ratio （LR） test statistic and its asymptotic distri-
文摘In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order： α1≥α2≥…≥αq and β1≥β2≥…≥βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio （LR） test statistic for the testing problem and derive its asymptotic null distribution.
文摘Deals with the determination of the nearly best linear estimates of location and scale parameters of a logistic population, when both parameters are unknown, by introducing Blom’s semi empirical ’α,β correction’ into the asymptotic mean and covariance formulae with complete and ordered samples taken into consideration and various nearly best linear estimates established and points out the high efficiency of these estimators relative to the best linear unbiased estimators (BLUEs) and other linear estimators makes them useful in practice.
文摘Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.
文摘In this paper, we study Robin boundary vlaue problem for third order equation εx'' = f(t, x, x', ω(ε)x', ε), x(0) = A, a1x'(0) - a2x'(0) = B, b1x'(1) +b2x'(1) = C. By means of upper and lower solutions method, and the existenceand asymptotic estimation of solution are established.
文摘We develop higher order accurate estimators of integrated volatility in a stochastic volatility models by using kernel smoothing method and using different weights to kernels. The weights have some relationship to moment problem. As the bandwidth of the kernel vanishes, an estimator of the instantaneous stochastic volatility is obtained. We also develop some new estimators based on smoothing splines.
文摘Let m be a positive integer, g(m) be the number of integers t for which 1≤t≤m and there does not exist a positive integer n satisfying (t=t(n))t~ n+1 ≡t(modm).For a number x≥3, letG(x)=∑m≤xg(m).In this paper, we obtain the asymptotic formula:G(x)=αx^2+O(xlogx),as x→∞. Our result improves the corresponding result with an error term O(xlog^2x) of Yang Zhaohua obtained in 1986.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271147,11471135partially supported by the National Natural Science Foundation of China under Grant No.11401239+1 种基金Funds of CCNU from the Colleges’s Basic Research and Operation of MOE(CCNU15A02032,CCNU15ZD011)a Fund from KLAS(130026507)
文摘The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social networks). In this paper, the authors study the asymptotic property of the moment estimator based on the degrees of vertices in ordered networks whose edges are ordered random variables. In particular, the authors establish the uniform consistency and the asymptotic normality of the moment estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.
文摘When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .
文摘When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to a good approximation, normally distributed. But, when the support boundaries are functions of the parameter, finding good approximation for the sampling distribution of MLE (needed to construct an accurate confidence interval for the parameter’s true value) may get very challenging. We demonstrate the nature of this problem, and show how to deal with it, by a detailed study of a specific situation. We also indicate several possible ways to bypass MLE by proposing alternate estimators;these, having relatively simple sampling distributions, then make constructing a confidence interval rather routine. .
