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用局部平均估计量进行时间序列非参数函数估计AI 解读

Let $(\mathbf{X}_t, Y_t)$ be a stationary time series with $\mathbf{X}_t$ being $R^d$-valued and $Y_t$ real valued, and where $Y_t$ is not necessarily bounded. Let $E(Y_0 \mid \mathbf{X}_0)$ be the conditional mean function. Under appropriate regularity conditions, local average estimators of this function can be chosen to achieve the optimal rate of convergence $(n^{-1} \log n)^{1/(d + 2)}$ in $L_\infty$ norm restricted to a compact. The result answers a question raised by…

短自回归时间序列均值的最佳线性无偏估计AI 解读

A simple formula for computing the best linear unbiased estimate of the mean of an autoregressive process as well as its variance is given. Numerical results show that the estimate can have much lower variance than that of the usual sample mean.

具有无限方差的一阶自回归过程AI 解读

For a first-order autoregressive process Y t = β Y t−1 + ∈ t where the ∈ t 'S are i.i.d. and belong to the domain of attraction of a stable law, the strong consistency of the ordinary least-squares estimator b n of β is obtained for β = 1, and the limiting distribution of b n is established as a functional of a Lévy process. Generalizations to seasonal difference models are also considered. These results are useful in testing for the presence of unit roots when the ∈ t 'S…

混合样本的参数估计AI 解读

Assume that a sample is a mixture of two samples from two different populations with distributions Fθ1 and Fθ2 . Given the form of Fθ , estimators of θ1 and θ2 are introduced. It is shown that the estimators are consistent and their asymptotic joint distribution is derived. The suggested estimators are compared with the maximum likelihood estimators and the method of moments estimators. For small sample sizes the comparison is done by a Monte Carlo study. For large sample…

混合样本中的参数估计AI 解读

Assume that a sample is a mixture of two samples from two different populations with distributions Fθ1 and Fθ2 . Given the form of Fθ , estimators of θ1 and θ2 are introduced. It is shown that the estimators are consistent and their asymptotic joint distribution is derived. The suggested estimators are compared with the maximum likelihood estimators and the method of moments estimators. For small sample sizes the comparison is done by a Monte Carlo study. For large sample…