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弱依赖下学生化统计量的 Edgeworth 展开AI 解读

In this paper, we derive valid Edgeworth expansions for studentized versions of a large class of statistics when the data are generated by a strongly mixing process. Under dependence, the asymptotic variance of such a statistic is given by an infinite series of lag-covariances, and therefore, studentizing factors (i.e., estimators of the asymptotic standard error) typically involve an increasing number, say, ℓ of lag-covariance estimators, which are themselves quadratic…

弱依赖下区块变量和的渐近展开AI 解读

Let {Xi}i=−∞∞ be a sequence of random vectors and $Y_{in}=f_{in}(\mathcal{X}_{i,\ell})$ be zero mean block-variables where $\mathcal{X}_{i,\ell}=(X_{i},\ldots,X_{i+\ell-1})$, i≥1, are overlapping blocks of length ℓ and where fin are Borel measurable functions. This paper establishes valid joint asymptotic expansions of general orders for the joint distribution of the sums ∑i=1nXi and ∑i=1nYin under weak dependence conditions on the sequence {Xi}i=−∞∞ when the block length ℓ…

短程与长程依赖下离散傅里叶变换渐近独立的充要条件AI 解读

Let $\{X_t\}$ be a stationary time series and let $d_T(\lambda)$ denote the discrete Fourier transform (DFT) of $\{X_0,\ldots,X_{T-1}\}$ with a data taper. The main results of this paper provide a characterization of asymptotic independence of the DFTs in terms of the distance between their arguments under both short- and long-range dependence of the process $\{X_t\}$. Further, asymptotic joint distributions of the DFTs $d_T(\lambda_{1T})$ and $d_T(\lambda_{2T})$ are also…

重尾随机变量归一化和的移动区块自助法渐近行为AI 解读

This paper studies the performance of the moving block bootstrap procedure for normalized sums of dependent random variables. Suppose that $X_1, X_2,\ldots$ are stationary $\rho$-mixing random variables with $\sum \rho (2^i) < \infty$. Let $T_n = (X_1 + \cdots + X_n - b_n)/a_n$, for some suitable constants $a_n$ and $b_n$, and let $T^\ast_{m,n}$ denote the moving block bootstrap version of $T_n$ based on a bootstrap sample of size $m$. Under certain regularity conditions, it…