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实数空间中的连续自回归移动平均随机场AI 解读

Summary We define an isotropic Lévy-driven continuous auto-regressive moving average CARMA(p, q) random field on Rn as the integral of a radial CARMA kernel with respect to a Lévy sheet. Such fields constitute a parametric family characterized by an auto-regressive polynomial a and a moving average polynomial b having zeros in both the left and the right complex half-planes. They extend the well-balanced Ornstein–Uhlenbeck process of Schnurr and Woerner to a well-balanced…

Lévy 驱动连续时间 ARMA 过程的预测AI 解读

The conditional expectations, E(Y(h)|Y(u),−∞<u≤0) and E(Y(h)|Y(u),−M≤u≤0) with h>0 and 0<M<∞ are determined for a continuous-time ARMA (CARMA) process (Y(t))t∈R driven by a Lévy process L with E|L(1)|<∞. If E(L(1)2)<∞ these are the minimum mean-squared error predictors of Y(h) given (Y(t))t≤0 and (Y(t))−M≤t≤0 respectively. Conditions are also established under which the sample-path of L can be recovered from that of Y, both when Y is causal and strictly stationary and…

非负 Lévy 驱动 CARMA 过程的估计AI 解读

Continuous-time autoregressive moving average (CARMA) processes with a nonnegative kernel and driven by a nondecreasing Lévy process constitute a useful and very general class of stationary, nonnegative continuous-time processes that have been used, in particular, for the modeling of stochastic volatility. Brockwell, Davis, and Yang (2007) derived efficient estimates of the parameters of a nonnegative Lévy-driven CAR(1) process and showed how the realization of the…

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基于多响应置换程序的一类非参数检验AI 解读

A class of univariate rank tests based on multiresponse permutation procedures is introduced. Asymptotic equivalence is established between one member of this class and the Kruskal-Wallis test. Simulated power comparisons for location shift detection indicate that another member of the class provides superior detection efficiency for location shifts of bimodal distributions and of heavy tailed unimodal distributions. Furthermore, both tests possess substantial computational…

基于多响应置换程序的一类非参数检验AI 解读

A class of univariate rank tests based on multiresponse permutation procedures is introduced. Asymptotic equivalence is established between one member of this class and the Kruskal-Wallis test. Simulated power comparisons for location shift detection indicate that another member of the class provides superior detection efficiency for location shifts of bimodal distributions and of heavy tailed unimodal distributions. Furthermore, both tests possess substantial computational…