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对数周期图的自动平滑AI 解读

We develop an objective optimum smoothing procedure for an estimate of the log spectral density, based on smoothing the log periodogram with a smoothing spline. We call the result the optimally smoothed spline (OSS) estimate. We show that an unbiased estimate [Rcirc](λ) of the expected integrated mean square error can be obtained as a function of the smoothing, or “bandwidth” parameter λ. The smoothing parameter then is chosen as that λ that minimizes [Rcirc](λ). The degree…

对数周期图的自动平滑AI 解读

We develop an objective optimum smoothing procedure for an estimate of the log spectral density, based on smoothing the log periodogram with a smoothing spline. We call the result the optimally smoothed spline (OSS) estimate. We show that an unbiased estimate [Rcirc](λ) of the expected integrated mean square error can be obtained as a function of the smoothing, or “bandwidth” parameter λ. The smoothing parameter then is chosen as that λ that minimizes [Rcirc](λ). The degree…

若干核等价类的回归设计AI 解读

Earlier results on asymptotically optimal sequences of regression designs for autoregressive stochastic processes are extended (nearly) to the equivalence classes of such processes.

平稳多元时间序列的若干独立性检验AI 解读

Summary Let X(t)=(X1(t)X2(t)⋮XP(t)),t=⋯−1,0,1…, be a p-dimensional zero-mean stationary Gaussian time series possessing a spectral density matrix F(ω) = {fij(ω)}, i, j = 1, 2, …, p, satisfying some mild regularity conditions. Let F^(ωl), l=1, 2, … ,M, F^(ωl)={f^ij(ωl)} be suitably defined sample spectral density matrices for M values of ω, based on a record of length T ≫ M. We consider the following (null) hypotheses: H1: Xi(t), Xi(s) independent if i ≠ j, all s, t, H2:…