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函数型时间序列实质性假设检验的统一理论AI 解读

In this paper, we develop a {\em unified} framework for testing relevant hypotheses in functional time series. The proposed approach accommodates one-sample, two-sample, and change point problems for contaminated observations under arbitrary sampling schemes. Combining B-spline estimation with self-normalization, we construct nuisance-parameter-free tests that bypass auxiliary estimation of long-run covariance functions and measurement-error variance functions. We establish…

从稀疏到稠密的函数型时间序列：结构突变检测的相变及拓展AI 解读

We develop a novel methodology for detecting abrupt break points in mean functions of functional time series, adaptable to arbitrary sampling schemes. By employing B-spline smoothing, we introduce $\mathcal L_{\infty}$ and $\mathcal L_2$ test statistics statistics based on a smoothed cumulative summation (CUMSUM) process, and derive the corresponding asymptotic distributions under the null and local alternative hypothesis, as well as the phase transition boundary from sparse…