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语言对象数据的空间建模：分析英国方言发音差异AI 解读

Dialect variation is of considerable interest in linguistics and other social sciences. However, traditionally it has been studied using proxies (transcriptions) rather than acoustic recordings directly. We introduce novel statistical techniques to analyze geolocalized speech recordings and to explore the spatial variation of pronunciations continuously over the region of interest, as opposed to traditional isoglosses, which provide a discrete partition of the region. Data…

随机曲面非参数协方差算子的可分离性检验AI 解读

The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible, either for computational reasons, or due to a small sample size. However, inferential tools to verify this assumption are somewhat lacking in high-dimensional or functional data analysis settings, where this assumption is most relevant. We…

函数型时间序列动态差异的检测与定位：分子生物物理案例AI 解读

Motivated by the problem of inferring the molecular dynamics of DNA in solution, and linking them with its base-pair composition, we consider the problem of comparing the dynamics of functional time series (FTS), and of localizing any inferred differences in frequency and along curvelength. The approach we take is one of Fourier analysis, where the complete second-order structure of the FTS is encoded by its spectral density operator, indexed by frequency and curvelength.…

函数空间中平稳时间序列的傅里叶分析AI 解读

We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which generalises the notion of a spectral density matrix to the functional setting, and characterises the second-order dynamics of the process. Our main tool is the functional Discrete Fourier Transform (fDFT). We derive an…