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对称性：非参数回归中的一般结构
In this paper, we present the framework of symmetry in nonparametric regression. This generalises the framework of covariate sparsity, where the regression function f:[0,1]d→R depends only on at most s
曲面上函数的统计分析及医学影像应用
–In functional data analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional manifold and the domain itself is subject to variability from sample to sample. We formulate a statistical model for such data, here called functions on surfaces, which enables a joint representation of the geometric and functional…
语言对象数据的空间建模：分析英国方言发音差异
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
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…
动态神经影像数据反卷积的函数型方法
Positron emission tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first-order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. To provide an analysis of PET data which…
三维列联表的似然比检验
Likelihood ratio (LR) tests for association and for interaction are examined for three-way contingency tables, particularly the widely used 2 × 2 × K table. Mutual information identities are used to characterize the information decomposition and the logical relationship between the omnibus LR test for conditional independence across K strata and its two independent components, LR tests for interaction and for uniform association. The latter two tests are logically connected…