WebMar 13, 2024 · We study the method for response variables taking values in a general Hilbert space and for local linear smoother. We show that the procedure always improves the bias of the local linear estimator regardless of the choice of parametric model. We also illustrate the method via a real data example where the response variable is a random density. WebMay 23, 2024 · In this article, we propose a test of independence for functional random variables modelled as elements of Hilbert spaces. First, we provide a general recipe for constructing measures of dependence among multiple random functions. These measures are non-negative, and under fairly general assumptions, they take the value zero only when …
FULLY HILBERTIAN FIELDS - arXiv
WebNov 22, 2024 · We develop versions of the Granger–Johansen representation theorems for I (1) and I (2) vector autoregressive processes that apply to processes taking values in an arbitrary complex separable Hilbert space. This more general setting is of central relevance for statistical applications involving functional time series. Web2. The Hilbertian case 10 2.1. The deterministic case 11 2.2. The case of common noise 12 3. Master equations on the set of probability measures 15 3.1. Setting and notation 15 3.2. Main definition and result 17 3.3. Return to the solutions of the initial master equation 20 3.4. Master equations associated to common noise 21 3.5. flocked skinny christmas tree
Ernest Hilbert - Wikipedia
WebIn this article we investigate the field of Hilbertian metrics on probability measures. Since they are very versatile and can therefore be applied in various problems they are of great … WebDec 6, 2024 · We demonstrate that, in a regression setting with a Hilbertian predictor, a response variable is more likely to be more highly correlated with the leading principal components of the predictor than with trailing ones. This is despite the extraction procedure being unsupervised. Our results are established under the conditional independence … WebAbstract. In this paper a new additive regression technique is developed for response variables that take values in general Hilbert spaces. The proposed method is based on the idea of smooth backfitting that has been developed mainly for real-valued responses. The local polynomial smoothing device is adopted, which renders various advantages of ... great lakes shipwreck diving