28 research outputs found
Intrinsic data depth for Hermitian positive definite matrices
Nondegenerate covariance, correlation and spectral density matrices are
necessarily symmetric or Hermitian and positive definite. The main contribution
of this paper is the development of statistical data depths for collections of
Hermitian positive definite matrices by exploiting the geometric structure of
the space as a Riemannian manifold. The depth functions allow one to naturally
characterize most central or outlying matrices, but also provide a practical
framework for inference in the context of samples of positive definite
matrices. First, the desired properties of an intrinsic data depth function
acting on the space of Hermitian positive definite matrices are presented.
Second, we propose two computationally fast pointwise and integrated data depth
functions that satisfy each of these requirements and investigate several
robustness and efficiency aspects. As an application, we construct depth-based
confidence regions for the intrinsic mean of a sample of positive definite
matrices, which is applied to the exploratory analysis of a collection of
covariance matrices associated to a multicenter research trial
Hyperoxemia and excess oxygen use in early acute respiratory distress syndrome : Insights from the LUNG SAFE study
Publisher Copyright: © 2020 The Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.Background: Concerns exist regarding the prevalence and impact of unnecessary oxygen use in patients with acute respiratory distress syndrome (ARDS). We examined this issue in patients with ARDS enrolled in the Large observational study to UNderstand the Global impact of Severe Acute respiratory FailurE (LUNG SAFE) study. Methods: In this secondary analysis of the LUNG SAFE study, we wished to determine the prevalence and the outcomes associated with hyperoxemia on day 1, sustained hyperoxemia, and excessive oxygen use in patients with early ARDS. Patients who fulfilled criteria of ARDS on day 1 and day 2 of acute hypoxemic respiratory failure were categorized based on the presence of hyperoxemia (PaO2 > 100 mmHg) on day 1, sustained (i.e., present on day 1 and day 2) hyperoxemia, or excessive oxygen use (FIO2 ≥ 0.60 during hyperoxemia). Results: Of 2005 patients that met the inclusion criteria, 131 (6.5%) were hypoxemic (PaO2 < 55 mmHg), 607 (30%) had hyperoxemia on day 1, and 250 (12%) had sustained hyperoxemia. Excess FIO2 use occurred in 400 (66%) out of 607 patients with hyperoxemia. Excess FIO2 use decreased from day 1 to day 2 of ARDS, with most hyperoxemic patients on day 2 receiving relatively low FIO2. Multivariate analyses found no independent relationship between day 1 hyperoxemia, sustained hyperoxemia, or excess FIO2 use and adverse clinical outcomes. Mortality was 42% in patients with excess FIO2 use, compared to 39% in a propensity-matched sample of normoxemic (PaO2 55-100 mmHg) patients (P = 0.47). Conclusions: Hyperoxemia and excess oxygen use are both prevalent in early ARDS but are most often non-sustained. No relationship was found between hyperoxemia or excessive oxygen use and patient outcome in this cohort. Trial registration: LUNG-SAFE is registered with ClinicalTrials.gov, NCT02010073publishersversionPeer reviewe
Time-varying spectral matrix estimation via intrinsic wavelet regression for surfaces of Hermitian positive definite matrices
Intrinsic wavelet transforms and denoising methods are introduced for the purpose of time-varying Fourier spectral matrix estimation. A non-degenerate time-varying spectral matrix constitutes a surface of Hermitian positive definite matrices across time and frequency and any spectral matrix estimator ideally adheres to these geometric constraints. Spectral matrix estimation of a locally stationary time series by means of linear or nonlinear wavelet shrinkage naturally respects positive definiteness at each time-frequency point, without any postprocessing. Moreover, the spectral matrix estimator enjoys equivariance in the sense that it does not nontrivially depend on the chosen basis or coordinate system of the multivariate time series. The algorithmic construction is based on a second-generation average-interpolating wavelet transform in the space of Hermitian positive definite matrices equipped with an affine-invariant metric. The wavelet coefficient decay and linear wavelet thresholding convergence rates of intrinsically smooth surfaces of Hermitian positive definite matrices are derived. Furthermore, practical nonlinear thresholding based on the trace of the matrix-valued wavelet coefficients is investigated. Finally, the time-varying spectral matrix of a nonstationary multivariate electroencephalography (EEG) time series recorded during an epileptic brain seizure is estimated
Intrinsic wavelet regression for curves of Hermitian positive definite matrices
Intrinsic wavelet transforms and wavelet estimation methods are introduced for curves in the non-Euclidean space of Hermitian positive definite matrices, with in mind the application to Fourier spectral estimation of multivariate stationary time series. The main focus is on intrinsic average-interpolation wavelet transforms in the space of positive definite matrices equipped with an affine-invariant Riemannian metric, and convergence rates of linear wavelet thresholding are derived for intrinsically smooth curves of Hermitian positive definite matrices. In the context of multivariate Fourier spectral estimation, intrinsic wavelet thresholding is equivariant under a change of basis of the time series, and nonlinear wavelet thresholding is able to capture localized features in the spectral density matrix across frequency, always guaranteeing positive definite estimates. The finite-sample performance of intrinsic wavelet thresholding is assessed by means of simulated data and compared to several benchmark estimators in the Riemannian manifold. Further illustrations are provided by examining the multivariate spectra of trial-replicated brain signal time series recorded during a learning experiment