Diaries or questionnaires for collecting self-reported healthcare utilisation and patient cost data? CHERE Project Report No 20

The literature comparing diaries and questionnaires was reviewed in order to identify the most appropriate method of collecting patient self-reported data, on health service utilisation and out-ofpocket costs, for a longitudinal study. Nine published studies met the review inclusion criteria; four compared the diary method with a self-completed questionnaire and five with an interviewer administered questionnaire. None of the eligible studies measured patient costs, and only two measured some aspects of health service utilisation. Most of the studies reported higher response rates for questionnaires than for diaries, and there was some evidence of selection bias. There was a tendency to report more symptoms, symptom intensity or health care utilisation by questionnaires compared to diaries, and compared to physician reports (included in only two studies). The review provides some information about the two approaches for collecting self-reported data, but does not provide sufficient evidence to favour either approach.diaries, health care utilisation

Spectrum Estimation: A Unified Framework for Covariance Matrix Estimation and PCA in Large Dimensions

Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or even larger. In such settings, there is a common remedy for both statistical problems: nonlinear shrinkage of the eigenvalues of the sample covariance matrix. The optimal nonlinear shrinkage formula depends on unknown population quantities and is thus not available. It is, however, possible to consistently estimate an oracle nonlinear shrinkage, which is motivated on asymptotic grounds. A key tool to this end is consistent estimation of the set of eigenvalues of the population covariance matrix (also known as the spectrum), an interesting and challenging problem in its own right. Extensive Monte Carlo simulations demonstrate that our methods have desirable finite-sample properties and outperform previous proposals.Comment: 40 pages, 8 figures, 5 tables, University of Zurich, Department of Economics, Working Paper No. 105, Revised version, July 201

Characterizing Driving Context from Driver Behavior

Because of the increasing availability of spatiotemporal data, a variety of data-analytic applications have become possible. Characterizing driving context, where context may be thought of as a combination of location and time, is a new challenging application. An example of such a characterization is finding the correlation between driving behavior and traffic conditions. This contextual information enables analysts to validate observation-based hypotheses about the driving of an individual. In this paper, we present DriveContext, a novel framework to find the characteristics of a context, by extracting significant driving patterns (e.g., a slow-down), and then identifying the set of potential causes behind patterns (e.g., traffic congestion). Our experimental results confirm the feasibility of the framework in identifying meaningful driving patterns, with improvements in comparison with the state-of-the-art. We also demonstrate how the framework derives interesting characteristics for different contexts, through real-world examples.Comment: Accepted to be published at The 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL 2017

The quest for the ultimate anisotropic Banach space

We present a new scale $U^{t,s}_p$ (with $s<-t<0$ and $1 \le p <\infty$) of anisotropic Banach spaces, defined via Paley-Littlewood, on which the transfer operator associated to a hyperbolic dynamical system has good spectral properties. When $p=1$ and $t$ is an integer, the spaces are analogous to the "geometric" spaces considered by Gou\"ezel and Liverani. When $p>1$ and $-1+1/p<s<-t<0<t<1/p$, the spaces are somewhat analogous to the geometric spaces considered by Demers and Liverani. In addition, just like for the "microlocal" spaces defined by Baladi-Tsujii, the spaces $U^{t,s}_p$ are amenable to the kneading approach of Milnor-Thurson to study dynamical determinants and zeta functions. In v2, following referees' reports, typos have been corrected (in particular (39) and (43)). Section 4 now includes a formal statement (Theorem 4.1) about the essential spectral radius if $d_s=1$ (its proof includes the content of Section 4.2 from v1). The Lasota-Yorke Lemma 4.2 (Lemma 4.1 in v1) includes the claim that $\cal M_b$ is compact. Version v3 contains an additional text "Corrections and complements" showing that s> t-(r-1) is needed in Section 4.Comment: 31 pages, revised version following referees' reports, with Corrections and complement

Cleaning large correlation matrices: tools from random matrix theory

This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marchenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.Comment: 165 pages, article submitted to Physics Report