Entropy inequalities for some multivariate distributions

AbstractIn this paper, we derive some monotonicity properties of generalized entropy functionals of various multivariate distributions. These include the distributions of random eigenvalues arising in many hypothesis testing problems in multivariate analysis; the multivariate Liouville distributions; and the noncentral Wishart distributions

Compact group actions, spherical bessel functions, and invariant random variables

The theory of compact group actions on locally compact abelian groups provides a unifying theory under which different invariance conditions studied in several contexts by a number of statisticians are subsumed as special cases. For example, Schoenberg’s characterization of radially symmetric characteristic functions on Iw” is extended to this general context and the integral representations are expressed in terms of the generalized spherical Bessel functions of Gross and Kunze. These same Bessel functions are also used to obtain a variant of the Lkvy-Khinchine formula of Parthasarathy, Ranga Rao, and Varadhan appropriate to invariant distributions

R.A.P.I.D. (Root Aggregated Prioritized Information Display): A single screen display for efficient digital triaging of medical reports

AbstractObjectiveThe timely acknowledgement of critical patient clinical reports is vital for the delivery of safe patient care. With current EHR systems, critical reports reside on different screens. This leads to treatment delays and inefficient work flows. As a remedy, the R.A.P.I.D. (Root Aggregated Prioritized Information Display) system represents all data on a single screen, and its simple and intuitive “button” array structure allows triaged sign-off/sign-out of critical and non-critical reports.Materials and methodsWith 100 hematology and chemistry reports from each of two EHR systems Meditech (Westwood, MA) and Orchard Labs, Inc. (Carmel, IN), we generated files of the reports in their individual standard display formats (enhanced Meditech-EM and enhanced Orchard-EO). We also displayed the same 200 reports in the R.A.P.I.D. format. We then conducted a randomized trial to compare the time and accuracy of acknowledgement of critical and non-critical results.ResultsThe sign-off times for reviewing the results for physician and non-physician providers, respectively, in seconds (with 95% confidence intervals) were for EM 1.78 (1.40–2.26) and 1.99 (1.72–2.30), for EO 2.69 (2.12–3.42) and 2.78 (2.40–3.21), and for R.A.P.I.D. 0.83 (0.70–0.98) and 1.58 (1.43–1.76). Non-physician providers reassigned system-defined non-critical results as critical with a frequency of 15.2% for EM, 18.4% for EO, and 7.83% for R.A.P.I.D., and critical results as non-critical with a frequency of 14.7%, 5.6%, and 5.8% respectively.DiscussionThe new display system was superior to two standard EHR systems that were significantly enhanced by first collecting the reports from their usual distributed locations and then by creating for each of the two standard EHRs a single file of reports for acknowledgement.ConclusionsFrom a single screen display of all reports, the new display system enables timely acknowledgement of critical reports for patient safety and non-critical report triage for improved provider work flows

Multivariate Liouville distributions

A random vector (X1, ..., Xn), with positive components, has a Liouville distribution if its joint probability density function is of the formf(x1 + ... + xn)x1a1.1 ... xnan.1 with theai all positive. Examples of these are the Dirichlet and inverted Dirichlet distributions. In this paper, a comprehensive treatment of the Liouville distributions is provided. The results pertain to stochastic representations, transformation properties, complete neutrality, marginal and conditional distributions, regression functions, and total positivity and reverse rule properties. Further, these topics are utilized in various characterizations of the Dirichlet and inverted Dirichlet distributions. Matrix analogs of the Liouville distributions are also treated, and many of the results obtained in the vector setting are extended appropriately.Dirichlet distribution regression total positivity reverse rule stochastic representation characterizations fractional integral

Finite-sample inference with monotone incomplete multivariate normal data, I

We consider problems in finite-sample inference with two-step, monotone incomplete data drawn from , a multivariate normal population with mean and covariance matrix . We derive a stochastic representation for the exact distribution of , the maximum likelihood estimator of . We obtain ellipsoidal confidence regions for through T2, a generalization of Hotelling's statistic. We derive the asymptotic distribution of, and probability inequalities for, T2 under various assumptions on the sizes of the complete and incomplete samples. Further, we establish an upper bound for the supremum distance between the probability density functions of and , a normal approximation to .Ellipsoidal confidence regions Hotelling's T2-statistic Matrix -distribution Maximum likelihood estimation Missing completely at random Multivariate Esseen's inequality Simultaneous confidence intervals Wishart distribution