Quasi-Likelihood Estimation for Ornstein-Uhlenbeck Diffusion Observed at Random Time Points

2000 Mathematics Subject Classification: 60J60, 62M99.In this paper, we study the quasi-likelihood estimator of the drift parameter θ in the Ornstein-Uhlenbeck diffusion process, when the process is observed at random time points, which are assumed to be unobservable. These time points are arrival times of a Poisson process with known rate. The asymptotic properties of the quasi-likelihood estimator (QLE) of θ, as well as those of its approximations are also elucidated. An extensive simulation study of these estimators is also performed. As a corollary to this work, we obtain the quasi-likelihood estimator iteratively in the deterministic framework with non-equidistant time points.The first and third authors greatly appreciate the support of the Naturel Sciences and Engineering Research Council of Canada for this research

The Importance of Relevance: Willingness to Share eHealth Data for Family Medicine Research

Objective: To determine the proportion of family medicine patients unwilling to allow their eHealth data to be used for research purposes, and evaluate how patient characteristics and the relevance of research impact that decision.Design: Cross-sectional questionnaire.Setting: Acute care respiratory clinic or an outpatient family medicine clinic in Montreal, Quebec.Participants: Four hundred seventy-four waiting room patients recruited via convenience sampling.Main Outcome Measures: A self-administered questionnaire collected data on age, gender, employment status, education, mother tongue and perceived health status. The main outcome of was self-reported relevance of three research scenarios and willingness or refusal to share their anonymized data. Responses were compared for family practice vs. specialty care patients.Results: The questionnaire was completed by 229 family medicine respondents and 245 outpatient respondents. Almost a quarter of all respondents felt the research was not relevant. Family medicine patients (15.7%) were unwilling to allow their data to be used for at least one scenario vs. 9.4% in the outpatient clinic. Lack of relevance (OR 11.55; 95% CI 5.12–26.09) and being in family practice (OR 2.13; 95% CI 1.06–4.27) increased the likelihood of refusal to share data for research.Conclusion: Family medicine patients were somewhat less willing to share eHealth data, but the overall refusal rate indicates a need to better engage patients in understanding the significance of full access to eHealth data for the purposes of research. Personal relevance of the research had a strong impact on the responses arguing for better efforts to make research more pertinent to patients

Small Area Estimation of Latent Economic Well-being

© The Author(s) 2019. Small area estimation (SAE) plays a crucial role in the social sciences due to the growing need for reliable and accurate estimates for small domains. In the study of well-being, for example, policy makers need detailed information about the geographical distribution of a range of social indicators. We investigate data dimensionality reduction using factor analysis models and implement SAE on the factor scores under the empirical best linear unbiased prediction approach. We contrast this approach with the standard approach of providing a dashboard of indicators or a weighted average of indicators at the local level. We demonstrate the approach in a simulation study and a real data application based on the European Union Statistics for Income and Living Conditions for the municipalities of Tuscany

Oscillation theorems for ordinary differential equations.

Many of the following arguments were mentioned in a paper by Licko and Svec [5]. We are going to use these lemmas throughout Chapter II. [...

Nonparametric Curve Estimation By Wavelet Thresholding With Locally Stationary Errors

In the modeling of biological phenomena, in living organisms whether the measurements are of blood pressure, enzyme levels, biomechanical movements or heartbeats, etc., one of the important aspects is time variation in the data. Thus, the recovery of a "smooth" regression or trend function from noisy time--varying sampled data becomes a problem of particular interest. Here we use non--linear wavelet thresholding to estimate a regression or a trend function in the presence of additive noise which, in contrast to most existing models, does not need to be stationary. (Here, nonstationarity means that the spectral behaviour of the noise is allowed to change slowly over time). We develop a procedure to adapt existing threshold rules to such situations, e.g., that of a time--varying variance in the errors. Moreover, in the model of curve estimation for functions belonging to a Besov class with locally stationary errors, we derive a near--optimal rate for the L 2 --risk between the unknown fu..

Shrinkage estimators for the dispersion parameter of the inverse Gaussian distribution

This article derives improved estimators of the dispersion parameter, [lambda], of an inverse Gaussian distribution by employing techniques similar to those of Brown (1968) and Brewster and Zidek (1974) in the normal variance problem.