All are welcome!
13:00-14:30, Saturday, June 10, 2017 at the University of Manitoba
We’re proud to present these speakers:
Michelle Carey (CANSSI Postdoctoral Fellow at McGill University, 2015-2016)
Title: Penalized smoothing for density estimation and its implications for risk management
Abstract: Pearson’s system of curves is a flexible class of continuous univariate distributions which includes many classical models. It can accommodate most combinations of mean, variance, skewness, and kurtosis. Each density f in this class is the unique solution to the differential equation f′ + gβf = 0 with gβ(x) = (x − β1)/(β2 + β3x + β4x2) that depends on the choice of β = (β1, β2, β3, β4) ∈ ℝ4. Estimating f from random observations is a challenging problem and the current approaches often fail to produce meaningful estimators. In this talk we show that both β and f can be estimated through an adaptation of a model-based smoothing procedure that incorporates differential equations. The resulting estimate f̂ of f is the distribution within Pearson’s wide class that best represents the data. The approach is illustrated using data on the TSX composite index from the 2008 financial crisis. Estimates of the Value-at-Risk and Expected Shortfall based on f̂ are shown to outperform the estimates currently used by financial institutions and regulators for market risk assessment.
Khurram Nadeem (CANSSI Postdoctoral Fellow at Acadia University, 2014-2015)
Title: Integrating population dynamics models and distance sampling data: a spatial hierarchical state‐space approach.
Abstract: Stochastic versions of Gompertz, Ricker and various other dynamics models play a fundamental role in quantifying strength of density dependence and studying long term dynamics of wildlife populations. These models are frequently estimated using time series of abundance estimates that are inevitably subject to observation error and missing data. This issue can be addressed with a state-space modeling framework that jointly estimates the observed data model and the underlying stochastic population dynamics (SPD) model. In cases where abundance data are from multiple locations with a smaller spatial resolution (e.g. from mark-recapture and distance sampling studies), models are conventionally fitted to spatially pooled estimates of yearly abundances. Here, we demonstrate that a spatial version of SPD models can be directly estimated from short time series of spatially referenced distance sampling data in a unified hierarchical state-space modeling framework that also allows for spatial variance (covariance) in population growth. We also show that a full range of likelihood based inference, including estimability diagnostics and model selection, is feasible in this class of models using a data cloning algorithm. We further show through simulation experiments that the hierarchical state-space framework introduced herein efficiently captures the underlying dynamical parameters and spatial abundance distribution. We apply our methodology by analysing a time series of line-transect distance sampling data for fin whales (Balaenoptera physalus) off the U.S. west coast. Although there were only seven surveys conducted during the study time frame, 1991-2014, our analysis detected presence of strong density regulation and provided reliable estimates of fin whale densities. In summary, we show that the integrative framework developed herein allows ecologists to better infer key population characteristics such as presence of density regulation and spatial variability in a population’s intrinsic growth potential.
Yassir Rabhi (StatLab-CANSSI-CRM Postdoctoral Fellow at the University of Sherbrooke, 2015-2016)
Title: Nonparametric inference for copula function and measures of dependence under length-biased sampling and informative censoring
Abstract: Selection bias is often encountered in cross-sectional surveys and prevalent-cohort studies on disease duration. Biased sampling is known to induce bias on estimating the lifetime and related covariate(s) of a population. In this presentation, we discuss the nonparametric estimation of copula function and its density when the collected data are length-biased and subject to informative censoring. First, we propose an empirical estimator for the bivariate distribution, which is a functional of two MLE, and study its oscillation behavior and i.i.d. representation. Second, based on this estimator, we define a copula estimator and present its limiting process. In addition, we propose a local-polynomials estimator for the copula density, that accounts for the boundary bias, and establish its triangular representation. We also introduce estimators for Kendall and Spearman measures of dependence. The proposed methodology is then applied to analyze a set of survival data collected on elderly Canadian citizens (65+) suffering from dementia.