# Two UBC Statistics Master's Students' Presentations - Tue, Aug 22 at 11am (ESB 4192)

Tuesday, August 22, 2017 - 11:00 to 12:00
Qiong Zhang and Yiwei Hou, UBC Statistics Master's Students
Statistics Seminar
Room 4192, Earth Sciences Building (2207 Main Mall)

11am - 11:30am:  Qiong Zhang

Title:  Small Area Quantile Estimation under Unit-Level Models

Abstract:  Sample surveys are widely used as a cost-effective way to collect information on variables of interest in target populations. In applications, we are generally interested in parameters such as population means, totals, and quantiles. Similar parameters for subpopulations or areas, formed by geographic areas and socio-demographic groups, are also of interest in applications. However, the sample size might be small or even zero in subpopulations due to the probability sampling and the budget limitation. There has been intensive research on how to produce reliable estimates for characteristics of interest for subpopulations for which the sample size is small or even zero. We call this line of research Small Area Estimation (SAE).

In this talk, I present the work from my Master's thesis, which studies a number of unit-level model-based small area quantile estimators. Since the model-based estimates can be misleading and their mean squared errors can be underestimated if the model assumption is wrong, simulation studies have been conducted to investigate the performance of three small area quantile estimators in the literature. They are found not to be very robust in some likely situations. Based on the observations, a few attempts have been made to obtain more robust small area quantile estimators. My talk will cover: (1) a brief introduction to small area estimation, (2) motivation for our new approach, and (3) simulation study results.

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11:30am - 12:00pm:  Yiwei Hou

Title:  Risk Region Estimation for Light-tailed Multivariate Samples

Abstract:  Accurate assessments for the probabilities of extreme events in multivariate cases are of great importance in various applications. Assuming the data can be described by a multivariate probability density, we can define risk regions as the multivariate quantile regions that correspond to very small probabilities.  In applications, these risk regions can serve as  multivariate stress test scenarios in financial risk management or be used for flagging events of extreme aviation risk when assessing airline performances.  However, estimation for such risk regions is difficult since the probability level  may be so small that there is hardly any or no data in these regions. There is an ongoing development of sophisticated statistical methods to estimate multivariate risk regions under different assumptions in the literature.  We investigate the problem of risk region estimation for a particular class of distributions that have homothetic level sets of non-specified shape. Such distributions generalize the family of elliptical distributions, moving away from the elliptical symmetry. For this class of distributions, we propose a new inference framework that allows flexible model assumptions and assess its performance through simulation studies.

In this talk, I present the work from my Master's thesis, which discusses this new estimation method. My talk will cover 1) the motivation for the new method, 2) details about this method and 3) simulation results and data examples.