**Jianqiang Wang**

Visiting Assistant Professor, CSU

**February 12, 2009**

**Mesa Laboratory - Chapman Room **

**Lecture 10:00am**

### Variance Estimation for Non-differentiable Survey Estimators and Variance Reduction Using Bootstrap Aggregating

Many survey estimators involve nondifferentiable functions defined at the population level, examples include lower-income proportions and sample quantiles. Some estimators are nondifferentiable functions of estimated quantities (e.g. lower-income proportions), and others are implicitly defined by estimating equations including sample quantiles.

In this presentation, I will describe the theoretical property of both types of estimators and provide analytic and replication variance estimators. We will also study the effect of bootstrap aggregating (bagging) on the estimators of interest and demonstrate the efficiency gained by bagging the survey estimators (especially quantiles.) The approach will be applied to the problem of outlier detection for survey data.