##### Department of Mathematics,

University of California San Diego

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### Statistics Seminar

## V. Vasiliev

#### Tomsk State University

## A truncated estimation method with guaranteed accuracy

##### Abstract:

The truncated estimation method of ratio type functionals based on a dependent sample of finite size will be presented. This method makes it possible to obtain estimators with guaranteed accuracy in the sense of the $L_{2m}$-norm for $m\geq 1.$ As an illustration, the parametric and non-parametric estimation problems on a time interval of a fixed length are considered. In addition to non-asymptotic properties, the limit behavior of presented estimators is investigated. It is shown that all the truncated estimators have asymptotic properties of basic estimators. In particular, the asymptotic efficiency in the mean square sense of the truncated estimator of the dynamic parameter of a stable autoregressive process is established. As an application, the problem of asymptotic efficiency of adaptive one-step predictors for a stable multivariate first order autoregressive process with unknown parameters is considered. The predictors are based on the truncated estimators of the dynamic matrix parameter. The criterion of optimality is based on the loss function, defined as a sum of sample size and squared prediction error's sample mean.

### October 22, 2014

### 11:00 AM

### AP&M 5829

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