## Research Interests

### Optimal designs for correlated observations

- A. Zhigljavsky, H. Dette, A. Pepelyshev (2010)
**A new approach to optimal design for linear models with correlated observations.**

*Abstract*

We consider the problem of designing experiments for regression in the presence of correlated observations with the location model as the main example. For a fixed correlation structure approximate optimal designs are determined explicitly, and it is demonstrated that under the model assumptions made by Bickel and Herzberg (1979) for the determination of asymptotic optimal design, the designs derived in this article converge weakly to the measures obtained by these authors. We also compare the asymptotic optimal design concepts of Sacks and Ylvisaker (1966, 1968) and Bickel and Herzberg (1979) and point out some inconsistencies of the latter. Finally, we combine the best features of both concepts to develop a new approach for the design of experiments for correlated observations, and it is demonstrated that the resulting design problems are related to the (logarithmic) potential theory. - H. Dette, A. Pepelyshev, T. Holland-Letz (2009)
**Optimal designs for random effect models with correlated errors with applications in population pharmacokinetics.**accepted to Ann. of Applied Stat.link

*Abstract*

We consider the problem of constructing optimal designs for population pharmacokinetics which use random effect models. It is common practice in the designing of experiments in such studies to assume uncorrelated errors for each subject, but we introduce a methodology to determine efficient designs for nonlinear least squares estimation with accounting the correlation dependence between observations corresponding to the same subject. We use asymptotic arguments to derive optimal design densities, which yield the designs for finite sample size by taking the quantiles of the corresponding optimal distribution function. It is demonstrated that these designs are very close to the optimal exact designs, whose determination is a hard numerical problem. Alternatively, the designs, derived from the asymptotic theory, can be used as starting designs for the numerical computation of the exact optimal designs. Several examples of linear and nonlinear models are presented in order to illustrate the methodology. In particular, it is demonstrated that naively chosen equally spaced designs may lead to less accurate estimation. - H. Dette, J. Kunert, A. Pepelyshev (2008)
**Exact optimal designs for weighted least squares analysis with correlated errors.**Statistica Sinica, 18, 135-154.link

*Abstract*

In the common linear and quadratic regression model with an autoregressive error structure exact D-optimal designs for weighted least squares analysis are determined. It is demonstrated that for highly correlated observations the D-optimal design is close to the equally spaced design. Moreover, the equally spaced design is usually very efficient, even for moderate sizes of the correlation, while the D-optimal design obtained under the assumptions of independent observations yields a substantial loss in efficiency. We also consider the problem of designing experiments for weighted least squares estimation of the slope in a linear regression and compare the exact D-optimal designs for weighted and ordinary least squares analysis. - Pepelyshev, A. (2007)
**Optimal designs for the exponential model with correlated observations.**mODa 8---Advances in model-oriented design and analysis, 165-172, Contrib. Statist.link

*Abstract*

In the exponential regression model with an autoregressive error structure exact D-optimal designs for weighted least squares analysis are investigated. It is shown that support points of a locally D-optimal design are discontinuous with respect to the correlation parameter. Also equidistant designs are proved to be considerably less efficient than maximin efficient D-optimal designs. A tool used in the study is the functional approach described in a recent book Melas (2006).