Andrey Pepelyshev

Learn More
In this paper we discuss a class of multiplicative algorithms for computing D-optimal designs for regression models on a finite design space. We prove a monotonicity result for a sequence of determinants obtained by the iterations, and as a consequence the procedure yields a sequence of designs converging to the D-optimal design. The class of algorithms is(More)
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 Doptimal design is close to the equally spaced design. Moreover, the equally spaced design is usually very efficient, even for(More)
The Zernike polynomials arise in several applications such as optical metrology or image analysis on a circular domain. In the present paper we determine optimal designs for regression models which are represented by expansions in terms of Zernike polynomials. We consider two estimation methods for the coefficients in these models and determine the(More)
The permutation approach for testing the equality of distributions and thereby comparing two populations of functional data has recently received increasing attention thanks to the flexibility of permutation tests to handle complex testing problems. The purpose of this work is to present some new insights in the context of nonparametric inference on(More)
We consider two frequently used PK/PD models and provide closed form descriptions of locally optimal designs for estimating individual parameters. In a novel way, we use these optimal designs and construct locally standardized maximin optimal designs for estimating any subset of the model parameters of interest. We do this by maximizing the minimal(More)
In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is provided, which extends the classical equivalence theory for optimal designs in models with uncorrelated errors to the(More)
We investigate optimal designs for discriminating between exponential regression models of different complexity, which are widely used in the biological sciences; see, e.g., Landaw (1995) or Gibaldi and Perrier (1982). We discuss different approaches for the construction of appropriate optimality criteria, and find sharper upper bounds on the number of(More)
We discuss the optimal design problem in regression models with long range dependence error structure. Asymptotic optimal designs are derived and it is demonstrated that these designs depend only indirectly on the correlation function. Several examples are investigated to illustrate the theory. Finally the optimal designs are compared with asymptotic(More)
In this paper the optimal design problem for the estimation of the individual coe cients in a polynomial regression on an arbitrary interval a b a b is considered Recently Sahm demonstrated that the optimal design is one of four types depending on the symmetry parameter s a b a b and the speci c coe cient which has to be estimated In the same paper the(More)