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- Holger Dette, Andrey Pepelyshev
- Technometrics
- 2010

Space filling designs, which satisfy a uniformity property, are widely used in computer experiments. In the present paper the performance of non-uniform experimental designs which locate more points in a neighborhood of the boundary of the design space is investigated. These designs are obtained by a quantile transformation of the one-dimensionalâ€¦ (More)

- Holger Dette, Andrey Pepelyshev, Anatoly A. Zhigljavsky
- Computational Statistics & Data Analysis
- 2008

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 isâ€¦ (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 forâ€¦ (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 theâ€¦ (More)

- Livio Corain, Viatcheslav B. Melas, Andrey Pepelyshev, Luigi Salmaso
- Adv. Data Analysis and Classification
- 2014

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 onâ€¦ (More)

- Holger Dette, Andrey Pepelyshev, Weng Kee Wong
- Journal of Pharmacokinetics and Pharmacodynamics
- 2012

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 minimalâ€¦ (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 theâ€¦ (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 ofâ€¦ (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 asymptoticâ€¦ (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 theâ€¦ (More)