Nripes Kumar Mandal

Optimal experimental designs for models with covariates

Abstract The model refers to a treatment design or to a block-treatment design in the presence of non-stochastic covariates, attached to each experimental unit. The problem is that of most efficient estimation of covariates parameters on one side and the treatment contrasts and/or block contrasts on the other side. If the components in the two sides are “orthogonal”, then we can invoke optimality [in some sense] separately in each side and thereby characterize optimal designs in such a set-up. Following Lopes Troya (J. Statist. Plann. Inference 6 (1982a) 373, J. Statist. Plann. Inference 7 (1982b) 49), we investigate the underlying combinatorial problems in the context of CRD, RBD and BIBD in order to accommodate maximum number of covariates. Hadamard matrices and mutually orthogonal Latin squares play a central role in this study.

Optimal designs in growth curve models: Part I Correlated model for linear growth: Optimal designs for slope parameter estimation and growth prediction

Abstract In the present paper we discuss the situation for a linear growth with correlated structure of the errors and indicate the nature of optimal designs for estimation and prediction problems. We study the intraclass structure of the error distribution. As regards estimation of the slope parameter, we look for robust optimal designs. Here robustness means that optimality should hold for a large variety of correlation parameters. The robust optimal designs for the prediction problem center around a performance measure of the predictors for all design points simultaneously. We have also studied the autocorrelated error structure and found similar results which are reported very briefly.

Minimax designs for estimating the optimum point in a quadratic response surface

Abstract We consider designs when interest is in estimating the optimal factor combination in a multiple quadratic regression setup, supposing that this factor combination belongs to a given set. By involving the concepts of admissibility and invariance of designs we substantially reduce the problem of calculating minimax designs. Exemplary, we give optimal designs for some setups on the ball and on the cube.

Optimum Mixture Design Using Deficiency Criterion

In a mixture experiment the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffe (1958, 1963) first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. The problem of estimating the optimum proportion of mixture components is of great practical importance. Pal and Mandal (2006, 2007) attempted to find a solution to this problem by adopting a pseudo-Bayesian approach and using the trace criterion. Subsequently, Pal and Mandal (2008) solved the problem using minimax criterion. In this article, the deficiency criterion due to Chatterjee and Mandal (1981) has been used as a measure for comparing the performance of competing designs.

Uncertain Resources and Optimal Designs : Problems and Perspectives

ABSTRACT: Considered is an experimental situation where an experimenter has a certain amount of guaranteed fund at the current period and a 100% chance of an enhanced fund to be made available at a later date. The objective is to decide on an optimal planned experiment. Ideally, the experimenter should start with an optimal experiment and extend it in an optimal fashion as and when the additional fund is made available. This, however, may not lead to an optimal strategy in the long run. We speciaiize to the set‐up of a block design and discuss variovs aspects of this prablcm, after properly formulating the same in proper perspectives. Severa 1 illustrative examples are presented to highlight the compiexities involved.

Optimum designs for estimation of optimum point under cost constraint

In this paper, we consider the estimation of the optimum factor combination in a response surface model. Assuming that the response function is quadratic concave and there is a linear cost constraint on the factor combination, we attempt to find the optimum design using the trace optimality criterion. As the criterion function involves the unknown parameters, we adopt a pseudo-Bayesian approach to resolve the problem.

Optimum Designs for Estimation of Parameters in a Quadratic Mixture-Amount Model

The authors propose a mixture-amount model, which is quadratic both in the proportions of mixing components and the amount of mixture. They attempt to find the A- and D-optimal designs for the estimation of the model parameters within a subclass of designs. The optimality of the derived designs in the entire class of competing designs has been investigated through equivalence theorem.

Pitman Nearness, Distance Criterion and Optimal Regression Designs:

Pitman Nearness is a criterion for point estimation while the Distance Criterion is an optimality criterion. There is indeed a striking similarity between the two. In this paper we will present a variety of basic results towards estimation and ⁄ or prediction in the context of a regression model , based on the distance criterion .

Optimum covariate designs in split-plot and strip-plot design set-ups

The problem considered is that of finding optimum covariate designs for estimation of covariate parameters in standard split-plot and strip-plot design set-ups with the levels of the whole-plot factor in r randomised blocks. Also an extended version of a mixed orthogonal array has been introduced, which is used to construct such optimum covariate designs. Hadamard matrices, as usual, play the key role for such construction.

D-Optimum Designs for Estimating Optimum Points in a Quantitative Multiresponse Experiment

The problem of estimating the optimum factor combinations in a multifactor, multiresponse experiment has been considered, The criterion used is the extended D-optimality criterion. The property of convexity of a transform of the criterion function and the principle of invariance have been used to find optimum designs. This is a generalization of the problem considered by Mandai (1982).