The outlier detection in multiple linear regression is a difficult problem because of the masking effect. A procedure that works successfully uses residuals based on a high breakdown estimator. The least trimmed squar...
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The outlier detection in multiple linear regression is a difficult problem because of the masking effect. A procedure that works successfully uses residuals based on a high breakdown estimator. The least trimmed squares (LTS) estimator, which was proposed by Rousseeuw (J. Amer. Statist. Assoc. 79 (1984)), is a high breakdown estimator. In this paper we propose two algorithms to compute the LTS estimator. The first algorithm is probabilistic and is based on an exchange procedure. The second algorithm is exact and based on a branch-and-bound technique that guarantees global optimality without exhaustive evaluation. We discuss the implementation of these algorithms using orthogonal decomposition procedures and propose several accelerations. The application of the new algorithms to real and simulated data sets shows that they significantly reduce the computational cost with respect to the algorithms previously described in the literature. (C) 2001 Elsevier Science B.V. All rights reserved.
Cost considerations have rarely been taken into account in optimum design theory. A few authors consider measurement costs, i.e. the cost associated with a particular factor level combination. A second cost approach r...
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Cost considerations have rarely been taken into account in optimum design theory. A few authors consider measurement costs, i.e. the cost associated with a particular factor level combination. A second cost approach results from the fact that it is often expensive to change factor levels from one observation to another. We refer to these costs as transition costs. In view of cost minimization, one should minimize the number of factor level changes. However, there is a substantial likelihood that there is some time-order dependence in the results. Consequently, when considering both time-order dependence and transition costs, an optimal ordering is not easy to find. There is precious little in the literature on how to select good time-order sequences for arbitrary design problems and up to now, no thorough analysis of both costs is found in the literature. Our proposed algorithm incorporates both costs in optimum design construction and enables one to compute cost-efficient and trend-free run orders for arbitrary design problems. The results show that cost considerations in the construction of trend-resistant run orders entail considerable reductions in the total cost of an experiment and imply a large increase in the amount of information per unit cost. (C) 2001 Elsevier Science B.V. All rights reserved.
In industrial experimentation, experimental designs are frequently constructed to estimate all main effects and a few prespecified interactions. The robust-product-design literature is replete with such examples. A ma...
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In industrial experimentation, experimental designs are frequently constructed to estimate all main effects and a few prespecified interactions. The robust-product-design literature is replete with such examples. A major limitation of this approach is the requirement that the experimenter know which interactions are likely to be active in advance. In this article, we develop a class of balanced designs that can be used for estimation of main effects and any combination of up to g interactions, where g is specified by the user. We view this as an issue of model-robust design: We construct designs that are highly efficient for all models involving main effects and g (or fewer) interactions. We compare the performances of these designs with the standard alternatives from the class of maximum-resolution fractional factorial designs for several criteria. The comparison reveals that the new designs are surprisingly robust to model misspecification, something that is generally not true for maximum-resolution fractional factorial designs. This robustness comes at a price: The new designs are frequently not orthogonal. We demonstrate, however, that the loss of orthogonality is, in general, quite small.
A new method for allpass filter design is presented. The method leads to a solution for the phase that is equal to the desired phase for 2N+1 values of frequency (if N is the order of the allpass filter). These values...
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A new method for allpass filter design is presented. The method leads to a solution for the phase that is equal to the desired phase for 2N+1 values of frequency (if N is the order of the allpass filter). These values can be chosen at will in the approximation interval. The resulting phase error therefore displays a ripple behaviour. The solutions obtained in this way could be used as an initial solution for an exchange algorithm in order to produce an equiripple solution.
We explore the viability of a time-independent quantum adiabatic switching algorithm in the Fourier grid Hamiltonian (FGH) framework in the presence of degeneracy, avoided crossing, and chaos. The algorithm is simple ...
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We explore the viability of a time-independent quantum adiabatic switching algorithm in the Fourier grid Hamiltonian (FGH) framework in the presence of degeneracy, avoided crossing, and chaos. The algorithm is simple and cost effective and provides information about the full eigenspectrum of the evolving Hamiltonian. It is shown to be capable of capturing accurately the change in the pattern of level spacing distribution statistics as one switches from a nonchaotic region of parameter values into the chaotic region. The Transition turns out to be less sharp than anticipated. (C) 1998 John Wiley & Sons, Inc.
The main characteristics of a Matlab program to select D-optimal subsets of calibration samples for multiple linear regression are described. The performance of Fedorov's exchange algorithm to select samples is co...
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The main characteristics of a Matlab program to select D-optimal subsets of calibration samples for multiple linear regression are described. The performance of Fedorov's exchange algorithm to select samples is compared with the Kennard-Stone algorithm and the random selection of samples into training and test sets.
The alternation theorem is at the core of efficient real Chebyshev approximation algorithms. In this paper, the alternation theorem is extended from the real-only to the complex case. The complex FIR filter design pro...
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The alternation theorem is at the core of efficient real Chebyshev approximation algorithms. In this paper, the alternation theorem is extended from the real-only to the complex case. The complex FIR filter design problem is reformulated so that it clearly satisfies the Haar condition of Chebyshev approximation. An efficient exchange algorithm is derived for designing complex FIR filters in the Chebyshev sense. By transforming the complex error function, the Remez exchange algorithm can be used to compute the optimal complex Chebyshev approximation. The algorithm converges to the optimal solution whenever the complex Chebyshev error alternates;in all other cases, the algorithm converges to the optimal Chebyshev approximation over a subset of the desired bands. The new algorithm is a generalization of the Parks-McClellan algorithm, so that arbitrary magnitude and phase responses can be approximated. Both causal and noncausal filters with complex or real-valued impulse responses can be designed. Numerical examples are presented to illustrate the performance of the proposed algorithm.
Latin-hypercube designs (Lhd) were considered by Mckay et al. (1979) as designs for computer experiments. Sacks et al. (1989a) and Shewry and Wynn (1987) proposed optimal designs for computer experiments which minimiz...
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Latin-hypercube designs (Lhd) were considered by Mckay et al. (1979) as designs for computer experiments. Sacks et al. (1989a) and Shewry and Wynn (1987) proposed optimal designs for computer experiments which minimize the integrated mean squared error (IMSE) and maximize entropy, respectively, based on some spatial prediction models. In this paper, optimal Latin-hypercube designs minimizing IMSE or maximizing entropy are considered. These designs turn out to be well spread over the design region without replicated coordinate values, often symmetric, and nearly optimal among all Latin-hypercube designs. A 2-stage (exchange- and Newton-type) computational algorithm for finding the proposed design is presented. An example is given to illustrate that a small prediction error is obtained from the optimal Lhd than from the usual Lhd's. Several pictures of designs constructed by the algorithm are presented.
With an optimization problem of minimax type, we associate another problem which is, in turn, of maxmin type. We show that both the problems are equivalent in a sense and they have the same optimal value. The results ...
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The nonlinear Chebyshev approximation of real-valued data is considered where the approximating functions are generated from the solution of parameter dependent initial value problems in ordinary differential equation...
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