Abstract
This book is about experiments; it concerns situations where we have to organize an experiment in order to gain some information about an object of interest. Fragments of this information can be obtained by making observations within some elementary experiments called trials. We shall confound the action of making an experiment with the variables that characterize this action and use the term experimental design for both.
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Notes
- 1.
Situations where the assumption of independence for different trials does not hold require a special treatment, and the methods to be used differ very much according to the type of prior knowledge about the dependence structure of the observations; see, e.g., Fedorov and Hackl [1997, Sect. 5.3], Pázman and Müller (2001, 2010), Müller and Pázman [2003], and Zhu and Zhang [2006]. However, replacing the assumption of independent errors by that of errors forming a martingale difference sequence does not modify the situation very much for regression models, in particular in the context of sequential design; see, e.g., Lai and Wei [1982] and Pronzato [2009a].
- 2.
There exist situations, however, where a continuous design can be implemented without any approximation; this is the case, for example, when designing the experiment corresponds to choosing the power spectral density of the input signal for a dynamical system; see Goodwin and Payne [1977, Chap. 6], Zarrop [1979], Ljung [1987, Chap. 14], and Walter and Pronzato [1997, Chap. 6].
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Pronzato, L., Pázman, A. (2013). Introduction. In: Design of Experiments in Nonlinear Models. Lecture Notes in Statistics, vol 212. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6363-4_1
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