Robust integral compounding criteria for trend and correlation structures

Optimal Designs for Series Estimation in Nonparametric Regression With Correlated Data

“…for example, Pázman and Müller (2001), Näther and Simák (2003), Müller and Stehlík (2004), Harman and Stulajter (2010), Amo-Salas et al (2012), Stehlik et al (2015), Rodríguez-Díaz (2017) among others]. Some general results on optimal designs for linear models with correlated observations can be found in the seminal work of Ylvisaker (1966, 1968), while more recently in a series of papers Dette et al (2013Dette et al ( , 2016Dette et al ( , 2017) provided a general approach for the problem of designing experiments in linear models with correlated observations by considering the problem of optimal (unbiased linear) estimation and optimal design simultaneously.…”

Optimal designs for series estimation in nonparametric regression with correlated data

“…The reason for this gap in the existing literature is that the design problem for models with correlated errors (even parametric models) is substantially harder compared to the uncorrelated case. In contrast to the latter case, where a very well developed and powerful methodology for the construction of optimal designs has been established [see, for example, the monograph of Pukelsheim (2006)], optimal designs for models with correlated observations are only available in rare circumstances considering parametric models [see, for example, Pázman and Müller (2001), Näther and Simák (2003), Müller and Stehlík (2004), Dette et al (2009), Zhigljavsky et al (2010); Pázman (2010), Harman and Stulajter (2010), Amo-Salas et al (2012), Stehlik et al (2015), Rodríguez-Díaz (2017) among others]. Some general results on optimal designs for linear models with correlated observations can be found in the seminal work of Ylvisaker (1966, 1968), while more recently in a series of papers Dette et al (2013Dette et al ( , 2016Dette et al ( , 2017 provided a general approach for the problem of designing experiments in linear models with correlated observations by considering the problem of optimal (unbiased linear) estimation and optimal design simultaneously.…”