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A functional multiple index model is given by
<math display="block">Y = g\left(\int_{\mathcal{T}} X^c(t) \beta_1(t)dt, \cdots, \int_{\mathcal{T}} X^c(t) \beta_p(t)dt \right) + \epsilon.</math>
Taking <math>p=1</math> yields a functional single index model. However, this model is problematic due to [[Curse of dimensionality|curse of dimensionality]]. In other words, with <math>p>1</math> and relatively small sample sizes, this model often leads to high variability of the estimator<ref>Chen, Hall and Müller (2011). "Single and multiple index functional regression models with nonparametric link". ''The Annals of Statistics''. '''39''' (3):1720–1747. [[Digital object identifier|doi]]:[http://www.jstor.org/stable/23033613 10.1214/11-AOS882]</ref>. Alternatively, a preferable <math>p</math>-component functional multiple index model can be formed as
<math display="block">Y = g_1\left(\int_{\mathcal{T}} X^c(t) \beta_1(t)dt\right)+ \cdots+ g_p\left(\int_{\mathcal{T}} X^c(t) \beta_p(t)dt \right) + \epsilon.</math>
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