Estimation of Causal Functional Linear Regression Models

J.C.S. de Miranda

Journal of Mathematics Research, 2017, vol. 9, issue 6, 106-111

Abstract: We present a methodology for estimating causal functional linear models using orthonormal tensor product expansions. More precisely, we estimate the functional parameters $\alpha$ and $\beta$ that appear in the causal functional linear regression model:$$\mathcal{Y}(s)=\alpha(s)+\int_a^b\beta(s,t)\mathcal{X}(t)\mathrm{d}t+\mathcal{E}(s),$$ where $\mbox{supp } \beta \subset \mathfrak{T},$ and $\mathfrak{T}$ is the closed triangular region whose vertexes are $(a,a) , (b,a)$ and $(b,b).$ We assume we have an independent sample $\{ (\mathcal{Y}_k,\mathcal{X}_k) : 1\le k \le N, k\in \mathbb{N}\}$ of observations where the $\mathcal{X}_k $'s are functional covariates, the $\mathcal{Y}_k$'s are time order preserving functional responses and $\mathcal{E}_k,$ $1\le k \le N,$ is i.i.d. zero mean functional noise.

Keywords: causal; functional linear model; orthonormal series expansions; tensor product. (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:9:y:2017:i:6:p:106

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