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Title: Estimating average derivative with multiple integrated regressors Authors:  Anurag Banerjee - Durham University (United Kingdom) [presenting]
Abstract: The model $y_{t}=m\left( \mathbf{x}_{t}\right) +u_{t}$ is considered, where the covariates $\mathbf{x}_{t}$ are $d-$dimensional integrated variables ($d\geq3)$. The equally weighted average derivative (AD) of the regression function $m$ within a bounded box $\mathcal{K}$ is defined as $(1/\left\vert \mathcal{K}\right\vert) \int_{\mathcal{K}}D\left[ m\left(z\right) \right] dz.$ The AD is then estimated using piecewise local linear regression. We study the asymptotic distribution of this estimator. The results indicate that the ADE converges at the rate $T^{-1/3}$ when $m(\mathbf{.})$ is non-linear and $T^{-1}$ if $m(\mathbf{.})$ is linear. We provide a randomised algorithm to estimate the AD. Using Monte-Carlo simulation experiments, we investigate the small sample properties of our estimator.