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This supplementary file contains the detailed proof of Lemma A.1 and Lemma A.2.Throughout the supplementary, we use M to represent a (generic) constant, which can take on different values at different places. Now, write ψ(t|x, u) = E[Q θ (Y − η(U, X) + t)|X = x, U = u], and denote ∂ψ(t|x, u)/∂t and ∂ 2 ψ(t|x, u)/∂t 2 by ψ ′ (t|x, u) and ψ ′′ (t|x, u) respectively.

Income elasticity dynamics of health expenditure is considered for the OECD and Eurozone over the period 1995-2014. Motivated by some modelling challenges, this paper studies a class of non-linear cointegration panel data models, controlling for cross-section dependence and certain endogeneity. Using the corresponding methods, our empirical analyses show a slight increase in the income elasticity of the healthcare expenditure over the years, but still with values under 1, meaning that healthcare is not a luxury good in the OECD and Eurozone.

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Deep learning as a service (DLaaS) has been intensively studied to facilitate the wider deployment of the emerging deep learning applications. However, DLaaS may compromise the privacy of both clients and cloud servers. Although some privacy preserving deep neural network (DNN) techniques have been proposed by composing cryptographic primitives, the challenges on computational efficiency have not been fully addressed due to the complexity of DNN models and expensive cryptographic primitives. In this paper, we propose a novel privacy preserving cloud-based DNN inference framework ("PROUD"), which greatly improves the computational efficiency. Finally, we conduct experiments on two datasets to validate the effectiveness and efficiency for the PROUD while benchmarking with the state-of-the-art techniques.