Jiti, Gao ; Tingting, Cheng ; Xibin, Zhang ; Xibin, Zhang ; Jiti, GAO. (2015) Bayesian Bandwidth Estimation In Nonparametric Time-Varying Coefficient Models.
In: Monash Econometrics and Business Statistics Working Papers. RePEc:msh:ebswps:2015-3.

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Assumption 2(i) is a standard assumption for kernel functions. The commonly used Gaussian and uniform kernel functions satisfy Assumption 2(i). Assumption 2(ii) imposes smoothness constraints on the coefficient functions βj (), which is commonly used in literature; see Cai (2007) and Robinson (1989). Assumption 3(i)(ii) ensures that f (v;θ) is differentiable and the fourth moment of γ(v;θ) exists. The conditions of Eθ[γ(v1;θ)] = 0 and Eθ[v1γ(v1;θ)] 6= 0 are automatically satisfied when f (v;θ) is the density function of a Normal random variable. As pointed out in the proofs of Theorems 1 and 2, we need not assume Eθ[γ(v1;θ)] = 0 when E[x1] = 0. Assumptions 3 and 4 are automatically satisfied when f (v;θ) is the density function of a Normal random variable of the form f (v;θ) = f (v;η) = 1 p 2π η exp −v2 2η and η has a density function of the form π(η) = exp −η I[η > 0].