Asymptotic theory for nonparametric regression with spatial data
Asymptotic theory for nonparametric regression with spatial data
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DOI：
10.1016/j.jeconom.2011.05.002
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发表时间：
2011-11
影响因子：
6.3
通讯作者：
P. Robinson
中科院分区：
文献类型：
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作者：
P. Robinson
考虑空间或时空数据的非参数回归。因变量的条件均值（给定解释变量）是非参数函数，而条件协方差反映空间相关性。还允许条件异方差性以及不同分布的观察值。代替混合条件，假设扰动采用（可能非平稳）线性过程，允许长程和短程相关性，而解释变量的相关性衰减则使用基于联合密度与边际密度乘积的偏差的测量来描述。采用基本的三角形阵列设置，旨在覆盖空间观测的各种模式。为核回归估计的一致性和渐近正态性建立了充分条件。当截面相关性足够温和时，中心极限定理中的渐近方差与观测值独立时相同；否则，收敛速度较慢。我们讨论了我们的条件在空间自回归模型以及在规则格子上定义的模型的应用。
Nonparametric regression with spatial, or spatio-temporal, data is considered. The conditional mean of a dependent variable, given explanatory ones, is a nonparametric function, while the conditional covariance reflects spatial correlation. Conditional heteroscedasticity is also allowed, as well as non-identically distributed observations. Instead of mixing conditions, a (possibly non-stationary) linear process is assumed for disturbances, allowing for long range, as well as short-range, dependence, while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities. A basic triangular array setting is employed, with the aim of covering various patterns of spatial observation. Sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates. When the cross-sectional dependence is sufficiently mild, the asymptotic variance in the central limit theorem is the same as when observations are independent; otherwise, the rate of convergence is slower. We discuss the application of our conditions to spatial autoregressive models, and models defined on a regular lattice.