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空间依赖下的一致模型设定检验AI 解读

We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the “space” being of a general economic or social nature. Dependence can be parametric, parametric with increasing dimension, semiparametric or any combination thereof, thus covering a vast variety of settings. These include spatial error models of varying types and levels of complexity. Under a new smooth spatial dependence condition, our test statistic is…

空间数据的非参数预测AI 解读

We describe a (nonparametric) prediction algorithm for spatial data, based on a canonical factorization of the spectral density function. We provide theoretical results showing that the predictor has desirable asymptotic properties. Finite sample performance is assessed in a Monte Carlo study that also compares our algorithm to a rival nonparametric method based on the infinite $AR$ representation of the dynamics of the data. Finally, we apply our methodology to predict…

大规模空间自回归模型的高效闭式估计AI 解读

Newton-step approximations to pseudo maximum likelihood estimates of spatial autoregressive models with a large number of parameters are examined, in the sense that the parameter space grows slowly as a function of sample size. These have the same asymptotic efficiency properties as maximum likelihood under Gaussianity but are of closed form. Hence they are computationally simple and free from compactness assumptions, thereby avoiding two notorious pitfalls of implicitly…

无限维与维度增长时间序列回归的稳健推断AI 解读

We develop a class of tests for time‐series models such as multiple regression with growing dimension, infinite‐order autoregression, and nonparametric sieve regression. Examples include the Chow test and general linear restriction tests of growing rank p . Employing such increasing p asymptotics, we introduce a new scale correction to conventional test statistics, which accounts for a high‐order long‐run variance (HLV), which emerges as p grows with sample size. We also…

随机权重矩阵下空间自回归模型的估计AI 解读

We examine a higher-order spatial autoregressive model with stochastic, but exogenous, spatial weight matrices. Allowing a general spatial linear process form for the disturbances that permits many common types of error specifications as well as potential ‘long memory’, we provide sufficient conditions for consistency and asymptotic normality of instrumental variables, ordinary least squares, and pseudo maximum likelihood estimates. The implications of popular weight matrix…

自回归型空间谱估计AI 解读

Nonparametric spectral density estimates find many uses in econometrics. For stationary random fields on a regular spatial lattice, we propose an autoregressive nonparametric spectral density estimate that is guaranteed positive even when suitable edge-effect correction is employed and is simple to compute using least squares. Our estimate is based on truncating a true half-plane infinite autoregressive representation, while also allowing the truncation length to diverge in…

基于三类检验原理的非参数设定检验AI 解读

Tests are developed for inference on a parameter vector whose dimension grows slowly with sample size. The statistics are based on the Lagrange Multiplier, Wald and (pseudo) Likelihood Ratio principles, admit standard normal asymptotic distributions under the null and are straightforward to compute. They are shown to be consistent and possessing non-trivial power against local alternatives. The settings considered include multiple linear regression, panel data models with…

参数维度增长的空间自回归模型伪极大似然估计AI 解读

Pseudo maximum likelihood estimates are developed for higher-order spatial autoregressive models with increasingly many parameters, including models with spatial lags in the dependent variables both with and without a linear or nonlinear regression component, and regression models with spatial autoregressive disturbances. Consistency and asymptotic normality of the estimates are established. Monte Carlo experiments examine finite-sample behaviour.

参数数量递增的高阶空间自回归模型推断AI 解读

This paper develops consistency and asymptotic normality of parameter estimates for a higher-order spatial autoregressive model whose order, and number of regressors, are allowed to approach infinity slowly with sample size. Both least squares and instrumental variables estimates are examined, and the permissible rate of growth of the dimension of the parameter space relative to sample size is studied. Besides allowing the number of parameters to increase with the data, this…