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利用非参数泛函估计探索回归结构AI 解读

Average derivative functionals of regression are proposed for nonparametric model selection and diagnostics. The functionals are of the integral type, which under certain conditions allows their estimation at the usual parametric rate of n –1/2. We analyze asymptotic properties of the estimators of these functionals, based on kernel regression. These estimators can then be used for assessing the validity of various restrictions imposed on the form of regression. In…

稳健谱回归AI 解读

This paper addresses the problem of linear regression estimation when the disturbances follow a stationary process with its spectral density known only to be in a neighborhood of some specified spectral density, for instance, that of white noise. Rather than trying to adapt to a small unspecified autocorrelation, we follow here the robustness approach, and establish the extent of the regressors and disturbance spectra interaction which require serial correlation correction.…

通过局部极小极大均方误差构造有界影响回归AI 解读

The class of “general” M-estimators for the stochastic linear regression model is considered, and influence and change-of-variance functions are used to approximate the main term of the mean squared error (MSE). The estimator is then found in the class that minimizes the maximum of that approximate MSE over the ϵ-contamination neighborhood. This approach allows for additional flexibility of designing estimators optimal for prediction in specific regions of the factor space,…