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众数因子分析：面向条件众数的高维降维方法AI 解读

The modal factor model represents a new factor model for dimension reduction in high dimensional panel data. Unlike the approximate factor model that targets for the mean factors, it captures factors that influence the conditional mode of the distribution of the observables. Statistical inference is developed with the aid of mode estimation, where the modal factors and the loadings are estimated through maximizing a kernel-type objective function. An easy-to-implement…

平滑非光滑性AI 解读

To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is established and an illustration of its application is then provided.

加性单指标协整时间序列模型的稳健 M 估计AI 解读

Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing the resultant estimators rests on the nonsmoothness of these losses. Generalized functions have advantages over ordinary functions in several aspects, especially generalized functions possess derivatives of any order. Generalized…

多指标非平稳时间序列模型：稳健估计理论与实践AI 解读

This paper proposes a class of parametric multiple-index time series models that involve linear combinations of time trends, stationary variables and unit root processes as regressors. The inclusion of the three different types of time series, along with the use of a multiple-index structure for these variables to circumvent the curse of dimensionality, is due to both theoretical and practical considerations. The M-type estimators (including OLS, LAD, Huber's estimator,…