中國人民大學(xué)統(tǒng)計學(xué)院邀請賓夕法尼亞州立大學(xué)統(tǒng)計系薛凌洲作了題為“Sufficient Forecasting Using Factor Models(充分利用預(yù)測模型的因子)”的講座。中國人民大學(xué)統(tǒng)計學(xué)院應(yīng)用統(tǒng)計學(xué)科布局不僅深入經(jīng)濟(jì)社會發(fā)展領(lǐng)域和保險精算與金融風(fēng)險管理領(lǐng)域，而且已經(jīng)擴展到社會科學(xué)的許多領(lǐng)域如法律、新聞、政治學(xué)、倫理學(xué)、教育學(xué)、心理學(xué)、文獻(xiàn)計量等領(lǐng)域之中，展示應(yīng)用統(tǒng)計量化社會科學(xué)研究的重要作用。

　　當(dāng)存在大量預(yù)測的和可能的非線性效應(yīng)我們考慮預(yù)測的單一的時間序列。維首先通過高維(近似)的因素由主成分分析模型來實現(xiàn)降低。使用提取的因素，我們開發(fā)名為足夠預(yù)測了一種新的預(yù)測方法，它提供了一套充分的預(yù)測指標(biāo)，從高維預(yù)測推斷的，以提供更多的預(yù)測能力。投影主成分分析將被用于增強的推斷因素精度被假定一個半?yún)��?shù)(近似)因子模型時。我們的方法也可以適用于使用提取因子剖足夠回歸。 {足夠預(yù)測和深學(xué)習(xí)架構(gòu)之間的連接被明確說明。}的充分的預(yù)測正確估計的潛在因素的投影索引即使是在一個非參數(shù)預(yù)測功能的存在。所提出的方法通過縮合通過因子模型的剖信息擴展了足夠的尺寸減少到高維制度。我們推導(dǎo)出對這些投影方向以及足夠的預(yù)測指數(shù)的估算值跨越的中央子空間的估算漸近性質(zhì)。進(jìn)一步的研究表明估計的因素移動靶的多元回歸自然的方法產(chǎn)生，實際上就屬于這一核心子空間的線性估計。我們的方法與理論預(yù)測允許的數(shù)量比觀測的數(shù)量較大。我們終于證明了足夠的預(yù)測在兩個模擬研究線性預(yù)測和預(yù)測宏觀經(jīng)濟(jì)變量的實證研究改進(jìn)。

　　原文：We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting method called the sufficient forecasting, which provides a set of sufficient predictive indices, inferred from high-dimensional predictors, to deliver additional predictive power. The projected principal component analysis will be employed to enhance the accuracy of inferred factors when a semi-parametric (approximate) factor model is assumed. Our method is also applicable to cross-sectional sufficient regression using extracted factors. {The connection between the sufficient forecasting and the deep learning architecture is explicitly stated.} The sufficient forecasting correctly estimates projection indices of the underlying factors even in the presence of a nonparametric forecasting function. The proposed method extends the sufficient dimension reduction to high-dimensional regimes by condensing the cross-sectional information through factor models. We derive asymptotic properties for the estimate of the central subspace spanned by these projection directions as well as the estimates of the sufficient predictive indices. We further show that the natural method of running multiple regression of target on estimated factors yields a linear estimate that actually falls into this central subspace. Our method and theory allow the number of predictors to be larger than the number of observations. We finally demonstrate that the sufficient forecasting improves upon the linear forecasting in both simulation studies and an empirical study of forecasting macroeconomic variables.