報告題目：Projected Estimation for Large-dimensional Matrix Factor Models
報 告 人：孔新兵教授 南京審計大學
報告時間：2020年7月3日 9:30-10:30
報告地點：騰訊會議 ID：709 754 043
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校内聯系人：朱複康 fzhu@jlu.edu.cn
報告摘要：
Large-dimensional factor models are drawing growing attention and widely applied to analyze the correlations of large datasets. Most related works focus on vector-valued data while nowadays matrix-valued or high-order tensor datasets are ubiquitous due to the accessibility to multiple data sources. In this article, we propose a projected estimation method for the matrix factor model under flexible conditions. We show that the averaged squared Frobenious norm of our projected estimators of the row (or column) loading matrix have convergence rates $\max\{(Tp_2)^{-1}, (Tp_1)^{-2}, (p_1p_2)^{-2}\}$ (or $\max\{(Tp_1)^{-1}, (Tp_2)^{-2}, (p_1p_2)^{-2}\}$), where $p_1$ and $p_2$ are the row and column dimension of each data matrix and $T$ is the number of observations. This rate is faster than the typical rates $T^{-1}$ and $\max\{(Tp_2)^{-1}, p_1^{-2}\}$ (or $\max\{(Tp_1)^{-1}, p_2^{-2}\}$) that are conceivable from the literature on vector factor models as long as the dimensions of observed data matrices are sufficiently large. An easily satisfied sufficient condition on the projection direction to achieve the given rates for the projected estimators is provided. Moreover, we established the asymptotic distributions of the estimated row and column factor loadings. We also introduced an iterative approach to consistently determine the numbers of row and column factors. Two real data examples related to financial engineering and image recognition show that the projection estimators contribute to explaining portfolio variances and achieving accurate classification of handwritten digit numbers.
報告人簡介：
孔新兵，南京審計大學教授，主要研究興趣為髙維數據分析、高頻數據分析。在統計學和計量經濟學頂級期刊Annals of Statistics、Journal of the American Statistical Association、Biometrika、Journal of Econometrics上發表論文10多篇。主持國家自然科學基金3項目。獲香港數學會最佳博士論文獎，複旦大學管理學院優秀青年教師新星獎，江蘇省應用統計最佳論文獎。入選江蘇省雙創計劃，江蘇省青藍工程中青年學術帶頭人。現在任SCI雜志《Random Matrices: Theory and Applications》的副主編。
