統計学輪講（第12回） 日時 2012年07月10日(火) 14時50分～15時40分 場所 経済学部新棟３階第３教室 講演者 井上 彰 (経済M2) 演題 Estimation of Covariance and Precision Matrices in High Dimension 概要 The problem of estimating covariance and precision matrices of multivariate normal distributions is addressed when both the sample size and the dimension of variables are large. A standard estimator is the inverse of the sample covariance matrix, but it may be unstable or cannot not defined in the high dimension. Ridge type estimators are alternative procedures which are useful and stable for large dimension. However, we are faced with questions about how to choose ridge parameters and their estimators and how to set up asymptotic order in ridge functions in high dimensional cases. We consider general types of ridge estimators for covariance and precision matrices, and derive asymptotic expansions of their risk functions.