統計学輪講（第１２回）

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.