A cautionary note on robust covariance plug-in methods

Many multivariate statistical methods rely heavily on the sample covariance matrix. It is well known though that the sample covariance matrix is highly non-robust. One popular alternative approach for "robustifying" the multivariate method is to simply replace the role of the covariance matrix with some robust scatter matrix. The aim of this paper is to point out that in some situations certain properties of the covariance matrix are needed for the corresponding robust "plug-in" method to be a valid approach, and that not all scatter matrices necessarily possess these important properties. In particular, the following three multivariate methods are discussed in this paper: independent components analysis, observational regression and graphical modeling. For each case, it is shown that using a symmetrized robust scatter matrix in place of the covariance matrix results in a proper robust multivariate method.Comment: 24 pages, 7 figure

Lexus Lanes or Corolla Lanes? Spatial Use and Equity Patterns on the I-394 MnPASS Lanes

A 2004-2006 longitudinal panel survey of I-394 residents found support levels at over 60 percent for the congestion priced High Occupancy Toll (HOT) lane, known to the Twin Cities of Minneapolis and St. Paul as MnPASS. This number varies only slightly when sorted by income levels, gender, and education levels, suggesting that the arrangement is perceived as equitable. However, people with higher incomes use the system more often and thereby capitalize on the direct benefit more often, a finding consistent with other studies. Previous research has not revealed whether higher incomes actually cause people to use the MnPASS option more often or whether HOT lanes have simply been built along high income corridors, such as I-394. This paper aims to separate the effects of income and location on use to provide a more robust understanding of equity concerns. Using data provided by the Minnesota Department of Transportation, Heteroskedasticity-Consistent Method 3 (HC3) regressions, this paper suggests that location and income both explain HOT lane use.Minnesota, Minneapolis, HOT Lanes, Congestion Pricing, Road Pricing, MnPASS, Value Pricing, Social Equity