Our finding is that we can use a kind of spurious correlations for multiple comparison problems with unknown correlations
This usage asymptotically controls the family-wise error rate and sometimes overwhelms the existing methods
The following example of its R-code is here (this will give the result in one minute)
An asymptotically guaranteed confidence interval in the context of selective inference is given for the case in which the inverse-probability-weighted (IPW) estimation with Lasso is used
Numerical experiments shows that a method that ignores the quiet scandal of statistics results in significant deviations from the preset coverage of the confidence intervals, whereas our method maintains the coverage
Real data analyses shows that there is a significant difference between two methods
For model selection in propensity score analysis such as IPW (inverse probability weighted) estimation or DR (doubly robust) estimation, an AIC-type (Cp-type) criterion is derived
Its penalty term is quite different from the number of parameters, that is, the criterion is quite different from the conventional AIC (or QICw)
This is derived as an asymptotically unbiased estimator of a weighted mean squared error, that is, theoretically assured
The following example of its R-code is here (in preparation)
In order to select tuning parameter (regularization parameter) for Lasso in generalized linear models such as logistic Lasso, Poisson Lasso or graphical Lasso, its AIC is derived from its original definition
Its penalty term is different from the number of variables in the active set, which becomes the penalty term for the case of Gaussian Lasso from the SURE theory, but the difference is not large, and so it may be OK to use the number of variables
Its R-package ``sAIC'' is obtained here