Picard groups of certain stably projectionless C*-algebras

We compute Picard groups of several nuclear and non-nuclear simple stably projectionless C*-algebras. In particular, the Picard group of Razak-Jacelon algebra W_2 is isomorphic to a semidirect product of Out(W_2) with R_+^\times. Moreover, for any separable simple nuclear stably projectionless C*-algebra with a finite dimensional lattice of densely defined lower semicontinuous traces, we show that Z-stability and strict comparison are equivalent. (This is essentially based on the result of Matui and Sato, and Kirchberg's central sequence algebras.) This shows if A is a separable simple nuclear stably projectionless C*-algebra with a unique tracial state (and no unbounded trace) and has strict comparison, the following sequence is exact: [{CD} {1} @>>> \mathrm{Out}(A) @>>> \mathrm{Pic}(A) @>>> \mathcal{F}(A) @>>> {1} {CD}] where $\mathcal{F}(A)$ is the fundamental group of A.Comment: 20 pages, to appear in J. London Math. So

A monte carlo analysis of the type II tobit maximum likelihood estimator when the true model is the type I tobit model

Type I (censored regression) and Type II Tobit (sample selection) models are widely used in the various fields of economics. The Type I Tobit model is a special case of the Type II Tobit model. However, the dimension of the error terms decreases and the distribution of the error terms degenerates in the Type I Tobit Model. Therefore, we cannot use the standard asymptotic theorems for the Type II Tobit Maximum Likelihood Estimator (MLE) when the sample is obtained from the Type I Tobit model. Results of Monte Carlo experiments show strange behavior that has never been reported before for the Type II MLE.