Some Statistics journals without mandatory Article Publication Fees 

Annals of Applied Probability

Annals of Applied Statistics

Annals of Statistics

Biometrika

Electronic Journal of Statistics

Environmetrics

IEEE Transactions of Information Theory 

IEEE Transactions on Pattern Analysis and Machine Intelligence

JASA

Journal of Computational and Graphical Statistics. 

Journal of Machine Learning Research" 

JRSS B

Journal of Statistical Software

Spatial Statistics

Statistical Science