Examples are given which show the necessity of various hypotheses in the known finite dimensional complement theorems. In addition, several positive results are presented which improve one direction ...

This is a preview. Log in through your library . Abstract We develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the ...

Consider a pencil lying on your desk. Try to spin it around so that it points once in every direction, but make sure it sweeps over as little of the desk’s surface as possible. You might twirl the ...