In 2005 four oil paintings previously attributed to Rembrandt 's students were reclassified as the work of Rembrandt himself : " Study of an Old Man in Profile " and " Study of an Old Man with a Beard " from a US private collection , " Study of a Weeping Woman " , owned by the Detroit Institute of Arts , and " Portrait of an Elderly Woman in a White Bonnet " , painted in 1640 .