@akitaeko Thanks a lot! We Japanese are often taught that the gerund(an ing form of verb functioning as a noun ) can take its own subject, in which case the subject of gerund should be possessive form such as my rather than me. But native speakers in fact use the objective case such as me, him, it etc for the gerund's meaning subject more than the possessive case such as my, his, it's etc. Right?
For example, Both 'I missed his smiling' and 'I missed him smiling' have the same meaning but the latter sentence perhaps would be better?!