possessive before a gerund
His leaving vs. him leaving; the mayor’s arriving vs. the mayor arriving.
Before a gerund, use the possessive: I appreciate your waiting, not I appreciate you waiting. The same rule holds for nouns: No one expected Dana’s resigning, not No one expected Dana resigning. A common error is to use the objective case before a gerund, as in We were surprised by him quitting. When the -ing form is a present participle describing someone already named as the object, keep the objective case: I heard him leaving means I heard him as he left. See also gerund / present participle.
Examples
UseI appreciate your waiting. (gerund; possessive)
AvoidI appreciate you waiting. (objective case before a gerund)
UseThey blamed the cost on the contractor’s missing the deadline. (gerund; possessive)
AvoidThey blamed the cost on the contractor missing the deadline. (objective case before a gerund)
UseI saw him leaving. (present participle; him is the object of saw)
Grammar books now commonly accept the objective case before a gerund. However, many people still consider this use an error, and they judge the speaker who uses the objective case there.