What is an example of midrash in Matthew's infancy narrative?

Matthew's infancy narrative has been likened to Jewish midrash because it made a fanciful use of Old Testament material to create a plausible, or at least useful, account of the nativity. The author decided to draw a parallel between Jesus and his father Joseph, and Moses and his forefather Joseph.

First, Matthew had to create a genealogy that showed an uncanny parallel. Just as the father of Joseph in the Old Testament was called Jacob, so the father of Matthew's Joseph was to be called Jacob (in Luke's Gospel, Joseph's father was called Heli). Matthew went further, not only was Jesus descended from Zorobabel and King David, but he could prove by numerology that Jesus was destined to be the Messiah. He demonstrated that there were 14 generations: from Abraham to David; from David to Josiah; from Josiah to Jesus. To do this, he had to ignore 3 kings in the Old Testament and have David in the preceding (as 14) and following (as 1) groups, but not so Josiah. Raymond E. Brown (An Introduction to the New Testament) says that there is little likelihood that Matthew's genealogy is strictly historical.

The infancy account of the flight to Egypt has parallels in the Old Testament account of Joseph, and the accounts of Herod's Slaughter of the Innocents has close parallels in the Old Testament account of the slaughter of the Hebrew infants by the pharaoh. The Star of Bethlehem was never mentioned by any of the numerous scholars and astrologers in the Near East and elsewhere during the reign of King Herod. But there was a strange star that raised a great deal of speculation about kings and Messiahs, and it occurred only about two decades before Matthew was actually written.