The
Tiny1 is the only compact camera I've seen dedicated to astrophotography. Its in production and I hope to get mine in the next month or so and see how it performs.
Otherwise for a compact I've always had good results from my Panasonic LX3 and Leica DLux. The mirrorless I've experienced (a few years ago) have all had partcularly bad chroma noise and seemed more a fashion accessory than a real camera. The Fuji X look great on paper but i've never used one.