If your house wiring is up to the task and you don't have your electric space heater on an extension cord then it's safe.
I sleep with 2 electric space heaters on every winter night and haven't had any trouble.
Check to make sure your plug to the space heater isn't getting hot and also the wall plug. A little warm is okay but if you can't keep your hand on the plug or outlet without getting burned then it's unsafe.
Make sure your plug isn't loose in the outlet either.
I recommend those oil filled electric radiator heaters, they work great and are quiet.
Remember to keep clothes and other combustibles at least 3 feet or farther away from the space heater to avoid fires.