How to remove the uninstalled app icons from my purchased list?

You can't permanently delete any item from your purchase, but you should be able to hide them via your computer's iTunes, that should stop them showing in the cloud for redownloading.

On the current version of iTunes click on your name towards the top-right of the iTunes screen, and then click Purchased on the popup

Or click on the Purchased link under Quick Links on the right-hand side of the iTunes store homepage.

Select the Apps section of Purchased, and click on the top left corner of an app that you want to hide (you should get an 'x' show on that corner, but on the current version of iTunes its invisible, it doesn't show on my Mac's iTunes and other people have posted the same comment, but clicking on the top left corner should still hide the app).

Hiding and unhiding : iTunes Store: Hiding and unhiding purchases - Apple Support

Also if you installed IOS 8 since you last updated your profile on your iPad try sliding the name of the app to the left and tapping hide.

That doesn't work for me, tapping the Hide button only hides it temporarily, if I select one of the other tabs in the app and then go back to Purchased it shows again.

Aloha King Penguin. Right you are. I read it was for people with family sharing but it seemed to be working for me. I tried selecting another tab and sure enough it was back. Thanks for pointing that out. Bob.

No, it can only be done via a computer's iTunes

I thought I discovered gold when I came accross the slide to hide in purchased. I hate being dependent on a computer to use my iPad but it appears the only way to hide a purchased app remains the one King Penguin has already described.