Hello Kristy,
I just wanted to give you some tips that have worked for me after losing 5 of the first Anthias I purchased (each bought with in 4 months) simply because they would not eat or do anything other than hide. At first I thought it was impossible to keep one alive but with these methods I have been successful in keeping the next 9 Anthias I purchased alive and thriving.
1. Definitely quarantine them; even if it's for a short time. It isn't because they are disease prone, but mainly because I have found that they don't like to compete for food when they are new to the tank. In a QT they are the only ones in there and they have a better chance of eating with out stiff competition from fish already adjusted in your DT. Also, I've found that this is the best thing to do if you have bought only one Anthias.
2. Don't have too much rock in the QT or they will spend most of their time hiding. You can have one or two medium sized caves, but that's it. That way when you do feed the tank, they can visually see the falling food, and dart out to grab a quick bite. After it or they are swimming and eating regularly, they are ready to be acclimated and introduced to the Display Tank.
3. Quarantine and Introduce them in the Display Tank altogether if you can. In my humble experience, One Male with one female or a couple of females, will do better than just one fish. It's not impossible to successfully introduce and have just 1 Anthias in the display tank because I have done it, and I know many others that have, too. It's just a bit harder on the fish (I think) to only add him or her to the the display tank to be by itself. I think they are genetically programmed to be part of a group. So I think it helps them to over come the stress of being new to a display tank if they have some of their own kind in there, too. When they are by themselves, they'd just rather hide. Males will come out of hiding to show their dominance and claim a female Anthias if she is swimming around his visual field. Females will come out of hiding if they see a male swimming about showing them that it is safe to be swimming around in that part of your DT.
Example: About a year and a half ago I bought a Male Square Anthias. I acclimated him for 4 hours before adding him to the tank and introduced him when the lights were out. He hid 99% of the time in the same cave and wouldn't eat or come out of hiding for more than just a couple of seconds at a time. I thought to myself, "Ahhhh here goes number 6, I give up". After week I was casually talking to a friend and I mentioned it to him. He was the only one I knew of at the time who kept Anthias in his display tank. He told me that he had the same Trio in his tank for over 3 years. I asked him how many died before he was successful and his reply was, "ONE". He told me that a friend in the hobby suggested to him that he should buy his next Anthias in a Male, Female, Female Trio. To which he told me that I should buy my Male Anthias some girl friends. I thought to myself "great thats all I need, 3 dead Anthias' instead of just one". But I went ahead and bought them the next day anyway. Well, I brought them home and acclimated the girls to the display tank. After 3 hours I put them in at about 4PM. Within 1 or so hours he was out strutting his stuff
. He was flashing his dorsal fin and showing off like he was the "Cat's Meow" and I was pretty happy
. After about 2 hours had passed I tried a combination of foods and he was eating Mysis and Formula One Flakes with vigor after not eating a bite for more than a week and a day. After 6 months months of having them, I sold the 3 to one of his friends because I wanted some smaller sized Lateral Anthias'. A year and a half later the same Trio is still alive and well, Even Though They Aren't In My Tank! So I guess his friend was right. They love the company of each other... "Thanks Dan & Robert!" 
4. Lastly, find a food that they like. They will spit out what they don't like... every time. Most of the first couple of feedings in the QT will be wasted because they will likely stay hidden. This can be a hard process of elimination, so feed often and in very small amounts. I used a turkey baster and only fed a couple of brine shrimp, mysis, and flake food at a time. Erik is right; for some reason Anthias really love flake food. When they start eating I like to put just one shrimp at a time in there to make sure that it gets eaten, but you can do what works for you.
If you are like me it hurts when even just one small fish dies no matter what he or she costs. That's why I go through so much just to keep them alive. My wife can usually tell when I lose a fish because I get pretty bummed. Thankfully it hasn't happen in quite some time.
I hope this helps to give you and others some ideas in keeping their swimming buddies alive. 
-David
40 Gallon Breeder on Steroids!!!
Where You'll Find An Acan, Dendro, and Orange Ricordea Garden In Bloom.