No.
That is NOT what COMPRESS() does. It removes individual characters. So to get that result using COMPRESS() you would have to remove any character that wasn't A,B or V. Which would work for that one example, but I doubt it would work for other strings you might have.
If the pattern is single letter followed by single word then use SCAN() function in a loop.
data test;
String = 'A Math B Cook V Deep';
length next_word new_string $10 ;
do i=1 by 2 until(next_word=' ');
next_word=scan(string,i,' ');
new_string=cats(new_string,next_word);
end;
drop i next_word;
run;
If the pattern is more complex 'D Earth Science E Chemistry' then you will need something more complicated.
If the goal is to find single uppercase letters then then perhaps something like:
data test;
String = 'A Math B Cook V Deep';
length next_word new_string $10 ;
do i=1 to countw(string,' ');
next_word=scan(string,i,' ');
if length(next_word)=1 and 'A' <= next_word <= 'Z' then
new_string=cats(new_string,next_word)
;
end;
drop i next_word;
run;
If not then you will probably need to use regular expressions instead.
So if the pattern is remove any word that is more than one character then try
data test;
String = 'A Math B Cook V Deep';
length new_string $10 ;
new_string=compress(prxchange('s/[^ ]{2,}//',-1,string),' ');
run;