"We owe a large debt to the vitality and variety of the music of the American people," they wrote.
In television, Letterman's unconventional wit and charm has made him "one of the most influential personalities," Rubenstein said.
Letterman said it was a wonderful honor for his family, his co-workers at CBS's "Late Night with David Letterman" and for himself. In 1993, Letterman helped honor one of his mentors, Johnny Carson, with the Kennedy Center prize, delivering one of his signature Top 10 lists about the longtime "Tonight Show" host.
"I believe recognition at this prestigious level confirms by belief that there has been a mix-up," he said in a written statement. "I am still grateful to be included."
Kennedy Center: http://www.kennedy-center.org/
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