Nearly every bit of biographical information about The Residents includes the qualifying word, “alleged.” That’s because the legendary multi-media pioneers have managed to maintain complete anonymity throughout their 30-year career. If you can call making ground-breaking music videos that are too weird for mainstream distribution a career. Oh, sure, some of their early ’70s video work is now part of the permanent collection at the Museum of Modern Art in New York — including The Third Reich ’n’ Roll, which The Rolling Stone Book of Rock Video claims is “the most utterly, exuberantly original and bizarre performance video ever.” Even some of their costumes — from their 1981-84 Mole Show — are in the Los Angeles Museum of Contemp-orary Art.

The Residents have also put out some 20 albums, but just try and find them. A search last weekend at Borders in Burling-ton turned up a “We’ve ordered some for the occasion, but they haven’t arrived yet.”

That “occasion” is the group’s performance at Higher Ground this Sunday, for which area fans should genuflect in gratitude. Not only do The Residents not go on the road much anymore, but this particular two-month tour — the first-ever tour in support of a DVD — has limited dates. And for anyone to voluntarily come to Vermont in the most frigid month of the year is something. Especially when they’re allegedly from California.

Actually, The Residents are allegedly from Louisiana, according to the guy who hosts the unofficial Residents Web site, at www.residents.com. This is “officially recognized” by Rez managers, appropriately dubbed the Cryptic Corporation. Around 1966, the four — or possibly then five — musicians abandoned Shreveport’s redneck culture for San Francisco, but landed in San Mateo when their truck broke down. Allegedly.

The group began to experiment with all manner of artsy technology, including tape machines. By 1971 they sent one of their recordings to Warner Bros. and it was rejected. Because there was no name on the package the record company received, Warner Bros. returned it addres-sed to “Residents” — and the group’s name was born.

After producing one more tape and a live show, The Residents decided to take charge of things; they formed Ralph Records, released their first single, “Santa Dog,” in 1972, and haven’t shown any signs of flagging yet.

Oh, and that anonymity? It’s pretty easy to maintain when the members have giant eyeballs for heads. Actually, three eyeballs — green, blue and brown — and a gruesome skull head. These anatomical oddities are dressed to the nines: They wear tuxedos and white gloves. In other words, the alleged humans are fully costumed, and it’s anyone’s guess as to their identity, race or gender. For that matter, no one even knows whether they are still the same members they were in 1970, though it wouldn’t really matter, would it? That oddity alone qualifies this group for a special place in the music world — performers who eschew the cult of personality, of celebrity, and all the usual trappings of fame, were they to achieve any. It’s remarkable, really, that their identities haven’t been leaked by some disgruntled stagehand or ex-lover.

What The Residents have achieved is impressive enough. After “Santa Dog,” they released an album nearly every year until 1980 — now considered their “classic” period. In the ’80s, the group began to create larger, multi-media projects and live tours. They also planned a series of albums, but finished only two, that explored the work of certain American composers. The 1988 album, God in 3 Persons, evolved into a soundtrack album and two singles; the following year The King and “Eye,” depicted by a top-hatted eyeball, turned into The Residents’ Cube E touring show. And 1990’s Freak Show spun into a single, a book, a stage show and a CD-ROM. Their 1998 CD and live show, Wormwood, explored the bad side of the Good Book — a quirky rock-opera approach to the darker stories in the Bible.

If Freak Show was the band’s last step up the technology ladder, Icky Flix represents another. The Residents have produced a DVD featuring new arrangements and recordings of some of their earlier music on video and film. The result is three hours of still-outlandish music and images — 90 minutes of which will be performed in a live show this Sunday night. Finally, The Residents face Vermonters, eye to eye.