LOS ANGELES (AP) -- Jessica Simpson and Nick Lachey, who turned mid-level music careers into a Hollywood star-spangled marriage, have separated following months of persistent breakup rumors.The couple announced their separation Wednesday."After three years of marriage, and careful thought and consideration, we have decided to part ways," they said in a joint statement released by their publicists. "This is the mutual decision of two people with an enormous amount of respect and admiration for each other."Calls seeking further comment from publicists Meredith O' Sullivan and Rob Shuter were not immediately returned early Thursday.The couple have been dogged by rumors that their marriage was in trouble -- Us Weekly reported that they split in an Oct. 17 issue -- but Simpson, 25, and Lachey, 32, brushed the speculation aside and insisted they were still together.In the December-January issue of Teen People, which went on newsstands earlier this month, Simpson denied rumors that the marriage was kaput."Hopefully mine and Nick's story will continue for the rest of our lives, like what we vowed, through sickness and in health," said Simpson, who famously professed that she remained a virgin until she got married.The couple wed in October 2002, back when they were known simply as pop singers. But Simpson hadn't achieved the multiplatinum successes of peers Britney Spears and Christina Aguilera, while Lachey was a member of the boy band 98 Degrees, which sold far fewer albums than such acts as 'N Sync and Backstreet Boys.The couple's reality show, "Newlyweds: Nick & Jessica," which chronicled their daily lives in a new California home, turned them into stars. The show, which ran for three seasons, made Simpson infamous for her dippy-blonde moments, including the time she confused the tuna she was eating for chicken, or when she eschewed Buffalo wings because "I don't eat buffalo."Simpson's star status has begun to outshine Lachey's. She played Daisy Duke in this summer's hit movie "The Dukes of Hazzard," and she endorses "Dessert," a beauty line that includes flavored body creams. Lachey, whose solo album has had disappointing sales, appeared in some episodes of the sitcom "Charmed."Besides appearing in "Newlyweds," the couple entertained U.S. troops earlier this year in the ABC special "Nick & Jessica's Tour of Duty," and last year they hosted the ABC variety special "Nick & Jessica's Family Christmas." A coffee table book, "Jessica Simpson I Do: Achieving Your Dream Wedding," also was released last year.Copyright 2005 The Associated Press. All rights reserved.This material may not be published, broadcast, rewritten, or redistributed.