KPMG L.L.P. has agreed to pay $8.2 million to settle allegations that it violated rules requiring auditors to remain independent from the public companies they audit to ensure their objectivity and impartiality, the U.S. Securities and Exchange Commission said Friday.

Responding to the settlement, KPMG said in a statement that it has changed its procedures.

The SEC said it has issued a separate report about the scope of the independence rules that forbid audit firms to loan members of their staff to audit clients “in a manner that results in the staff acting as employees of those companies.”

The SEC said its investigation found that KPMG, whose U.S. headquarters is in New York, broke auditor independence rules of the Securities and Exchange Act of 1934 by providing prohibited nonaudit expert services such as bookkeeping to affiliates or companies whose books they were auditing.

Some KPMG personnel also owned stock in companies or affiliates of companies that were KPMG audit clients, further violating auditor independence rules, the SEC said.

According to the SEC order in the matter, KPMG violated the rules with three unidentified companies from 2007 through the end of 2011.

“Auditors are vital to the integrity of financial reporting, and the mere appearance that they may be conflicted in exercising independent judgment can undermine public confidence in our markets,” John T. Dugan, associate director for enforcement in the SEC’s Boston regional office, said in a statement. “KPMG compromised its role as an independent audit firm by providing prohibited nonaudit services to companies that it was supposed to be auditing without any potential conflicts.”

In its statement, KPMG said it is “fully committed to ensuring our independence with respect to all of our audit clients. In the years since the events discussed in this SEC action, KPMG has implemented internal changes that are designed to ensure its ability to comply with restrictions on providing nonaudit services to SEC audit clients and/or their affiliates.”