It has become, for the Street, an embarrassing quarterly tradition.

The Apple (AAPL) independent analysts — a growing community of bloggers, private investors and assorted amateurs — file estimates that look, by Wall Street’s standards, outrageously optimistic.

But as the day of reckoning approaches — in this case, Tuesday Oct. 18, when Apple is scheduled to announce its fourth quarter earnings for fiscal 2011 — the estimates filed by the professional analysts inch closer to the bloggers’. Three months ago the Street’s consensus EPS for the quarter was $6.37. Today, according to Thomson Financial, it is $7.20.

But that’s still nearly 26% lower than $9.07, the consensus offered the bloggers.

The disparity is even more striking when you look at individual calls. They range for EPS from a low of $6.30 filed by Morgan Stanley’s Katy Huberty to a high of $10.1 from Posts at Eventide‘s Robert Paul Leitao.

Which group is right? Judging from the chart above, kindly prepared by reader Adam Bushman from data we’ve been collecting for the past six quarters, you should probably take your professional broker’s advice with a grain of salt. In every one of those quarters, the bloggers have clobbered the pros — often by a considerable margin.

Below the fold: Bushman’s chart for Apple’s revenue, updated with the Tuesday’s data from Thomson Financial. Beneath that chart: The estimates for individual analysts (bloggers in green, pros in blue) with the date of their estimates and their rank as determined by the accuracy of their revenue and EPS estimates over the past three quarters.