New York Mayor Michael Bloomberg said on Wednesday he has filed a formal challenge with the U.S. Census Bureau over the 2010 count, saying it may have overlooked at least "tens of thousands" of New Yorkers.

While acknowledging the difficulty of getting a firm grip on New York's varied and sometimes elusive population, Bloomberg said the city would work with federal authorities to correct what the city believes is a clearly inaccurate count.

This will in turn assure the city, the single largest U.S. municipality, qualifies for an accurate amount of federally funded entitlements, officials said.

The 2010 Census put the city's population at about 8.175 million people when it began releasing final results in March, a 2.1 percent rise over 2000 but a decrease of about 225,000 from the bureau's provisional estimate in 2010.

The borough of Queens, one of the most densely populated areas in the country, recorded a population increase of just 1,300 people over the decade, a statistic that many city officials said was implausible.

"I recognize that enumerating the population of New York City is a herculean and unenviable challenge, given the city's large, diverse and dense population, which lives primarily in difficult-to-count housing arrangements," Bloomberg said in his letter to the Census Bureau.

Focusing on what the city claimed are the most egregious mistakes, the mayor singled out two Census offices, one covering Bay Ridge and Bensonhurst in Brooklyn, the other covering Astoria and Jackson Heights in Queens.

The city says those offices mistakenly recorded a large number of housing units as being vacant, leading to an undercount which could result in the city being shortchanged in its federal aid entitlements.

"Numerous data sources cited in our submission refute the prevalence of widespread vacant housing units in those areas, which are and continue to be among our most stable, growing and vibrant neighborhoods," Bloomberg wrote in his letter to Robert Groves, the director of the U.S. Census Bureau.

According to the 2010 census, both areas recorded much higher increases in the number of vacant units over the past decades than adjoining areas.

The city said an abundance of new construction and a rise in foreclosures are two ways of explaining an increase in vacant units, but neither area has seen an increase in these factors relative to its neighbors.

Nor do real estate data in these two areas -- such as decreases in housing market values or average rents -- support the idea of a large increase in vacant homes, the city says.

"It is our expectation that the city's population could increase by tens of thousands of New Yorkers if the errors from those two Census offices alone were corrected," Bloomberg said.

Senators Charles Schumer and Kirsten Gillibrand, both New York Democrats, said they supported the city's challenge.

"In all my years as a legislator, I have never seen a census so poorly conducted," Schumer said in a statement.

"To say there are abandoned buildings in growing, bustling neighborhoods is on its face absurd....The Census Bureau needs to conduct a recount immediately to get this right, and I will continue pushing them to do just that," he said.

As of last week, 48 other municipalities -- including at least one town of only about 1,000 people -- had filed challenges with the Census Bureau through its Count Question Resolution Process, although none of these are remotely as large as New York City.

This is the first time the city has challenged the census data in this way, a spokesman for the mayor said, although the city did unsuccessfully sue after the 1980 Census.

The Census Bureau did not immediately respond to a request for comment.

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