Newswise — University of Chicago statistician Wei Biao Wu has more than 30 research collaborators around the world. From Taiwan and England to New York and California, he works with biologists, economists, computer scientists and electrical engineers. But for an article that appeared in the October 2007 issue of Econometric Theory, he tapped one of his graduate students, Xiaofeng Shao, PhD'06, as co-author.

Wu, an associate professor in statistics, and Shao have received the Tjalling C. Koopmans Econometric Theory Prize 2008 for their article, given for the best article published in the journal during the previous three years. The $1,000 prize, named for the 1975 Nobel Laureate in economic science, is supported by Cambridge University Press and the late Mrs. Truus Koopmans.

Notification of the award surprised Wu, given the list of distinguished econometricians who have previously received the award. "I view myself as a statistician instead of an econometrician," Wu said.

Among the three judges who selected the prize-winning paper was Nobel laureate Clive W.J. Granger, who died in May. Granger shared the 2003 Nobel Prize in economic sciences for the statistical methods he developed for analyzing economic time series data (of a different type than Wu and Shao address in their Econometric Theory paper).

Wu and Shao's 25-page, equation-packed paper also tackles time series data. Titled, "A limit theorem for quadratic forms and its applications," the paper presents a new statistical method for analyzing time series data. More technically and precisely, it presents a new martingale approximation method to derive the large sample theory for quadratic forms of time series.

These data represent a series of values charted over uniform time intervals. Times series data include, for example, monthly unemployment figures. But Wu and Shao's highly theoretical paper is entirely devoid of economic terminology.

Before the publication of Wu and Shao's 2007 paper, econometricians generally replied upon Murray Rosenblatt's statistical approach to the analysis of random processes. Rosenblatt, a professor emeritus in mathematics at the University of California, San Diego, devised the approach as a member of the mathematics faculty at Chicago in the mid-1950s.

"He proposed a strong mixing condition in 1955," Wu said. "It's a way to characterize a time-series dependence. In time series, people believe things are dependent. What happened today, what happened yesterday, are related," he explained.

Wu estimates that scholars have generated thousands of papers based on Rosenblatt's dependence condition. But in their paper, Wu and Shao instead used what they call a "physical dependence measure." They interpret a time series as a physical system.

"In a physical system, of course, you have some inputs and some outputs," We said. "We interpret dependence based on the relationship between input and output."

A recipient of a 2005 National Science Foundation Faculty Early Career Development Award, Wu splits his research evenly between theoretical and applied research. In the applied arena, his work has included an assessment of trends in global warming data.

"I think most people agree it's getting warmer," Wu said. "However what's the pattern of the trend?" Is it more or less slow and steady, or does it jump in dramatic leaps and bounds?

Wu and another former graduate student, Zhibiao Zhao, PhD'07, analyzed monthly global temperature data collected from 1856 to 2000.

"Our conclusion is that the variability is getting bigger, which means the warm days are getting even warmer, and cold days are getting colder," Wu said.

Shao and Zhao were the first two students to receive their doctoral degrees under Wu's supervision since he joined the Chicago faculty in 2001. A third student, Zhou Zhou, will complete his doctorate in August. All three have received faculty appointments.

In addition to Shao, an assistant professor of statistics at the University of Illinois at Urbana-Champaign, Zhao is an assistant professor of statistics at Pennsylvania State University. Zhou has been named an assistant professor in statistics at the University of Toronto.

"Somehow we are able to get the best students," Wu said.

Shao, in turn, praised Wu and his other graduate adviser, Michael Stein, the Ralph and Mary Otis Isham Professor in Statistics.

"I was very fortunate to have these two wonderful advisers," Shao said. "I owe him, and Michael Stein, too, for excellent advising."

Wu combines hard work, high energy and strong technical skills in probability and statistics with a humble and easygoing personality, according to Shao. In Wu's role as a graduate mentor, he encouraged Shao to independently develop and pursue new research problems.

"The experience of finding good research problems and solving them helped a lot in my current academic career," Shao said.