Pao-Lu Hsu
| P. L. Hsu | |
|---|---|
 |
|
| Born |
September 1, 1910 Beijing |
| Died | December 18, 1970 (aged 60) Beijing |
| Nationality | China |
| Fields | Mathematics |
| Institutions |
School of Mathematical Sciences Peking University |
| Doctoral advisors |
Egon Pearson Jerzy Neyman |
Pao-Lu Hsu (simplified Chinese: 许宝騄; traditional Chinese: 許寶騄; pinyin: Xǔ Bǎolù; September 1, 1910 – December 18, 1970) was a Chinese mathematician noted for his work in probability theory and statistics.
In 1938, Hsu's first two statistical papers, which appeared in Vol. II of the Neyman–Pearson edited Statistical Research Memoirs, were concerned with Behrens–Fisher problem and the optimal estimate of σ2 in the Gauss–Markov model. The most important paper in this series is where Hsu obtains the first optimum property for the likelihood ratio test of the univariate linear hypothesis, in fact essentially the first nonlocal optimum property for any hypothesis specifying the value of more than one parameter. From 1938 to 1945, Hsu published several papers in the forefront of the development of the theory of multivariate analysis. He obtained several exact or asymptotic distributions of important statistics in the theory of multivariate analysis.
Hsu was an expert in manipulating characteristic functions. He used characteristic functions as a tool to obtain distribution of certain random variables, to determine the limiting distribution of series of random variables. For one example, the Hsu–Robbins–Erdős theorem.
For another example, around 1940, a challenging problem was to find a solution of the most general form of the Central Limit Theorem, which drew the attention of many famed mathematicians, such as Levy, Feller, A. N. Kolmogorov, and Gnedenko. Hsu was a competitor and the competition showed that he was also on the peak. Paper was Professor Hsu's manuscript which Hsu mailed to Professor K. L. Chung in 1947. In this paper Hsu independently obtained the necessary and sufficient condition under which the row sums of a triangular array of infinitesimal random variables, independent in each row, converges in distribution to a given infinitely divisible distribution. Despite the fact that Gnedenko obtained the same result in 1944, Hsu's method is direct and has its own trait.
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