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矩阵的分数次幂
Statisticians occasionally need to compute a fractional power of a matrix. In certain practical cases a matrix A is given, and the statistician wants to compute the pth power of A, where p is a fractional or negative number; that is, a matrix R, such that R 1/p = A. He can often get a satisfactory approximation to Ap by using several leading terms of a power series. This procedure is similar to that of inverting certain matrices by power series.
矩阵的分数次幂
Statisticians occasionally need to compute a fractional power of a matrix. In certain practical cases a matrix A is given, and the statistician wants to compute the pth power of A, where p is a fractional or negative number; that is, a matrix R, such that R 1/p = A. He can often get a satisfactory approximation to Ap by using several leading terms of a power series. This procedure is similar to that of inverting certain matrices by power series.
最小二乘法在计量经济学中的地位
IN A RECENT paper,' Frederick V. Waugh argues strongly for the use of ordinary least squares in simultaneous systems. His argument is not that least squares gives unbiased estimates of structural parameters2 but that they do (as consistent structural estimators do not) give unbiased estimates of the dependent variable in the regression equation given the values of the other variables and that this is what is needed for forecasting purposes. This note argues that Waugh's…
桥牌中的概率
In the game of bridge, the probability of a successful finesse, or a favorable “break” in a suit, depends not only upon the original deal, but also upon all the bids and plays which have been made by one's opponents. The widely quoted a priori probabilities, based solely upon the deal, are not generally correct, and are often misleading, after play has begun. This paper shows that the evaluation of probabilities during the course of play of bridge requires the use of the…
桥牌中的概率
In the game of bridge, the probability of a successful finesse, or a favorable “break” in a suit, depends not only upon the original deal, but also upon all the bids and plays which have been made by one's opponents. The widely quoted a priori probabilities, based solely upon the deal, are not generally correct, and are often misleading, after play has begun. This paper shows that the evaluation of probabilities during the course of play of bridge requires the use of the…
两组变量之间的回归
PROFESSOR HOTELLING'S PAPER, Relations between Two Sets of Variates,'l should be widely known and his method used by practical statisticians. Yet, few practical statisticians seem to know of the paper, and perhaps those few are inclined to regard it as a mathematical curiosity rather than an important and useful method of analyzing concrete problems. This may be due to two reasons: first, that Hotelling's paper makes use of rather complicated mathematics and does not spell…