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Topics in the Investigation of Linear Relations Fitted by the Method of Least Squares

最小二乘拟合线性关系的若干研究主题

Summary Various topics are reviewed: the effect of modern computers on statistical calculation; analysis by vector components rather than analysis merely of variance; “stepwise regression”; testing goodness of fit by examining residuals. Possible alternatives to the method of least squares appropriate when the distribution of errors has long tails, and computation of the likelihood function resulting from a Pearson Type VII distribution of errors, are considered. Some of the…

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Tests of Goodness of Fit

拟合优度检验

SUMMARY An explicit account is given of a procedure for assessing goodness of fit of some observations with a hypothesis, generally known as a “test of significance”; the description is close in spirit to R. A. Fisher’s original conception. The relation of this test procedure with Bayesian procedures and with the Neyman–Pearson theory of tests is discussed. Some very tentative suggestions are made regarding the choice of a test criterion and the use to which the result of…

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Estimating a Mixed-Exponential Response Law

混合指数响应规律的估计

This paper is concerned with the estimation of the parameters of a mixed-exponential response law, given some sample observations. Two alternative laws are considered, each having two parameters. The first law expresses the proportion F(t) of the population who have responded within time t in the form F(t) = (1 – e −αt )ξ. The second law states that F(t) = 1 – (1 + λt)−v. The problem has been encountered in the context of market research, in estimating the “penetration” of a…

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Estimating a Mixed-Exponential Response Law

混合指数响应规律的估计

This paper is concerned with the estimation of the parameters of a mixed-exponential response law, given some sample observations. Two alternative laws are considered, each having two parameters. The first law expresses the proportion F(t) of the population who have responded within time t in the form F(t) = (1 – e −αt )ξ. The second law states that F(t) = 1 – (1 + λt)−v. The problem has been encountered in the context of market research, in estimating the “penetration” of a…

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Sequential Estimation

序贯估计

Summary The literature on sequential estimation is reviewed, with special reference to inverse binomial sampling, double sampling, and asymptotic theory. An approximate distribution for the sample size is found for a certain type of sequential sampling rule, in which a cumulative sum of independent random variables all having the same continuous distribution is plotted against their number until a fixed boundary is first reached or crossed. Approximate methods are given for…

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