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最小卡方，而非最大似然！AI 解读

The sovereignty of MLE is questioned. Minimum $\chi^2_\lambda$ yields the same estimating equations as MLE. For many cases, as illustrated in presented examples, and further algorithmic exploration in progress may show that for all cases, minimum $\chi^2_\lambda$ estimates are available. In this sense minimum $\chi^2$ is the basic principle of estimation. The criterion of asymptotic sufficiency which has been called "second order efficiency" is rejected as a criterion of…

方差下界的另一面：一则附有更正的札记AI 解读

This note has as its primary purpose the correction of a statement made in a previous paper regarding the attainment of the variance of a proposed estimator of its lower bound. At the same time it seemed useful, as an expository function, to recapitulate a development of the lower bound which led this writer to a better understanding of it, and to the realization of the indicated error. Here the bound is developed ab initio from a simple identity, instead of secondarily from…

方差下界的另一面：一则更正札记AI 解读

This note has as its primary purpose the correction of a statement made in a previous paper regarding the attainment of the variance of a proposed estimator of its lower bound. At the same time it seemed useful, as an expository function, to recapitulate a development of the lower bound which led this writer to a better understanding of it, and to the realization of the indicated error. Here the bound is developed ab initio from a simple identity, instead of secondarily from…

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是否存在两条回归线？AI 解读

If, in sampling from an existent population, we wish to know the regression of u on v, a line is fitted by least squares, minimizing the sum of the squared residuals of v (or y). If there is no error in measuring the independent variate u, regardless of whether the dependent variate has been measured without error as v or with error as y, the regression is an estimate of the true regression. If, however, the independent variate is measured with error in x, the regression…

以线性变换求最小卡方与最大似然解：侧重生物测定AI 解读

An old and commonly used device for fitting a curve y = F(x, α, β) is to find a function of y which is linearly related to x, or a function of x which is linearly related to y, or functions of y and x which are linearly related to each other. The linearly related functions are plotted against one another, and a line is fitted to the points, usually by eye, sometimes by “least squares” in terms of the transforms. Texts dealing with empirical curve-fitting characteristically…

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