THE ESTIMATION OF NON-LINEAR PARAMETERS BY INTERNAL LEAST SQUARES
成果类型：
Article
署名作者：
HARTLEY, HO
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/35.1-2.32
发表日期：
1948
页码：
3245
关键词：
摘要：
If a non-linear regression law may be regarded as a soln. of a linear differential equation, data may be fitted directly to the linear equation, the least squares technic giving linear equations for the parameters. In order to fit an empirical series, it is necessary to use an equivalent difference equation. Summing the difference equation gives an equation for the dependent variable in terms of its own repeated sums and the independent variable. Such an equation is called an internal regression. The 1st order internal regression is considered for the exponential law of diminishing returns. It is shown that by suitable transformations, the logistic and Gompertz curves may be reduced to exponential form. The asymptotic variances are given for internal least squares estimators and comparisons made with the max. likelihood estimators. The efficiency of the internal regression technic is quite good for moderate curvature of the exponential law.