Statistical Method of Estimating Isolines

抄録

In this paper, it is pointed out firstly that the so-called objective method of drawing isolines which is based on the method of least squares can be generalized but that it is disadvantageous in practice. As an alternative, a method based on the simultaneous confidence region of true value at each station is proposed. What has the objective meaning is the confidence region by which the existence region of isolines is provided. Especially, the confidence interval of proportional division point of two adjacent stations can be easily found by a graphical method. A definite set of isolines may be drawn arbitrarily in the restricted limit, by considering several points in each local area successively. The method is developed for two cases; the one concerns the distribution of mean values and the other the directly observed values. In the former the only assumption is that every set of random fluctuations of simultaneously observed values submits to the same multivariate normal probability distribution law, and in the latter the assumption that the covariances of observed values are known must be added.