SUMMARY This article investigates the family {Iλ;λ ϵ ℝ} of power divergence statistics for testing the fit of observed frequencies {Xi; i = 1, …, k} to expected frequencies {Ei; i = 1, …, k}. From the definition 2nIλ=2λ(λ+1)∑i=1kXi{(XiEi)λ−1} ; λ∈ℝ, it can easily be seen that Pearson's X2 (λ = 1), the log likelihood ratio statistic (λ = 0), the Freeman‐Tukey statistic (λ = –½) the modified log likelihood ratio statistic (λ = –1) and the Neyman modified X2 (λ = –2), are all special cases. Most of the work presented is devoted to an analytic study of the asymptotic difference between different Iλ however finite sample results have been presented as a check and a supplement to our conclusions. A new goodness‐of‐fit statistic, where λ = ⅔, emerges as an excellent and compromising alternative to the old warriors, I0 and I1.

No abstract

No abstract

Summaryhdemie-Verlag Berlin h u n t s data from spatially conthguoue regions offer a challenge to the statistician both from the data snalytic and the statistical modeling point of view. Important applications include epidemiological studies (e. g., cancer mortality over the counties of the USA) and Census surveys (e. g., undercount over the Census blocks of an urban ares). It has long been recognized by time-series anelysta that data close together in time usually exhibit higher dependence than those far apart. Time-series data analysis relies on methods of data transformation, detrending, and autocorrelation plotting. It is our intention in this article to generalize this approach to a spatial setting. To do this we consider 8 smell spatial deb set of 100 observations. Through the use of 8 square-root transformation, a weighted median polish and a variogram analysis of the median-polish residuals, we represent the transformed data 88 a trend plus stationary error. Thus we show how standard dab-analytic techniques can be modified both to mitigate and to exploit the spatial relationships.