Suppose that distribution of Y = (Y_{1} , ... , Y_{n}) belongs to the parametric family \{f_{Y}(y | \theta): \theta \in \Theta \}. Then, the statistic S = S(Y_{1} , ... , Y_{n}) is sufficient for \theta if and only if there exit functions h of y and g of...
Statistical Estimation in the Space of a Certain Sufficient Statistic of the Extremal Value Distribution, and Group Classificationdoi:10.1023/A:1020260002659Journal of Mathematical Sciences -Abusev, R. A.Perm State University, Perm, RussiaKluwer Academic Publishers-Plenum PublishersJournal of Mathematical ...
Alternatively, the F statistic can be transformed to a statistic, B that has a Beta distribution with parameters (k − 1)/2 and (N − k)/2, where B=(k−1)F(k−1)F+N−k=SSTreatSSTotalandSSTotal=SSTreat+SSE=∑j=1k∑i=1nj(Yij−Y¯)2. The null hypothesis is reject...
(1966): Minimum variance unbiased estimation of the distribution function admitting a sufficient statistic. Ann. Inst. Statist. Math., 18, 39–47.Patil GP., Wani JK. Minimum variance unbiased estimation of the distribution function admitting a sufficient statistic. Ann Inst Stat Math Tokyo 1966,...
A parametric model is tested for a dataset by conditioning on the value of a sufficient statistic and determining the probability of obtaining another dataset as extreme or more extreme relative to the general model, where extremeness is determined by the value of a test statistic such as the ...