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The logrank test statistic compares estimates of the hazard functions of the two groups at each observed event time. It is constructed by computing the observed and expected number of events in one of the groups at each observed event time and then adding these to obtain an overall summary across all-time points where there is an event.
Let () denote the deterministic communication complexity of a function, and let denote the rank of its input matrix (over the reals). Since every protocol using up to c {\displaystyle c} bits partitions M f {\displaystyle M_{f}} into at most 2 c {\displaystyle 2^{c}} monochromatic rectangles, and each of these has rank at most 1,
In statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.. For example, if the numerical data 3.4, 5.1, 2.6, 7.3 are observed, the ranks of these data items would be 2, 3, 1 and 4 respectively.
The corresponding log partial likelihood is =: = (:), where we have written = using the indexing introduced above in a more general way, as :. Crucially, the effect of the covariates can be estimated without the need to specify the hazard function λ 0 ( t ) {\displaystyle \lambda _{0}(t)} over time.
The motivation to test differences between samples is that ranks are in some sense maximally invariant to monotone transformations. This may be important when there is outliers or when dealing with ordinal data .
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Bowker's test of symmetry; Categorical distribution, general model; Chi-squared test; Cochran–Armitage test for trend; Cochran–Mantel–Haenszel statistics; Correspondence analysis; Cronbach's alpha; Diagnostic odds ratio; G-test; Generalized estimating equations; Generalized linear models; Krichevsky–Trofimov estimator; Kuder ...
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).