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In Stata, one specifies the full regression, and then enters the command estat hettest followed by all independent variables. [9] [10] In SAS, Breusch–Pagan can be obtained using the Proc Model option. In Python, there is a method het_breuschpagan in statsmodels.stats.diagnostic (the statsmodels package) for Breusch–Pagan test. [11]
Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.
Youden's J statistic is = + = + with the two right-hand quantities being sensitivity and specificity.Thus the expanded formula is: = + + + = (+) (+) In this equation, TP is the number of true positives, TN the number of true negatives, FP the number of false positives and FN the number of false negatives.
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".
In statistics, the likelihood-ratio test is a hypothesis test that involves comparing the goodness of fit of two competing statistical models, typically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods.
The Hosmer–Lemeshow test is a statistical test for goodness of fit and calibration for logistic regression models. It is used frequently in risk prediction models. The test assesses whether or not the observed event rates match expected event rates in subgroups of the model population.
The Anderson–Darling test assesses whether a sample comes from a specified distribution. It makes use of the fact that, when given a hypothesized underlying distribution and assuming the data does arise from this distribution, the cumulative distribution function (CDF) of the data can be transformed to what should follow a uniform distribution.
In statistics, the Wald test (named after Abraham Wald) assesses constraints on statistical parameters based on the weighted distance between the unrestricted estimate and its hypothesized value under the null hypothesis, where the weight is the precision of the estimate.