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Given this procedure, the PRESS statistic can be calculated for a number of candidate model structures for the same dataset, with the lowest values of PRESS indicating the best structures. Models that are over-parameterised ( over-fitted ) would tend to give small residuals for observations included in the model-fitting but large residuals for ...
The basic form of a linear predictor function () for data point i (consisting of p explanatory variables), for i = 1, ..., n, is = + + +,where , for k = 1, ..., p, is the value of the k-th explanatory variable for data point i, and , …, are the coefficients (regression coefficients, weights, etc.) indicating the relative effect of a particular explanatory variable on the outcome.
The initial, "prediction" step, starts from a function fitted to the function-values and derivative-values at a preceding set of points to extrapolate ("anticipate") this function's value at a subsequent, new point.
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".
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.
The positive predictive value (PPV), or precision, is defined as = + = where a "true positive" is the event that the test makes a positive prediction, and the subject has a positive result under the gold standard, and a "false positive" is the event that the test makes a positive prediction, and the subject has a negative result under the gold standard.
The normal range for a healthy person not using warfarin is 0.8–1.2, and for people on warfarin therapy an INR of 2.0–3.0 is usually targeted, although the target INR may be higher in particular situations, such as for those with a mechanical heart valve. If the INR is outside the target range, a high INR indicates a higher risk of bleeding ...
Further, by the Lehmann–Scheffé theorem, an unbiased estimator that is a function of a complete, sufficient statistic is the UMVUE estimator. Put formally, suppose δ ( X 1 , X 2 , … , X n ) {\displaystyle \delta (X_{1},X_{2},\ldots ,X_{n})} is unbiased for g ( θ ) {\displaystyle g(\theta )} , and that T {\displaystyle T} is a complete ...