Class ListOfTalliesWithCovariance<E extends Tally>
public class ListOfTalliesWithCovariance<E extends Tally>extends ListOfTallies<E>Extends
ListOfTalliesto add support for the computation of the sample covariance between each pair of elements in a list, without storing all observations. This list of tallies contains internal structures to keep track of bar(X)n, i for i = 0,…, d - 1, and ∑k=0n-1(Xi, k - bar(X)k, i)(Xj, k - bar(X)k, j)/n, for i = 0,…, d - 2 and j = 1,…, d - 1, with j > i. Here, bar(X)n, i is the ith component of bar(X)n, the average vector, and bar(X)0, i = 0 for i = 0,…, d - 1. The value Xi, k corresponds to the ith component of the kth observation Xk. These sums are updated every time a vector is added to this list, and are used to estimate the covariances.
Note: the size of the list of tallies must remain fixed because of the data structures used for computing sample covariances. As a result, the first call to init makes this list unmodifiable.
Note: for the sample covariance to be computed between a pair of tallies, the number of observations in each tally should be the same. It is therefore recommended to always add complete vectors of observations to this list. Moreover, one must use the
addmethod in this class to add vectors of observations for the sums used for covariance estimation to be updated correctly. Failure to use this method, e.g., adding observations to each individual tally in the list, will result in an incorrect estimate of the covariances, unless the tallies in the list can store observations. For example, the following code, which adds the vector v in the list of tallies list, works correctly only if the list contains instances of
TallyStore:for (int i = 0; i < v.length; i++)But the following code is always correct:
list.get (i).add (v[i]);