Fitting Piecewise Linear Copulas to Data
نویسندگان
چکیده
Given a set of n data points (xi, yi, zi) ∈ [0, 1] , two methods are established for constructing two piecewise linear copulas, respectively denoted CA(x, y) and CB(x, y), in such a way that CA(xi, yi) and CB(xi, yi) both yield an approximation of zi for all i. If the data points are (randomly) sampled from an unknown copula C, i.e. zi = C(xi, yi), then CA and CB provide two piecewise linear estimates of C. The quality of both estimations is illustrated on synthetic randomized data sets.
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