Fitting Piecewise Linear Copulas to Data

摘要

Given a set of n data points (x_i, y_i, z_i) 2 [0, 1]~3, two methods are established for constructing two piecewise linear copulas, respectively denoted C_A(x, y) and C_B(x, y), in such a way that C_A(x_i, y_i) and C_B(x_i, y_i) both yield an approximation of z_i for all i. If the data points are (randomly) sampled from an unknown copula C, i.e. z_i = C(x_i, y_i), then C_A and C_B provide two piecewise linear estimates of C. The quality of both estimations is illustrated on synthetic randomized data sets.