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THE ESTIMATION PROCEDURE
SIMULATIONS 2 9
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21 equidistant x-observations 25 000 replications algorithm approximation bending point bias calculate cointegration direction compared component concave regression function concave-up regression constant curvature convex corresponding Denote extreme-value function fiction point fractional order functions with constant Goteborg increasing and concave inflection interval inflection point influence interval 0.5A isotonic regression least squares estimate linear combination linear regression logistic long memory process max max memory parameter nearest x-value nonstationary normalized curvature observations obtained periodogram roughness piecewise linear functions properties proposed estimation method Random numbers rate of convergence regression line result from 25 sample shown in table shows sigmoid function simulation results simulation study situation spectral density standard deviation standardized kurtosis standardized skewness stationary statistics study was performed successive x-observations sum of squares Suppose theoretical trend uniformly distributed unimodal function unimodal regression Var(Y vector vector autoregressive weighted least squares white noise Wiener process x-interval x-value was uniformly