STAT444 Lecture Notes - Lecture 7: Cubic Hermite Spline, Basis Function, Piecewise
14 Feb 2018
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Breakdown point least mean square least kms = median of ( yi. For continuous polynomial function flx ) the simplest is piecewise linear. Recall y= bot f. xt pz c x. Equivalently y= pot pix t be ( x - a) * Truncated power ( x - a) + series we can easily generalize the model to accomodate many break points continuous in fcx ) filx ) Me most commonly used spline is the cubic. Cubic and continuous in fix ) filx ) f ( x ) let t. cn. < tk be k fixed known knots , where t , tk are boundary knots and tz. 3 (x-g) (x - tk )3 form a basis for the cubic knots till. , any cubic spline fcx ) pot p , xt pax "t b 3 + zjk, pjt } ( ktj. Quick check : fix ) is obviously continuous between knots for ti fcti ftp. titpzt. it.
