Dewi Noor Hidayati, 090610216 M (2008) PERBANDINGAN METODE GENERALIZED MAXIMUM LIKELIHOOD SPLINE UNTUK MEMPERKIRAKAN JUMLAH LEUKOSIT PADA TERSANGKA FLU BURUNG DI JAWA. Thesis thesis, UNIVERSITAS AIRLANGGA.

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Abstract

Suppose that response variables yl, Y2, • • • , yn have been observed at design points t1t2 ..., to following the regression model: Yl = f (t1) + £t, i = 1, 2, ... ,n Where f(.) is an unknown regression function and £1, E2, £3, £4 ... , En are zero mean, uncorrelated random errors, and a-2 variance. The regression curve shape f is unknown but only assumed smooth, included in the Sobolev space W2 [a, b] = { f : f, f ', ... , f (m_1) absolutely continuous fQ (f (m))z dt < x}. This paper will study how to estimate the regression curve f from the sample. It will be explaining the estimator regression curve f by declaration f (ti) as the truncated polynomial spline which relatively simpler than other nonparametric regression curve approximation. The regression curve estimation f using least square optimization: Furthermore, to know the smoothness of regression curve by using Generalized Cross Validation (GCV) and Generalized Maximum Likelihood (GML) methods. Which one of the methods is smoothest? Therefore from by using that estimator, so we can estimate the leukocytes of the avian influenza suspects in east Java. The result of this research found that the linier GCV method gives smoothest curve compared with the other GML methods. It came from the conclusion of the least value of MSE. This method also found the knot point is t = 8, and the models are: = 8004 — 587t , t < 8 ~Y = 8004 — 587t + 611(t -- 8), t 8

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