REGRESI SPLINES BENTUK-TERBATAS MONOTON (MONOTONE SHAPE-RESTRICTED REGRESSION SPLINES)
Regression analysis is a statistical analysis that is often used to explore the relationship between predictor variable and response variable. If the assumption of a parametric form was known, parametric regression can be performed. But if the parametric form was not known, the estimated regression...
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| 格式: | Theses and Dissertations NonPeerReviewed |
| 出版: |
[Yogyakarta] : Universitas Gadjah Mada
2013
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| 在線閱讀: | https://repository.ugm.ac.id/124009/ http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=64127 |
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| 總結: | Regression analysis is a statistical analysis that is often used to explore the
relationship between predictor variable and response variable. If the assumption
of a parametric form was known, parametric regression can be performed. But if
the parametric form was not known, the estimated regression functions can be
performed with nonparametric regression. Nonparametric regression method that
is often preferred is regression splines because it uses less parameters in the
estimation process.
Regression splines can model the data that have different characteristics
in the interval , . Estimation process is done by deviding , to be some
sub intervals that have similar characteristics. Regression splines is known to be
sensitive to number and location of knot so it need Generalized Cross-Validation
to determine the optimal number and location of knot.
In many practical settings, the predictor and response variable are known
to preserve certain shape restrictions such as monotonicity. That monotonicity
assumptions can be imposed on the regression splines estimation process, which
is then called monotone shape-restricted regression splines. Estimate monotone
shape-restricted function can be obtained using linear combination of I-splines
basis functions and restrict the coefficients of these basis function to be positive.
The restricted version have smaller mean squared error (MSE) and greater Rsquare
than unrestricted version.
In this paper, monotone shape-restricted regression splines is applied to
analyze the relationship of age and toddler height in posyandu Sakura,
Caturharjo village, Pandak subdistrict, Bantul regency. Then monotone shaperestricted
regression splines estimation results are compared with regression
splines and simple linear regression. By looking at the estimation results of the
regression curve, MSE and R-square, it is concluded that monotone shaperestricted
regression splines better than others. |
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