Hafiyusholeh, Moh (2006) Pemilihan Bandwidth Untuk Regresi Nonparametrik Kernel Dengan Metode Rule Of Thumb, Shibata Dan Cross Validation. Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
The choice of bandwidth is crucial in the nonparametric estimation procedure.
When bandwidth is too small, the resulting curve is too under smoothing. When
bandwidth is too large, the resulting curve is over smoothing.
In this research we study three existing bandwidth selectors for nonparametric
kernel regression. The first method is based on Mean Squared Error estimate. With
penalize Shibata and leave-one-out estimate, bias term of Mean Square Error cancel
asymptotically. The other method is based on Q= E[rn11 (x)-m(x)f by combining bias
and variance and then derive it to h, we obtained Rule of Thumb bandwidth selector
hliOT.
With illustrate three methods to the data we examine represent the voltage drops
in the battery of a guided missile motor during its flight (Eubank, 1988). We obtained
hopt Shibata 0.9500, huor 0,3402 and hopr Cross Validation 0,3050. The value of MSE
and R2 is 0,0137 and 0,9978 for Cross Validation, 0,0617 and 0, 9898 for Rule of
Thumb and 0,0727, 0,9878 for Shibata.
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Pemilihan bandwidth dalam estimasi nonparametrik merupakan sesuatu yang
sangat krusial, jika ditetapkan bandwidth yang terlalu kecil, maka akan berakibat
estimasi kurva regresi undersmoothing. Begitu juga sebaliknya jika ditetapkan
bandwidth yang terlalu besar, maka akan menyebabkan estimasi kurva oversmoothing.
Dalam penelitian ini kita mengkaji tiga metode pemilihan bandwidth untuk
regresi nonparametrik kernel . Metode pertama berdasar pada estimasi Mean Square
Error. Dengan menetapkan penalize Shibata dan leave-one-out estimate, maka bias dari
Mean Square Error (MSE) akan terhapuskan. Metode lain berdasar pada
Q=E[mh(x)-m(x)]2 dengan mengkombinasikan antara bias dan varians dan
menurunkannya terhadap h didapatkan bandwidth Rule ofThumb hum .
Dengan menerapkan ketiga metode tersebut ke dalam data penurunan voltage
baterai dari motor peluru kendali selama waktu penerbangan (Eubank, 1988) diperoleh
hopr Shibata sebesar 0.9500, Rule ofThumb sebesar 0,8170 dan Cross Validation sebesar
0,3050. Nilai MSE dan R2 masing-masing metode sebesar 0,0137 dan 0,9978 untuk
Cross Validation, sedangkan untuk ROT sebesar 0,0617 dan 0,9898 serta Shibata
sebesar 0,0727, dan 0,9878.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | RTST 519.536 Haf p |
| Uncontrolled Keywords: | Nonparametric kernel regression, Rule-of-Thumb bandwidth, Penalize Shibata, Cross Validation, Regresi nonparametrik kernel, Rule-of-Thumb bandwidth, Penalize Shibata, Cross Validation |
| Subjects: | H Social Sciences > HA Statistics > HA31.3 Regression. Correlation |
| Divisions: | Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | ansi aflacha |
| Date Deposited: | 10 Sep 2018 02:56 |
| Last Modified: | 10 Sep 2018 02:56 |
| URI: | http://repository.its.ac.id/id/eprint/59608 |
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