Abstract
Kernel adjusted density estimation is a modification of the regular kernel density estimation. The modification is applied to a kernel function. This kernel function is derived from the location-scale transformation. Simulation study shows that this estimation have better results than the regular estimation because it has smaller MSE value. In addition, if normal kernel is used as a kernel function then the curve estimation will be smoother than other kernel function such as uniform kernel and Epachenikov kernel.
Highlights
Kernel adjusted density estimation is a modification of the regular kernel density estimation
The modification is applied to a kernel function
This kernel function is derived from the location-scale transformation
Summary
Analisis data bertujuan untuk memperoleh informasi dari suatu data, seperti pola sebaran data, maupun penyajian data supaya mudah dipahami. Pola sebaran data dapat diperiksa melalui bentuk fungsi densitasnya. Bentuk suatu fungsi denstitas biasanya belum diketahui. Untuk mengestimasi fungsi densitas tersebut, digunakan pendekatan nonparametrik, yaitu dengan fungsi kernel (Wand dan Jones, 1995). Menurut Hardle (1991), pemilihan bandwidth (h) dan kernel (K ) sangat penting dalam estimasi densitas kernel. Pemilihan kernel tidak begitu berpengaruh dalam estimasi. Srihera dan Stute (2011) memodifikasi estimasi tersebut pada bentuk kernelnya dengan menggunakan transformasi skala-lokasi, dan selanjutnya disebut estimasi densitas kernel adjusted. Suatu estimasi yang baik dapat dilihat berdasarkan nilai Mean Square Error (MSE) yang minimum. Pada tulisan ini akan dibandingkan estimasi densitas kernel dengan estimasi densitas kernel adjusted berdasarkan nilai MSE
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