Estimation of second moment function with adujusted sample by an estimator of jump size of discontinuity point
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(2) 758. Jib Huh. ᄇᄃ ᆫ ᅡ ᅬᅥ ᄋᄋ ᅣ ᄒ ᆫᄃ ᅡ ᅡ. (Fanᄀ ᅪ Gijbels, 1996) ᄋ ᅵᅪ ᄋ ᄀ ᇀᄋ ᅡ ᅵ ᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄂ ᆫ ᄒ ᅳ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄋ ᅴ ᄎ ᅮᄅ ᆫᄋ ᅩ ᅦᄉ ᅥ ᄑ ᆯᄉ ᅵ ᅮᄌ ᆨᄋ ᅥ ᅳᄅ ᅩ ᄎ ᅮᄌ ᆼ ᅥ ᅬᄋ ᄃ ᅥᄋ ᅣ ᄒ ᆯ ᄃ ᅡ ᅢᄉ ᆼᄋ ᅡ ᅵᄃ ᅡ. ᄒ ᅬᄀ ᅱᄆ ᅩᄒ ᆼᄋ ᅧ ᅴ ᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄋ ᅴ ᄏ ᅥᄂ ᆯᄒ ᅥ ᆼ ᄎ ᅧ ᅮᄌ ᆼ ᅧ ᅥ ᆫ ᄋᄀ ᅮᄅ ᅩᄂ ᆫ Rice (1984), Gasser ᄃ ᅳ ᆼ (1986), ᅳ M¨ ullerᄋ ᅪ Stadtm¨ uller (1987), Hallᄀ ᅪ Carroll (1989) ᄃ ᆼᄋ ᅳ ᅵ ᄋ ᆻᄃ ᅵ ᅡ. ᄐ ᆨᄒ ᅳ ᅵ, Ruppert ᄃ ᆼ (1997)ᄀ ᅳ ᅪ Yuᄋ ᅪ Jones (2004)ᄂ ᆫᅮ ᅳ ᆫ ᄇᄉ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄏ ᅥᄂ ᆯᄎ ᅥ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄀ ᅳ ᆨᄉ ᅮ ᅩᄃ ᅡᄒ ᆼᄎ ᅡ ᅮᄌ ᆼᄅ ᅥ ᆼ (local polynomial estimator)ᄋ ᅣ ᅳᄅ ᅩᄌ ᅦᄉ ᅵᄒ ᅡᄋ ᆻ ᅧ ᅡ. Huh (2020)ᄂ ᄃ ᆫᄃ ᅳ ᅡᄋ ᆼᄒ ᅣ ᆫᄄ ᅡ ᅵᄑ ᆨᄋ ᅩ ᅦᄄ ᅡᄅ ᅡᄒ ᆷᄉ ᅡ ᅮᄋ ᅴᄌ ᆼᄀ ᅳ ᆷᄋ ᅡ ᆯᄉ ᅳ ᅵᄀ ᆨᄌ ᅡ ᆨᄋ ᅥ ᅳᄅ ᅩᄑ ᅭᄒ ᆫᄒ ᅧ ᅡᄂ ᆫ SiZer (SIgnificant ZERo ᅳ crossings of derivatives)ᄅ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧᄆ ᅩᄐ ᅥᄉ ᅡᄋ ᅵᄏ ᆯᄌ ᅳ ᅡᄅ ᅭᄋ ᅴᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᅬᅱ ᄒ ᄀᄆ ᅩᄒ ᆼᄋ ᅧ ᅴ ᄎ ᅮᄅ ᆫᄋ ᅩ ᅦᄉ ᅥ ᄋ ᅵᄅ ᅥᄒ ᆫ ᄌ ᅡ ᆼᄋ ᅮ ᅭᄒ ᆫ ᄋ ᅡ ᆨᄒ ᅧ ᆯᄋ ᅪ ᆯ ᄒ ᅳ ᅡᄂ ᆫ ᄇ ᅳ ᆫᄉ ᅮ ᆫᄒ ᅡ ᆷᄉ ᅡ ᅮᄋ ᅴ ᄏ ᅥᄂ ᆯᅧ ᅥ ᆼ ᄒ ᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅴ ᄎ ᅮᄌ ᆼ ᄌ ᅥ ᆼᄃ ᅥ ᅩ (precision)ᄂ ᆫᄒ ᅳ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄂ ᅡᄒ ᆨᄅ ᅪ ᆯᄆ ᅲ ᆯᄃ ᅵ ᅩᄒ ᆷᄉ ᅡ ᅮᄃ ᆼᄋ ᅳ ᅴᄏ ᅥᄂ ᆯᅧ ᅥ ᆼ ᄒᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅴᄎ ᅮᄌ ᆼᅥ ᅥ ᆼ ᄌᄃ ᅩᄀ ᅡᄀ ᅳᄃ ᆯᄒ ᅳ ᆷᄉ ᅡ ᅮᄋ ᅴᄇ ᅮᄃ ᅳᄅ ᅥᄋ ᆷ (smoothᅮ ness)ᄋ ᅦ ᄋ ᅴᄌ ᆫᄒ ᅩ ᅡᄂ ᆫ ᄀ ᅳ ᆺᄎ ᅥ ᅥᄅ ᆷ (Fanᄀ ᅥ ᅪ Gijbels, 1996) ᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄋ ᅴ ᄇ ᅮᄃ ᅳᄅ ᅥᄋ ᆷᄋ ᅮ ᅦ ᄋ ᅴᄌ ᆫᄒ ᅩ ᆷᄋ ᅡ ᆫ ᄌ ᅳ ᅡᄆ ᆼᄒ ᅧ ᅡᄃ ᅡ. M¨ uller (1992)ᄋ ᅪ Huhᄋ ᅪ Park (2004)ᄋ ᆫ ᄒ ᅳ ᅬᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄀ ᅡ ᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᆯ ᄀ ᅳ ᅡᄌ ᆯ ᄄ ᅵ ᅢ, ᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅦᄉ ᅥ ᄒ ᅬᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄋ ᅴ ᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅴ ᆫᄋ ᅧ ᄑ ᅴ (bias)ᄀ ᅡ 0ᄋ ᅳᄅ ᅩ ᄉ ᅮᄅ ᆷᄒ ᅧ ᅡᄌ ᅵ ᄋ ᆭᄋ ᅡ ᆷᄋ ᅳ ᆯ ᄉ ᅳ ᆯᅧ ᅥ ᆼ ᄆᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄇ ᆫᄉ ᅮ ᆫᄒ ᅡ ᆷᄉ ᅡ ᅮᄀ ᅡ ᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᆯ ᄀ ᅳ ᅡᄌ ᆯ ᄄ ᅵ ᅢᄋ ᅴ ᄋ ᆫᄀ ᅧ ᅮᄅ ᅩᄂ ᆫ Delᅳ gadoᄋ ᅪ Hidalgo (2000), Chen ᄃ ᆼ (2004), Kangᄀ ᅳ ᅪ Huh (2006), Huh (2016a) ᄃ ᆼᄋ ᅳ ᅵᄋ ᆻᄃ ᅵ ᅡ. Huh (2016b, 2017)ᄂ ᆫᅮ ᅳ ᆯ ᄇᄋ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵ (jump size)ᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄌ ᆫᄎ ᅡ ᅡᄌ ᅦᄀ ᆸᄀ ᅩ ᅪᄅ ᅩᄀ ᅳᄌ ᆫᄎ ᅡ ᅡᄌ ᅦᄀ ᆸᅳ ᅩ ᆯ ᄋᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆫᄇ ᅵ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄅ ᅩᄇ ᅮ ᅥᄋ ᄐ ᅴᄀ ᆯᄀ ᅧ ᅪᄋ ᆫᄀ ᅵ ᆺᄎ ᅥ ᅥᄅ ᆷᄇ ᅥ ᅩᄌ ᆼ (adjusted)ᄒ ᅥ ᅡᄋ ᅧᄇ ᆫᄉ ᅮ ᆫᄒ ᅡ ᆷᄉ ᅡ ᅮᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄀ ᅩᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄋ ᆨᄇ ᅧ ᅩᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨ ᅩ ᆫᄉ ᅮ ᄇ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄒ ᆫᄑ ᅡ ᆫ, ᄒ ᅧ ᅬᄀ ᅱᄆ ᅩᄒ ᆼᄋ ᅧ ᅦᄉ ᅥ Kang ᄃ ᆼ (2000)ᄋ ᅳ ᆫᄒ ᅳ ᅬᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄋ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼ ᅥ ᆼᄋ ᅣ ᄅ ᅳᄅ ᅩᄇ ᆫᄋ ᅡ ᆼᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅴᄑ ᅭᄇ ᆫᅳ ᅩ ᆯ ᄋᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆫᄒ ᅵ ᅬᄀ ᅱᄆ ᅩᄒ ᆼᄋ ᅧ ᅦᄉ ᅥᄎ ᅮᄎ ᆯᄃ ᅮ ᆫᄀ ᅬ ᆺᄎ ᅥ ᅥᄅ ᆷᄇ ᅥ ᅩᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄒ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄀ ᅩᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵ ᅮᄌ ᄎ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄋ ᆨᄇ ᅧ ᅩᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄒ ᅩ ᅬᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᆫᄎ ᅡ ᄌ ᅡᄅ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᆫᄇ ᅡ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᅮ ᅩ ᆫ ᄇᄉ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄋ ᅥ ᆫᄒ ᅳ ᅬᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄋ ᅥ ᅵᄌ ᆫᄌ ᅥ ᅦᅬ ᄃᄋ ᅥᄋ ᅣᄒ ᅡᄆ ᅳᄅ ᅩᄒ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᅥ ᅥ ᆼ ᄌ ᅩᄋ ᄃ ᅦᅴ ᄋᄌ ᆫᄒ ᅩ ᅡᄀ ᅦᄃ ᆫᄃ ᅬ ᅡ. Huh (2005)ᄂ ᆫᄒ ᅳ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄋ ᅥ ᆹᄋ ᅥ ᅵᄇ ᆫᄋ ᅡ ᆼᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅴᄑ ᅭᄇ ᆫᄋ ᅩ ᅴᄌ ᅦᄀ ᆸᄃ ᅩ ᆯᄅ ᅳ ᅩᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮ (second moment function)ᄋ ᅴ ᄎ ᅮᄌ ᆼᄋ ᅥ ᆯ ᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧ ᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄋ ᅴ ᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴ ᄋ ᅱᄎ ᅵ (location)ᄀ ᅪ ᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄅ ᆯ ᅳ ᅮᄌ ᄎ ᆼᅡ ᅥ ᄒᄋ ᆻᄃ ᅧ ᅡ. Huh (2005)ᄂ ᆫᄇ ᅳ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄀ ᅡᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆫᄀ ᅵ ᆺᄋ ᅥ ᆫᄒ ᅳ ᅬᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄀ ᅡᄋ ᆫᄋ ᅯ ᆫᄋ ᅵ ᆯᄉ ᅵ ᅮᄃ ᅩᄋ ᆻᄋ ᅵ ᅳᄂ ᅡ, ᄋ ᅵᄄ ᅢᄂ ᆫᄇ ᅳ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨ ᅩ ᆷᄋ ᅥ ᄌ ᅴᅮ ᄎᄌ ᆼᄋ ᅥ ᆫᄒ ᅳ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄋ ᅥ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄂ ᆫᄀ ᅳ ᆺᄋ ᅥ ᅵᄐ ᅡᄃ ᆼᄒ ᅡ ᅡᄆ ᅧ, ᄒ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄀ ᅡᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆯᄄ ᅵ ᅢᄇ ᆫᄉ ᅮ ᆫᄒ ᅡ ᆷᄉ ᅡ ᅮᄀ ᅡᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆫᅧ ᅵ ᆼ ᄀ ᅮᄋ ᄋ ᅦᅬ ᄒᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄋ ᅥ ᆹᄋ ᅥ ᅵᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄂ ᆫᄀ ᅳ ᆺᄋ ᅥ ᅵᄑ ᆫᄅ ᅧ ᅵᄒ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡᄀ ᅩᄉ ᆯᅧ ᅥ ᆼ ᄆ ᅡᄋ ᄒ ᆻᅡ ᅧ ᄃ. ᆫ ᄋ ᅩ ᄇ ᆫᄀ ᅧ ᅮᄋ ᅦᄉ ᅥᄂ ᆫ ᄇ ᅳ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄀ ᅡ ᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆯ ᄄ ᅵ ᅢ ᄒ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄀ ᅡ ᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᅵᄆ ᆫ ᄋ ᅧ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄀ ᅡ ᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄋ ᅩ ᅵᄆ ᅳᄅ ᅩ ᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨ ᅩ ᅵᄎ ᄋ ᅡᅥ ᆨ ᄌᄅ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄋ ᅥ ᆯᄋ ᅳ ᅱᄒ ᅡᄋ ᅧᄇ ᆫᄋ ᅡ ᆼᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅴᄑ ᅭᄇ ᆫᄋ ᅩ ᅴᄌ ᅦᄀ ᆸᅳ ᅩ ᆯ 우 ᆯ ᄇᄋ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄇ ᅩᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄆ ᅡ ᅵᄋ ᄎ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆫᄋ ᅵ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄀ ᅩᄃ ᅡᄉ ᅵᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄋ ᅳ ᆨᄇ ᅧ ᅩᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄋ ᅩ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷ ᅡ ᅮᄅ ᄉ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄂ ᆫᄇ ᅳ ᆼᄇ ᅡ ᆸᄋ ᅥ ᆯᄌ ᅳ ᅦᄋ ᆫᄒ ᅡ ᅡᄀ ᅩᄌ ᅡᄒ ᆫᄃ ᅡ ᅡ. 2ᄌ ᆯᄋ ᅥ ᅦᄉ ᅥᄂ ᆫᄇ ᅳ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᆯᄀ ᅳ ᅡᄌ ᅵᄂ ᆫᄋ ᅳ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄆ ᅩᄒ ᆼᄋ ᅧ ᆯᄉ ᅳ ᆯᄆ ᅥ ᆼᄒ ᅧ ᅡ ᅩ ᄌ ᄀ ᅦᄋ ᆫᅡ ᅡ ᆯ ᄒ ᄎ ᅮᄌ ᆼᄇ ᅥ ᆼᄇ ᅡ ᆸᄋ ᅥ ᆯ ᄉ ᅳ ᅩᄀ ᅢᄒ ᆫᄃ ᅡ ᅡ. 3ᄌ ᆯᄋ ᅥ ᅦᄉ ᅥᄂ ᆫ ᄆ ᅳ ᅩᄋ ᅴᄉ ᆯᄒ ᅵ ᆷ ᄀ ᅥ ᆯᄀ ᅧ ᅪᄋ ᅪ Ruppert ᄃ ᆼ (1997)ᄋ ᅳ ᅴ ᄋ ᆫᄀ ᅧ ᅮᄋ ᅦᄉ ᅥ ᄉ ᅡᄋ ᆼᄒ ᅭ ᆫ ᅡ LIDAR ᄌ ᅡᄅ ᅭᄋ ᅴᄇ ᆫᄉ ᅮ ᆨᅧ ᅥ ᆯ ᄀᄀ ᅪᄅ ᆯᄐ ᅳ ᅩᄃ ᅢᄅ ᅩᄌ ᅦᄋ ᆫᅡ ᅡ ᆫ ᄒᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄋ ᅩ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄃ ᅣ ᆯᄋ ᅳ ᅴᄎ ᅮᄌ ᆼᅥ ᅥ ᆼ ᄌᄃ ᅩᄅ ᆯᄇ ᅳ ᅵᄀ ᅭᄒ ᆫᄃ ᅡ ᅡ.. 2. 불연속 이차적률함수의 추정 휘 ᅬ ᄀᄆ ᅩᄒ ᆼ (1.1)ᄋ ᅧ ᅴᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮ v(x)ᄂ ᆫᄋ ᅳ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮ s(x) = E(Y 2 |X = x)ᄋ ᅪᄒ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮ m(x)ᄋ ᅦᅴ ᄋᄒ ᅢᄃ ᅡ ᆷᄀ ᅳ ᄋ ᅪᄀ ᇀᄋ ᅡ ᅵᄑ ᅭᄒ ᆫᄃ ᅧ ᆫᄃ ᅬ ᅡ. v(x) = s(x) − m2 (x). (2.1) Huh (2005)ᄀ ᅡᄋ ᆫᄀ ᅥ ᆸᄒ ᅳ ᅡᄋ ᆻᄃ ᅧ ᆺᄋ ᅳ ᅵᄒ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅦᄋ ᅴᄒ ᅢᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄀ ᅡᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᆯᄀ ᅳ ᅡᄌ ᆫᄃ ᅵ ᅡᄆ ᆫᄒ ᅧ ᅬᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄋ ᅴ ᆯᄋ ᅮ ᄇ ᆫᅩ ᅧ ᆨ ᄉᄌ ᆷᄋ ᅥ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄂ ᆫᄀ ᅳ ᆺᄋ ᅥ ᅵᄒ ᆸᄅ ᅡ ᅵᄌ ᆨᄋ ᅥ ᅵᄆ ᅧ, ᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅦᄋ ᅴᄒ ᅢᄉ ᆼᄀ ᅢ ᆫᄇ ᅵ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᆫᅧ ᅵ ᆼ ᄀᄋ ᅮᄋ ᅦᄂ ᆫᄒ ᅳ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄎ ᅮ ᆼᄋ ᅥ ᄌ ᅵᆯ ᅵᄋ ᄑ ᅭᄒ ᆫᄌ ᅡ ᆫᄎ ᅡ ᅡᄃ ᆯᄋ ᅳ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᆫᄇ ᅡ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄇ ᅩ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄇ ᅥ ᅩᄃ ᅡᄂ ᆫᄋ ᅳ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄋ ᅥ ᆯᄒ ᅳ ᆯᄋ ᅪ ᆼᄒ ᅭ ᅡᄂ ᆫᄀ ᅳ ᆺᄋ ᅥ ᅵᄋ ᆼ ᅭ ᅵᄒ ᄋ ᆯᅮ ᅡ ᄉᄋ ᆻᄃ ᅵ ᅡ..
(3) Estimation of second moment function with adujusted sample. 759. ᅵᅡ ᄋ ᄎᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄀ ᅡᄃ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄋ ᅡ ᅵᄒ ᆫᄌ ᅡ ᆷ τᄋ ᅥ ᅦᄉ ᅥᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄋ ᅩ ᅵᄅ ᅡᄀ ᅩᄀ ᅡᄌ ᆼᄒ ᅥ ᅡᄌ ᅡ. s(x) = t(x) + ∆ × I(τ ≤ x ≤ 1),. (2.2). ᄋᄀ ᅧ ᅵᅥ ᄉᄒ ᆷᄉ ᅡ ᅮ t(x)ᄂ ᆫ [0, 1]ᄋ ᅳ ᅦᄉ ᅥᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᅵᄀ ᅩ Iᄂ ᆫᄌ ᅳ ᅵᄑ ᅭᄒ ᆷᄉ ᅡ ᅮ (index function)ᄋ ᅵᄆ ᅧ, 0ᄋ ᅵᄋ ᅡᄂ ᆫᄉ ᅵ ᆯᄉ ᅵ ᅮ ∆ᄂ ᆫᅮ ᅳ ᆯ ᄇᄋ ᆫᄉ ᅧ ᆨ ᅩ ᆷ τᅦ ᅥ ᄌ ᄋᄉ ᅥᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄋ ᅵᄃ ᅡ. ᄒ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄀ ᅡᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᅵᄆ ᆫ τᄋ ᅧ ᅪ ∆ᄂ ᆫᄀ ᅳ ᆨᄀ ᅡ ᆨᄇ ᅡ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄋ ᅱᄎ ᅵᅪ ᄋᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵ ᅡᄃ ᄀ ᆷᄋ ᅬ ᆫᄉ ᅳ ᆨ (2.1)ᄋ ᅵ ᅦᄋ ᅴᄒ ᅢᄌ ᅡᄆ ᆼᄒ ᅧ ᅡᄃ ᅡ. ᄌ ᆨ, v+ (x)ᄋ ᅳ ᅪ s+ (x)ᄅ ᆯᄋ ᅳ ᆷᄋ ᅵ ᅴᄋ ᅴᄌ ᆷ xᄋ ᅥ ᅦᄉ ᅥ vᄋ ᅪ sᄋ ᅴᄋ ᅮᄀ ᆨᄒ ᅳ ᆫᄀ ᅡ ᆹᄋ ᅡ ᅵᄅ ᅡᄒ ᅡᄀ ᅩ v− (x)ᄋ ᅪ s− (x)ᄅ ᆯᄋ ᅳ ᆷᄋ ᅵ ᅴᄋ ᅴᄌ ᆷ xᄋ ᅥ ᅦᄉ ᅥ vᄋ ᅪ sᄋ ᅴᄌ ᅪᄀ ᆨᄒ ᅳ ᆫᄀ ᅡ ᆹᄋ ᅡ ᅵᄅ ᅡᄒ ᅡᄆ ᆫ, τ ᄋ ᅧ ᅦᄉ ᅥᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵ ∆ᄂ ᆫᄃ ᅳ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄃ ᅡ ᅡ. ∆ = v+ (τ ) − v− (τ ) = s+ (τ ) − s− (τ ).. (2.3). Kangᄀ ᅪ Huh (2006)ᄂ ᆫ ᄌ ᅳ ᆫᄎ ᅡ ᅡᄌ ᅦᄀ ᆸᄃ ᅩ ᆯᄀ ᅳ ᅪ ᄐ ᅩᄃ ᅢᄀ ᅡ [0, 1]ᄋ ᆫ ᄒ ᅵ ᆫᄍ ᅡ ᆨᄇ ᅩ ᆼᅣ ᅡ ᆼ ᄒᄏ ᅥᄂ ᆯᄒ ᅥ ᆷᄉ ᅡ ᅮ (one-sided kernel function)ᄅ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧ v+ (τ )ᄋ ᅪ v− (τ )ᄋ ᅴᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅴᄎ ᅡᄅ ᅩ τᄋ ᅪ ∆ᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄋ ᅵᄄ ᅢᄌ ᆫᄎ ᅡ ᅡᄋ ᅦᄉ ᅥᄋ ᅴᄎ ᅮᄌ ᆼᄃ ᅥ ᆫᄒ ᅬ ᅬᄀ ᅱ ᆷᄉ ᅡ ᄒ ᅮᅴ ᄋᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩ Nadaraya-Watson ᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄒ ᆫᅧ ᅡ ᆫ ᄑ, Huh (2005)ᄂ ᆫᄒ ᅳ ᅬᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄀ ᅡᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆯ ᅵ 2 ᅢᄌ ᄄ ᆫᄎ ᅡ ᅡᄃ ᅢᄉ ᆫᄇ ᅵ ᆫᄋ ᅡ ᆼᄇ ᅳ ᆫᄉ ᅧ ᅮ Yᄋ ᅴᄑ ᅭᄇ ᆫᄋ ᅩ ᅴᄌ ᅦᄀ ᆸ Yi ᄃ ᅩ ᆯᄀ ᅳ ᅪᅡ ᆫ ᄒᄍ ᆨᄇ ᅩ ᆼᅣ ᅡ ᆼ ᄒᄏ ᅥᄂ ᆯᄒ ᅥ ᆷᄉ ᅡ ᅮᄅ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧ s+ (τ )ᄋ ᅪ s− (τ )ᄋ ᅴᄎ ᅮᄌ ᆼ ᅥ ᆼᄋ ᅣ ᄅ ᅴᄎ ᅡᄅ ᅩ τᄋ ᅪ ∆ᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄋ ᆻᄃ ᅧ ᅡ. Huh (2005)ᄋ ᅦᄂ ᆫ Kangᄀ ᅳ ᅪ Huh (2006)ᄋ ᅪᄂ ᆫᄃ ᅳ ᆯᄅ ᅡ ᅵᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄅ ᆯᄋ ᅳ ᅵᄋ ᆼ ᅭ ᆫᄇ ᅡ ᄒ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄎ ᅮᄌ ᆼᄋ ᅥ ᅵᄆ ᅳᄅ ᅩᄒ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄋ ᅥ ᅵᄑ ᆯᄋ ᅵ ᅭᄒ ᅡᄌ ᅵᄋ ᆭᄃ ᅡ ᅡ. Kangᄀ ᅪ Huh (2006)ᄋ ᅴᄇ ᆫᄉ ᅮ ᆫᄒ ᅡ ᆷᄉ ᅡ ᅮᄋ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧ Huh (2016b)ᄂ ᆫᄌ ᅳ ᆫᄎ ᅡ ᅡᄌ ᅦᄀ ᆸ ᅩ ᆯᅳ ᅳ ᄃ ᆯ ᄋᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆫᄇ ᅵ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄋ ᅦᄉ ᅥᄇ ᅵᄅ ᆺᄃ ᅩ ᆫᄌ ᅬ ᆫᄎ ᅡ ᅡᄌ ᅦᄀ ᆸᄃ ᅩ ᆯᄋ ᅳ ᆫᅥ ᅵ ᆺ ᄀᄎ ᅥᄅ ᆷᄇ ᅥ ᅩᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᆫᄒ ᅡ ᅮᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ ᅣ ᅳᄅ ᄋ ᅩᅧ ᆨ ᄋᄇ ᅩᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄇ ᅩ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄌ ᅳ ᅦᄋ ᆫᄒ ᅡ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄇ ᆫᄋ ᅩ ᆫᄀ ᅧ ᅮᄋ ᅦᄉ ᅥᄂ ᆫ Huh (2016b)ᄋ ᅳ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄇ ᅩ ᆫᄉ ᅮ ᆫ ᅡ ᆷᄉ ᅡ ᄒ ᅮᅴ ᄋᄎ ᅮᄌ ᆼᄀ ᅥ ᅪᄀ ᇀᄋ ᅡ ᅵ Huh (2005)ᄋ ᅴᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄇ ᆫᄋ ᅡ ᆼᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅴᄑ ᅭᄇ ᆫᄋ ᅩ ᅴ 2 ᆯᅳ ᅳ ᆯ ᄋᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆫᄋ ᅵ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅦᄉ ᅥᄎ ᅮᄎ ᆯᄃ ᅮ ᆫᄇ ᅬ ᆫᄋ ᅡ ᆼᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅴᄑ ᅭᄇ ᆫᄋ ᅩ ᅴᄌ ᅦᄀ ᆸᄃ ᅩ ᆯᄋ ᅳ ᆫᅥ ᅵ ᆺ ᄀᄎ ᅥᄅ ᆷᄇ ᅥ ᅩᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯ ᅲ ᅦᄀ ᄌ ᆸ Yi ᄃ ᅩ ᆷᄉ ᅡ ᄒ ᅮᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᆫᄒ ᅡ ᅮᄉ ᅡᄋ ᆼᄒ ᅭ ᆫᄌ ᅡ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄋ ᆨᄇ ᅧ ᅩᄌ ᆼᄒ ᅥ ᅡᄂ ᆫᅮ ᅳ ᆯ ᄇᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄌ ᅳ ᅦᄋ ᆫᄒ ᅡ ᆫᄃ ᅡ ᅡ. ᆫᄋ ᅡ ᄇ ᆼᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅴ ᄑ ᅭᄇ ᆫᄋ ᅩ ᅴ ᄌ ᅦᄀ ᆸ Yi2 ᄃ ᅩ ᆯᅳ ᅳ ᆯ ᄋ ᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆫ ᄋ ᅵ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄅ ᅩᄇ ᅮᄐ ᅥ ᄎ ᅮᄎ ᆯᄃ ᅮ ᆫ ᄀ ᅬ ᆺᄎ ᅥ ᅥᄅ ᆷ ᄇ ᅥ ᅩᄌ ᆼᄒ ᅥ ᅡᄀ ᅵ ᄋ ᅱᄒ ᅡᄋ ᅧ Huh (2005)ᄋ ᅴᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄋ ᅱᄎ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄀ ᅣ ᅪᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅡᄀ ᅩᄌ ᅡᄒ ᆫᄃ ᅡ ᅡ. Huh (2005)ᄂ ᆫ ᅳ ᆷᄋ ᅵ ᄋ ᅴᄋ ᅴᄌ ᆷ xᄋ ᅥ ᅦᄉ ᅥᄋ ᅴ s+ (x)ᄋ ᅪ s− (x)ᄋ ᅴᄏ ᅥᄂ ᆯᄎ ᅥ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄃ ᅳ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄋ ᅡ ᅵᄌ ᆼᄋ ᅥ ᅴᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. n 1 X Xi − x 2 K Yi nh i=1 h sˆ+ (x) = , n 1 X Xi − x K nh i=1 h. n 1 X x − Xi 2 K Yi nh i=1 h sˆ− (x) = , n 1 X x − Xi K nh i=1 h. (2.4). ᄋᄀ ᅧ ᅵᅥ ᄉ hᄂ ᆫᄏ ᅳ ᅥᄂ ᆯᄎ ᅥ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅴᄑ ᆼᄒ ᅧ ᆯᄅ ᅪ ᆼᄋ ᅣ ᆫᄄ ᅵ ᅵᄑ ᆨᄋ ᅩ ᅵᄀ ᅩ Kᄂ ᆫᄒ ᅳ ᆫᄍ ᅡ ᆨᄇ ᅩ ᆼᅣ ᅡ ᆼ ᄒᄏ ᅥᄂ ᆯᄒ ᅥ ᆷᄉ ᅡ ᅮᄅ ᅩ [0, 1]ᄋ ᅴᄐ ᅩᄃ ᅢᄅ ᆯᄀ ᅳ ᅡᄌ ᅵᄀ ᅩᄋ ᆻᄃ ᅵ ᅡ. ᄋ ᅵ ᅥᄒ ᄅ ᆫ [0, 1]ᄋ ᅡ ᅴᄐ ᅩᄃ ᅢᄂ ᆫ sˆ+ (x)ᄋ ᅳ ᅦᄉ ᅥᄂ ᆫ xᄋ ᅳ ᅴᄋ ᅩᄅ ᆫᄍ ᅳ ᆨᄋ ᅩ ᅴᄑ ᅭᄇ ᆫᄋ ᅩ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧᄎ ᅮᄌ ᆼᄒ ᅥ ᅡᄀ ᅦᄒ ᅡᄀ ᅩ, ᄇ ᆫᄆ ᅡ ᆫᄋ ᅧ ᅦ sˆ− (x)ᄂ ᆫ xᄋ ᅳ ᅴ ᆫᄍ ᅬ ᄋ ᆨᅭ ᅩ ᄑᄇ ᆫᅳ ᅩ ᆯ ᄋᄋ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧᄎ ᅮᄌ ᆼᄒ ᅥ ᅡᄀ ᅦᄒ ᆫᄃ ᅡ ᅡ. ᄒ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᆫᄀ ᅧ ᅮᄃ ᆯᄋ ᅳ ᆫ M¨ ᅵ uller (1992), Loader (1996), Huhᄋ ᅪ Park (2004) ᄃ ᆼᄋ ᅳ ᅦᄉ ᅥᄒ ᆫᄍ ᅡ ᆨᄇ ᅩ ᆼᅣ ᅡ ᆼ ᄒᄏ ᅥᄂ ᆯᄒ ᅥ ᆷᄉ ᅡ ᅮᄅ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᅮᅮ ᄃ ᄎᄌ ᆼᄅ ᅥ ᆼ (2.4)ᄋ ᅣ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧᄋ ᆷᄋ ᅵ ᅴᄋ ᅴᄌ ᆷ xᄋ ᅥ ᅦᄉ ᅥᄋ ᅴᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄅ ᆯ ᅳ ˆ ∆(x) = sˆ+ (x) − sˆ− (x). (2.5). ᅩᄎ ᄅ ᅮᄌ ᆼᄒ ᅥ ᅡᄀ ᅩᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄋ ᅱᄎ ᅵ τᄋ ᅴᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄃ ᅳ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄋ ᅡ ᅵᄌ ᅦᄋ ᆫᄒ ᅡ ᅡᄋ ᆻᄃ ᅧ ᅡ. ˆ ˆ τˆ = inf{z ∈ Q : |∆(z)| = sup |∆(x)|}.. (2.6). x∈Q. ᅱᄎ ᄋ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ τˆᄋ ᅣ ᅦᄉ ᅥᄋ ᅴᄎ ᅮᄌ ᆼᄃ ᅥ ᆫᄌ ᅬ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵ ˆ τ ) = sˆ+ (ˆ ∆(ˆ τ ) − sˆ− (ˆ τ). (2.7).
(4) 760. Jib Huh. ᆯᄉ ᅳ ᄋ ᆨ (2.3)ᄋ ᅵ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵ ∆ᄋ ᅴᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄌ ᅦᄋ ᆫᄒ ᅡ ᅡᄋ ᆻᄃ ᅧ ᅡ. ˆ τ )ᄋ Huh (2005)ᄋ ᅴᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ ∆(ˆ ᅣ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧᄇ ᆫᄋ ᅡ ᆼᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅴᄑ ᅭᄇ ᆫᄋ ᅩ ᅴᄌ ᅦᄀ ᆸ Yi2 ᄃ ᅩ ᆯᄋ ᅳ ᆯᄃ ᅳ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄋ ᅡ ᅵᄇ ᅩᄌ ᆼ ᅥ ᅡᄌ ᄒ ᅡ. ˆ τ ) × I[ˆ Y˜i2 = Yi2 − ∆(ˆ τ ≤ Xi ≤ 1], i = 1, 2, · · · , n. (2.8) ᅩᄌ ᄇ ᆼᄃ ᅥ ᆫ Y˜i2 ᅳ ᅬ ᄋᄋ ᆯ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧᄉ ᆨ (2.2)ᄋ ᅵ ᅴᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆫᄒ ᅵ ᆷᄉ ᅡ ᅮ t(x)ᄅ ᆯ Nadaraya-Watson ᄎ ᅳ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄃ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄋ ᅡ ᅵ n 1 X Xi − x ˜ 2 L Yi nb i=1 b tˆ(x) = n 1 X Xi − x L nb i=1 b. (2.9). ᄅ ᄎ ᅩ ᅮᄌ ᆼᄒ ᅥ ᆫᄃ ᅡ ᅡ. ᄋ ᅧᄀ ᅵᄉ ᅥ ᄏ ᅥᄂ ᆯᄒ ᅥ ᆷᄉ ᅡ ᅮ Lᄋ ᆫ ᄐ ᅳ ᅩᄃ ᅢᄀ ᅡ [−1, 1]ᄋ ᅵᄆ ᅧ bᄂ ᆫ hᄋ ᅳ ᅪ ᄃ ᅡᄅ ᆫ ᄄ ᅳ ᅵᄑ ᆨᄋ ᅩ ᅵᄃ ᅡ. ᄉ ᆨ (2.2)ᄋ ᅵ ᅴ s(x)ᄋ ᅪ t(x)ᄋ ᅴᄀ ᆫᄀ ᅪ ᅨᄋ ᅦᄋ ᅴᄒ ᅡᄋ ᅧᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮ s(x)ᄋ ᅴᄏ ᅥᄂ ᆯᄎ ᅥ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄃ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄋ ᅡ ᅵᄌ ᅦᄋ ᆫᅡ ᅡ ᆫ ᄒᄃ ᅡ. ˆ τ ) × I[ˆ sˆ(x) = tˆ(x) + ∆(ˆ τ ≤ x ≤ 1].. (2.10). ᆯᄋ ᅮ ᄇ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᆯᄀ ᅳ ᅡᄌ ᅵᄀ ᅩᄋ ᆻᄂ ᅵ ᆫᄒ ᅳ ᅬᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄂ ᅡᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄃ ᆼᄋ ᅳ ᅴᄏ ᅥᄂ ᆯᄎ ᅥ ᅮᄌ ᆼᄅ ᅥ ᆼᄃ ᅣ ᆯᄋ ᅳ ᆫᅮ ᅳ ᆯ ᄇᄋ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄒ ᅥ ᆨᄋ ᅩ ᆫᄀ ᅳ ᅳᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄀ ᅳ ᅵᄌ ᆫ ᅮ ᄋᄅ ᅳ ᅩᄌ ᅪᄎ ᆨᄀ ᅳ ᅪᄋ ᅮᄎ ᆨᄋ ᅳ ᅴᄑ ᅭᄇ ᆫᄋ ᅩ ᅳᄅ ᅩᄂ ᅡᄂ ᅮᄋ ᅥᄉ ᅥᄃ ᆨᄅ ᅩ ᆸᄌ ᅵ ᆨᄋ ᅥ ᅳᄅ ᅩᄎ ᅮᄌ ᆼᄒ ᅥ ᅡᄀ ᅩᄌ ᅡᄒ ᅡᄂ ᆫᄒ ᅳ ᆷᄉ ᅡ ᅮᄋ ᅴᄋ ᆫᄍ ᅬ ᆨᄎ ᅩ ᅮᄌ ᆼᄅ ᅥ ᆼᄀ ᅣ ᅪᄋ ᅩᄅ ᆫᄍ ᅳ ᆨᄎ ᅩ ᅮᄌ ᆼ ᅥ ᆼᄋ ᅣ ᄅ ᆯᄀ ᅳ ᅩᄅ ᅧᄒ ᅡᄂ ᆫᄀ ᅳ ᆺᄋ ᅥ ᅵᄋ ᆯᄇ ᅵ ᆫᄌ ᅡ ᆨᄋ ᅥ ᆫᄇ ᅵ ᆼᄇ ᅡ ᆸᄋ ᅥ ᅵᄃ ᅡ. ᄃ ᅢᄑ ᅭᄌ ᆨᄋ ᅥ ᆫᅧ ᅵ ᆫ ᄋᄀ ᅮᄅ ᅩᄒ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄋ ᅦᄉ ᅥᄂ ᆫ M¨ ᅳ uller (1992), Huhᄋ ᅪ Park (2004) ᄃ ᆼᄋ ᅳ ᅵᄋ ᆻᄋ ᅵ ᅳᄆ ᅧᄇ ᆫᄉ ᅮ ᆫᄒ ᅡ ᆷᄉ ᅡ ᅮᄋ ᅦᄉ ᅥᄂ ᆫ Kangᄀ ᅳ ᅪ Huh (2006), Huh (2016b) ᄃ ᆼᄋ ᅳ ᅵᄋ ᆻᄃ ᅵ ᅡ. ᆯᄋ ᅮ ᄇ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄋ ᅱᄎ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄀ ᅳ ᅵᄌ ᆫᄋ ᅮ ᅳᄅ ᅩᄑ ᅭᄇ ᆫᅳ ᅩ ᆯ ᄋᄌ ᅪᄋ ᅮᄅ ᅩᄇ ᆫᄅ ᅮ ᅵᄒ ᅡᄋ ᅧᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄅ ᆯ Nadaraya-Watson ᄎ ᅳ ᅮᄌ ᆼ ᅥ ᆼᄋ ᅣ ᄅ ᅳᄅ ᅩ n 1 X ˜ Xi − x 2 L ; τˆ Yi nb i=1 b s˜(x) = (2.11) n 1 X ˜ Xi − x L ; τˆ nb i=1 b ˜ ᅪᄀ ᄀ ᇀᅵ ᅡ ᄋᄌ ᅦᄋ ᆫᅡ ᅡ ᆯ ᄒᄉ ᅮᄋ ᆻᄃ ᅵ ᅡ. ᄋ ᅵᄄ ᅢᄉ ᅡᄋ ᆼᄒ ᅭ ᆫᄏ ᅡ ᅥᄂ ᆯᄒ ᅥ ᆷᄉ ᅡ ᅮ L((u − x)/b; z)ᄂ ᆫᄃ ᅳ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄃ ᅡ ᅡ. u − x × I[x − b ≤ u < z], z − b ≤ x < z, L b u − x u − x ˜ ;z = L L × I[z ≤ u < x + b], z ≤ x < z + b, b b u − x L , ᅳᅬ ᄀ ᄋ. b ˜ ᄎᄌ ᅮ ᆼᄅ ᅥ ᆼ (2.11)ᄋ ᅣ ᅴᄏ ᅥᄂ ᆯᄒ ᅥ ᆷᄉ ᅡ ᅮ L((X ˆ)ᄂ ᆫ τˆᄋ ᅳ ᆯᄀ ᅳ ᅵᄌ ᆫᄋ ᅮ ᅳᄅ ᅩᄑ ᅭᄇ ᆫᅳ ᅩ ᆯ ᄋᄋ ᆫᄍ ᅬ ᆨᄀ ᅩ ᅪᄋ ᅩᄅ ᆫᄍ ᅳ ᆨᄋ ᅩ ᅳᄅ ᅩᄇ ᆫᄅ ᅮ ᅵᄒ ᅡᄂ ᆫᄋ ᅳ ᆨᄒ ᅧ ᆯ ᅪ i − x)/b; τ ᆯᄒ ᅳ ᄋ ᆫᄃ ᅡ ᅡ. Nadaraya-Watson ᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅴᄒ ᆼᄐ ᅧ ᅢᄋ ᆫᄎ ᅵ ᅮᄌ ᆼᄅ ᅥ ᆼ (2.11)ᄂ ᅣ ᆫᄀ ᅳ ᆨᄉ ᅮ ᅩᄉ ᆼᄉ ᅡ ᅮᄒ ᆼᄎ ᅡ ᅮᄌ ᆼᄅ ᅥ ᆼ (local constant estiᅣ mator)ᄋ ᅵᄆ ᅳᄅ ᅩᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄋ ᅱᄎ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅵᄀ ᆼᄀ ᅧ ᅨᄌ ᆷᄋ ᅥ ᅵᅬ ᄃᄋ ᅥᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅵᄀ ᆼᄀ ᅧ ᅨᄌ ᆷᄆ ᅥ ᆫᄌ ᅮ ᅦ (boundary problem)ᄅ ᆯ ᅳ ᅡᄌ ᄀ ᅵᅦ ᄀᄃ ᆫᄃ ᅬ ᅡ. ᅵᄅ ᄋ ᇂᄃ ᅥ ᆺᄇ ᅳ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄒ ᅥ ᆨᄋ ᅩ ᆫᄀ ᅳ ᅳᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄀ ᅳ ᅵᄌ ᆫᄋ ᅮ ᅳᄅ ᅩᄌ ᅪᄋ ᅮᄋ ᅴᄑ ᅭᄇ ᆫᅳ ᅩ ᆯ 우 ᆫ ᄇᄅ ᅵᄒ ᅡᄋ ᅧᄇ ᆫᄅ ᅮ ᅵᄃ ᆫᄑ ᅬ ᅭᄇ ᆫᄃ ᅩ ᆯᄋ ᅳ ᅵᄉ ᅥᄅ ᅩᄋ ᆼᄒ ᅧ ᆼᄋ ᅣ ᆯ ᅳ ᅮᄌ ᄌ ᅵᅡ ᆭ ᄋᄀ ᅩᄎ ᅮᄌ ᆼᄒ ᅥ ᅡᄀ ᅩᄌ ᅡᄒ ᅡᄂ ᆫᄒ ᅳ ᆷᄉ ᅡ ᅮᄅ ᆯᄏ ᅳ ᅥᄂ ᆯᄎ ᅥ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄎ ᅮᄌ ᆼᄒ ᅥ ᆯᅧ ᅡ ᆼ ᄀᄋ ᅮ, ᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄌ ᅥ ᅮᄇ ᆫᄋ ᅧ ᅦᄉ ᅥᄀ ᆼᄀ ᅧ ᅨᄌ ᆷᄆ ᅥ ᆫᄌ ᅮ ᅦᄌ ᆷᄋ ᅥ ᆯᄀ ᅳ ᅡ ᆯᄉ ᅵ ᄌ ᅮᄋ ᆻᄀ ᅵ ᅵᄋ ᅦᄋ ᅵᄅ ᅥᄒ ᆫᄃ ᅡ ᆫᄌ ᅡ ᆷᄋ ᅥ ᆯᄀ ᅳ ᆨᄇ ᅳ ᆨᄒ ᅩ ᅡᄀ ᅵᄋ ᅱᄒ ᅡᄋ ᅧ Kang ᄃ ᆼ (2000)ᄋ ᅳ ᆫᅮ ᅳ ᆯ ᄇᄋ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄒ ᅥ ᅬᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄋ ᅴᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ ᅣ ᆯᄇ ᅳ ᄋ ᆫᅳ ᅡ ᆼ ᄋᄇ ᆫᄉ ᅧ ᅮᄋ ᅴᄑ ᅭᄇ ᆫᄋ ᅩ ᅦᄇ ᅩᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᆫᄒ ᅵ ᅬᄀ ᅱᅡ ᆷ ᄒᄉ ᅮᄅ ᅩᄇ ᅮᄐ ᅥᄎ ᅮᄎ ᆯᄃ ᅮ ᆫᄑ ᅬ ᅭᄇ ᆫᄋ ᅩ ᅳᄅ ᅩᄀ ᆫᄌ ᅡ ᅮᄒ ᅡᄋ ᅧᄑ ᅭᄇ ᆫᅳ ᅩ ᆯ ᄋᄇ ᆫᄅ ᅮ ᅵᄒ ᅡᄌ ᅵᄋ ᆭ ᅡ ᅩᄒ ᄀ ᅬᅱ ᄀᄒ ᆷᄉ ᅡ ᅮᄅ ᆯᄎ ᅳ ᅮᄌ ᆼᄒ ᅥ ᅡᄀ ᅩᄌ ᅡᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄋ ᅵᄅ ᅥᄒ ᆫᄇ ᅡ ᆼᄇ ᅡ ᆸᄋ ᅥ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧ Huh (2016b)ᄋ ᅪ Hongᄀ ᅪ Hub (2017)ᄂ ᆫᄌ ᅳ ᆫ ᅡ ᅡᄌ ᄎ ᅦᄀ ᆸᄀ ᅩ ᅪᄅ ᅩᄀ ᅳᄌ ᆫᄎ ᅡ ᅡᄌ ᅦᄀ ᆸᅳ ᅩ ᆯ ᄋᄇ ᅩᄌ ᆼᄒ ᅥ ᅡᄋ ᅧᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᅪ ᄋᄅ ᅩᄀ ᅳᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄏ ᅥᄂ ᆯᄎ ᅥ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄌ ᅳ ᅦᄋ ᆫᄒ ᅡ ᅡᄋ ᆻᄃ ᅧ ᅡ..
(5) Estimation of second moment function with adujusted sample. 761. 3. 모의실험과 LIDAR자료 분석 3.1. 모의실험 ᆫᄌ ᅩ ᄇ ᆯᄋ ᅥ ᅦᄉ ᅥᄂ ᆫ 2ᄌ ᅳ ᆯᄋ ᅥ ᅦᄉ ᅥᄉ ᅩᄀ ᅢᄒ ᆫᄋ ᅡ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄃ ᅮᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ (2.10)ᄀ ᅣ ᅪ (2.11)ᄅ ᆯᄆ ᅳ ᅩᄋ ᅴᄉ ᆯᄒ ᅵ ᆷᄀ ᅥ ᅪᄉ ᆯᄌ ᅵ ᅦᄌ ᅡᄅ ᅭᄇ ᆫᄉ ᅮ ᆨ ᅥ ᄋᄐ ᆯ ᅳ ᆼᅡ ᅩ ᄒᄋ ᅧᄇ ᅵᄀ ᅭᄒ ᅢᄇ ᅩᄀ ᅵᄅ ᅩᄒ ᆫᄃ ᅡ ᅡ. ᄒ ᅬᄀ ᅱᄆ ᅩᄒ ᆼ (1.1)ᄋ ᅧ ᅦᄉ ᅥᄐ ᅩᄃ ᅢ [0, 1]ᄅ ᆯᄀ ᅳ ᅡᄌ ᅵᄂ ᆫᄉ ᅳ ᆯᄆ ᅥ ᆼᅧ ᅧ ᆫ ᄇᄉ ᅮ Xᄋ ᅴᄒ ᆨᄅ ᅪ ᆯᄆ ᅲ ᆯᄃ ᅵ ᅩᄒ ᆷᄉ ᅡ ᅮᄅ ᅩ ᆫᄃ ᅲ ᄀ ᆼᄇ ᅳ ᆫᄑ ᅮ ᅩᄅ ᆯᄉ ᅳ ᆫᅢ ᅥ ᆨ ᄐᄒ ᅡᄋ ᆻᄀ ᅧ ᅩᄒ ᅬᄀ ᅱᄒ ᆷᄉ ᅡ ᅮᄂ ᆫ ᅳ m(x) = x, 0 ≤ x ≤ 1 (3.1) ᆯᄀ ᅳ ᄋ ᅩᄅ ᅧᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᆫᄉ ᅮ ᄇ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄂ ᆫᄃ ᅳ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄋ ᅡ ᅵᄃ ᅮᄀ ᅡᄌ ᅵᄅ ᆯᄀ ᅳ ᅩᄅ ᅧᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. 1 (1 − x)2 , v1 (x) = 9 9x2 ,. 0 ≤ x < 0.65,. (3.2). 0.65 ≤ x ≤ 1.. 9(1 − x)2 , 0 ≤ x < 0.35, v2 (x) = 1 x2 , 0.35 ≤ x ≤ 1. 9 ᅮᄇ ᄃ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄃ ᆯᄀ ᅳ ᅪᄒ ᅬᄀ ᅱᅡ ᆷ 후 ᄉ (3.1)ᄋ ᅦᄋ ᅴᄒ ᅡᄆ ᆫᄋ ᅧ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄃ ᆯᄋ ᅳ ᆫᄃ ᅳ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄃ ᅡ ᅡ. 1 (1 − x)2 + x2 , 0 ≤ x < 0.65, s1 (x) = 9 10x2 , 0.65 ≤ x ≤ 1.. (3.3). (3.4). 9(1 − x)2 + x2 , 0 ≤ x < 0.35, s2 (x) = (3.5) 10 2 x , 0.35 ≤ x ≤ 1. 9 v1 ᄀ ᅪ s1 ᄋ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄋ ᅱᄎ ᅵᄂ ᆫ τ1 = 0.65ᄋ ᅳ ᅵᄀ ᅩᄋ ᅵᄄ ᅢᄋ ᅴᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄂ ᆫ ∆1 = 3.788889ᄋ ᅳ ᅵᄃ ᅡ. v2 ᄋ ᅪ s2 ᄋ ᅴᄇ ᆯᄋ ᅮ ᆫ ᅧ ᆨᄌ ᅩ ᄉ ᆷᅴ ᅥ ᄋᄋ ᅱᄎ ᅵᅪ ᄋᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄂ ᆫᄀ ᅳ ᆨᄀ ᅡ ᆨ τ2 = 0.35ᄋ ᅡ ᅪ ∆2 = −3.788889ᄋ ᅵᄃ ᅡ. ᅬᅱ ᄒ ᄀᄆ ᅩᄒ ᆼ (1.1)ᄋ ᅧ ᅴᄋ ᅩᄎ ᅡᄋ ᅴᄇ ᆫᄑ ᅮ ᅩᄂ ᆫᄑ ᅳ ᅭᄌ ᆫᄌ ᅮ ᆼᄀ ᅥ ᅲᄇ ᆫᄑ ᅮ ᅩᄅ ᅩᄉ ᆯᄌ ᅥ ᆼᄒ ᅥ ᅡᄋ ᆻᄀ ᅧ ᅩᄑ ᅭᄇ ᆫᄋ ᅩ ᅴᄉ ᅮᄂ ᆫ n = 500ᄋ ᅳ ᅳᄅ ᅩᄒ ᅡᄀ ᅩᄃ ᅮᄎ ᅮᄌ ᆼ ᅥ ᆼᄋ ᅣ ᄅ ᅴᅥ ᆨ ᄌᄇ ᆫᄌ ᅮ ᅦᄀ ᆸᄋ ᅩ ᅩᄎ ᅡ (integrated squared error)ᄋ ᆯᄇ ᅳ ᅵᄀ ᅭᄒ ᅡᄀ ᅵᄋ ᅱᄒ ᅡᄋ ᅧ 1000ᄇ ᆫᄋ ᅥ ᅴᅡ ᆫ ᄇᄇ ᆨᄉ ᅩ ᅵᄒ ᆼᄋ ᅢ ᆯᄉ ᅳ ᆯᄉ ᅵ ᅵᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᆯᄋ ᅮ ᄇ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄋ ᅱᄎ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ (2.6)ᄀ ᅣ ᅪᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ (2.7)ᄋ ᅣ ᆯᄋ ᅳ ᅱᅡ ᆫ ᄒᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ (2.4)ᄋ ᅣ ᅴᅡ ᆫ ᄒᄍ ᆨᄇ ᅩ ᆼᅣ ᅡ ᆼ ᄒᄏ ᅥᄂ ᆯᄒ ᅥ ᆷᄉ ᅡ ᅮ Kᄂ ᆫ ᅳ Epanechnikov ᄏ ᅥᄂ ᆯᄋ ᅥ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᆫᄐ ᅡ ᅩᄃ ᅢᄀ ᅡ [0, 1]ᄋ ᆫᄃ ᅵ ᅡᄋ ᆷᄋ ᅳ ᅴᅡ ᆷ ᄒᄉ ᅮ K(x) =. 3 (1 − x2 ) × I[0 ≤ x ≤ 1] 2. (3.6). ᄋᄉ ᆯ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅡᄋ ᆻᄀ ᅧ ᅩ, ᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᅪ 와 ᄀᄅ ᆫ ᆫᄃ ᅧ ᆫᄎ ᅬ ᅮᄌ ᆼᄅ ᅥ ᆼᄃ ᅣ ᆯ (2.9)ᄋ ᅳ ᅪ (2.10)ᄅ ᆯᄋ ᅳ ᅱᄒ ᅡᄋ ᅧ Epanechnikov ᄏ ᅥᄂ ᆯᄋ ᅥ ᆫᄃ ᅵ ᅡᄋ ᆷ ᅳ ᆷᄉ ᅡ ᄒ ᅮᄅ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᆻᄃ ᅧ ᅡ. 3 L(x) = (1 − x2 ) × I[−1 ≤ x ≤ 1]. (3.7) 4 ᅮᄌ ᄎ ᆼᄅ ᅥ ᆼ (2.4)ᄋ ᅣ ᅦ ᄊ ᅳᄋ ᆫ ᄄ ᅵ ᅵᄑ ᆨᄋ ᅩ ᅳᄅ ᅩ h = 0.05, 0.10, 0.15ᄅ ᆯ ᄀ ᅳ ᅩᄅ ᅧᄒ ᅡᄋ ᅧ ᄋ ᅧᄅ ᅥ ᄄ ᅵᄑ ᆨᄋ ᅩ ᅦ ᄋ ᅴᄒ ᅢ ᄀ ᅮᄒ ᅢᄌ ᆫ ᄇ ᅵ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷ ᅥ ᅴ ᄋ ᄋ ᅱᄎ ᅵᅪ ᄋ ᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄅ ᅩ ᄉ ᆨ (2.8)ᄋ ᅵ ᅴ ᄇ ᆫᄋ ᅡ ᆼᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅴ ᄑ ᅭᄇ ᆫᄋ ᅩ ᅴ ᄌ ᅦᄀ ᆸᄃ ᅩ ᆯᅳ ᅳ ᆯ ᄋ ᄇ ᅩᄌ ᆼᄒ ᅥ ᅡᄋ ᅧ ᄌ ᅦᄋ ᆫᅡ ᅡ ᆫ ᄒ ᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮ ᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ ᅣ (2.10)ᄋ ᅦᄆ ᅵᄎ ᅵᄂ ᆫᄋ ᅳ ᆼᄒ ᅧ ᆼᄋ ᅣ ᅴᄌ ᆼᄃ ᅥ ᅩᄅ ᆯᄉ ᅳ ᆯᄑ ᅡ ᅧᄇ ᅩᄋ ᆻᄃ ᅡ ᅡ. 2ᄌ ᆯᄋ ᅥ ᅦᄉ ᅥᄌ ᅦᄋ ᆫᅡ ᅡ ᆫ ᄒᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄋ ᅩ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄃ ᅮᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ (2.10)ᄀ ᅣ ᅪ (2.11)ᄅ ᆯᄇ ᅳ ᅵᄀ ᅭᄒ ᅢᄇ ᅩᄀ ᅵᄋ ᅱᄒ ᅡᄋ ᅧᄃ ᅮᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅴ ᆨᄇ ᅥ ᄌ ᆫᅦ ᅮ ᄌᄀ ᆸᄋ ᅩ ᅩᄎ ᅡᄅ ᆯᄀ ᅳ ᅨᄉ ᆫᄒ ᅡ ᅡᄋ ᆻᄃ ᅧ ᅡ. Figure 3.1ᄀ ᅪ 3.2ᄂ ᆫᄀ ᅳ ᆨᄀ ᅡ ᆨᄋ ᅡ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄆ ᅩᄒ ᆼ (3.4)ᄀ ᅧ ᅪ (3.5)ᄋ ᅦᄃ ᅢᄒ ᆫᄆ ᅡ ᅩᄋ ᅴᄉ ᆯ ᅵ ᆷᄋ ᅥ ᄒ ᆯᄐ ᅳ ᆼᄒ ᅩ ᆫᄌ ᅡ ᆨᄇ ᅥ ᆫᄌ ᅮ ᅦᄀ ᆸᄋ ᅩ ᅩᄎ ᅡᄅ ᆯᄇ ᅳ ᅩᄋ ᅧᄌ ᅮᄀ ᅩᄋ ᆻᄃ ᅵ ᅡ. ᄃ ᅡᄋ ᆼᅡ ᅣ ᆫ ᄒᄄ ᅵᄑ ᆨ bᄅ ᅩ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅡᄋ ᅧᄀ ᅨᄉ ᆫᄃ ᅡ ᆫᄌ ᅬ ᆨᄇ ᅥ ᆫᄌ ᅮ ᅦᄀ ᆸᄋ ᅩ ᅩᄎ ᅡᄃ ᆯᄋ ᅳ ᅴᄇ ᆫᄒ ᅧ ᅪᄅ ᆯ ᅳ ᅩᄋ ᄇ ᅧᅮ ᄌᄀ ᅩᄋ ᆻᄋ ᅵ ᅳᄆ ᅧ, ᄉ ᆯᅥ ᅵ ᆫ ᄉᄋ ᆫᄇ ᅳ ᆫᄋ ᅡ ᆼᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅴᄑ ᅭᄇ ᆫᄋ ᅩ ᅴᄌ ᅦᄀ ᆸᄋ ᅩ ᆯᄌ ᅳ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄇ ᅩᄌ ᆼᄒ ᅥ ᆫᄒ ᅡ ᅮᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄅ ᆯᄀ ᅳ ᅨ.
(6) 762. Jib Huh. 0.46 0.40. 0.42. 0.44. ISE. 0.48. 0.50. 0.52. ᄉᄒ ᆫ ᅡ ᅡᄀ ᅩᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩᄋ ᆨᄇ ᅧ ᅩᄌ ᆼᄒ ᅥ ᆫᄋ ᅡ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ (2.10)ᄋ ᅣ ᅴ sˆ(x)ᄋ ᅴᄌ ᆨᄇ ᅥ ᆫᄌ ᅮ ᅦᄀ ᆸᄋ ᅩ ᅩᄎ ᅡᄋ ᅵᄆ ᅧᄌ ᆷᅥ ᅥ ᆫ ᄉᄋ ᆫ ᅳ ᆯᄋ ᅮ ᄇ ᆫᅩ ᅧ ᆨ ᄉᄌ ᆷᄋ ᅥ ᅴ ᄋ ᅱᄎ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯ ᄀ ᅳ ᅵᄌ ᆫᄋ ᅮ ᅳᄅ ᅩ ᄑ ᅭᄇ ᆫᅳ ᅩ ᆯ ᄋ ᄇ ᆫᄅ ᅮ ᅵᄒ ᆫ ᄒ ᅡ ᅮ ᄀ ᅨᄉ ᆫᄃ ᅡ ᆫ ᄋ ᅬ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴ ᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ (2.11)ᄋ ᅣ ᅴ s˜(x)ᄋ ᅴ ᆨᄇ ᅥ ᄌ ᆫᅦ ᅮ ᄌᄀ ᆸᄋ ᅩ ᅩᄎ ᅡᄋ ᅵᄃ ᅡ. ᅮᄌ ᄎ ᆼᄅ ᅥ ᆼ (2.10)ᄋ ᅣ ᅴ sˆ(x)ᄋ ᅴᄌ ᆨᄇ ᅥ ᆫᄌ ᅮ ᅦᄀ ᆸᄋ ᅩ ᅩᄎ ᅡᄂ ᆫᄌ ᅳ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅴᄄ ᅵᄑ ᆨ hᄋ ᅩ ᅴᄇ ᆫᄒ ᅧ ᅪᄋ ᅦᄏ ᆫᄋ ᅳ ᆼᄒ ᅧ ᆼᄋ ᅣ ᆯᄇ ᅳ ᆮᄌ ᅡ ᅵᄋ ᆭᄀ ᅡ ᅩᄀ ᅳ ᆯᄀ ᅧ ᄀ ᅪᅳ ᆯ ᄃᄋ ᅵ ᄆ ᅢᄋ ᅮ ᄋ ᅲᄉ ᅡᄒ ᅡᄋ ᅧ h = 0.1ᄋ ᆫ ᄀ ᅵ ᆼᄋ ᅧ ᅮᄋ ᅴ ᄌ ᆨᄇ ᅥ ᆫᄌ ᅮ ᅦᄀ ᆸᄋ ᅩ ᅩᄎ ᅡᄆ ᆫ Figure 3.1ᄀ ᅡ ᅪ 3.2ᄋ ᅦ ᄌ ᅦᄉ ᅵᄒ ᅡᄋ ᆻᄀ ᅧ ᅩ, ᄀ ᅳ ᄋ ᅬᄋ ᅴ hᄋ ᅦᅢ ᄃᄒ ᆫ sˆ(x)ᄋ ᅡ ᅴᄌ ᆨᄇ ᅥ ᆫᄌ ᅮ ᅦᄀ ᆸᄋ ᅩ ᅩᄎ ᅡᄋ ᅴᄀ ᅳᄅ ᆷᄃ ᅵ ᆯᄋ ᅳ ᆫᄉ ᅳ ᆼᄅ ᅢ ᆨᄒ ᅣ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᅩᅧ ᄀ ᄅᄒ ᆫᄋ ᅡ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄃ ᅮᄆ ᅩᄒ ᆼᄋ ᅧ ᅦᄃ ᅢᄒ ᆫᄌ ᅡ ᆨᄇ ᅥ ᆫᄌ ᅮ ᅦᄀ ᆸᄋ ᅩ ᅩᄎ ᅡᄋ ᅴᄀ ᆯᄀ ᅧ ᅪᄋ ᅦᄋ ᅴᄒ ᅡᄆ ᆫᄌ ᅧ ᅮᄋ ᅥᄌ ᆫᄃ ᅵ ᅢᄇ ᅮᄇ ᆫᄋ ᅮ ᅴᄄ ᅵᄑ ᆨ bᄋ ᅩ ᅦᄃ ᅢᄒ ᅡ ᅧ, ᄌ ᄋ ᆷᅳ ᅥ ᄑᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅦᄋ ᅴᄒ ᅢᄇ ᅩᄌ ᆼᄒ ᅥ ᆫᄑ ᅡ ᅭᄇ ᆫᅳ ᅩ ᆯ ᄋᄐ ᆼᄒ ᅩ ᆫᄋ ᅡ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ sˆ(x)ᄀ ᅣ ᅡᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄋ ᅱᄎ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ ᅣ ᆯᄀ ᅳ ᄋ ᅵᄌ ᆫᄋ ᅮ ᅳᄅ ᅩᄑ ᅭᄇ ᆫᅳ ᅩ ᆯ ᄋᄇ ᆫᄅ ᅮ ᅵᄒ ᅡᄋ ᅧᄎ ᅮᄌ ᆼᄒ ᅥ ᅡᄂ ᆫᄋ ᅳ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ s˜(x)ᄇ ᅣ ᅩᄃ ᅡᄌ ᆨᄇ ᅥ ᆫᄌ ᅮ ᅦᄀ ᆸᄋ ᅩ ᅩᄎ ᅡᄀ ᅡᄌ ᆨᄋ ᅡ ᅡ sˆ(x)ᄀ ᅡ s˜(x) ᅩ ᄇᄃ ᅡᄃ ᅥᄋ ᅮᄉ ᅮᄒ ᆫᄆ ᅡ ᅩᄋ ᅴᄉ ᆯᄒ ᅵ ᆷᅧ ᅥ ᆯ ᄀᄀ ᅪᄅ ᆯᄇ ᅳ ᅩᄋ ᅧᄌ ᅮᄀ ᅩᄋ ᆻᄃ ᅵ ᅡ.. 0.10. 0.14. 0.18. 0.22. b. Figure 3.1 The ISE as function of b for the case of s1 . The solid line represents the ISE of sˆ(x) and the dotted line represents the ISE of s˜(x). ISE=integrated squared error.. 3.2. LIDAR 자료 분석 R ᄉ ᅩᄑ ᅳᄐ ᅳᄋ ᅰᄋ ᅥᄋ ᅴ SemiPar libraryᄋ ᅦᄀ ᆼᄀ ᅩ ᅢᄃ ᅬᄋ ᅥᄋ ᆻᄂ ᅵ ᆫ LIDAR (light detection and range) ᄌ ᅳ ᅡᄅ ᅭᄂ ᆫᅮ ᅳ ᆫ ᄇ ᆫᅡ ᅡ ᄉ ᆷ 후 ᄉᄋ ᅴᄇ ᅵᄆ ᅩᄉ ᅮᄌ ᆨᄎ ᅥ ᅮᄌ ᆼᄋ ᅥ ᆫᄀ ᅧ ᅮᄋ ᅦᄌ ᅡᄌ ᅮᄒ ᆯᄋ ᅪ ᆼᄃ ᅭ ᅬᄋ ᅥᄋ ᆻᄃ ᅪ ᅡ. Ruppert ᄃ ᆼ (1997)ᄋ ᅳ ᆫᄒ ᅳ ᅬᄀ ᅱᄆ ᅩᄒ ᆼᄋ ᅧ ᅴᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄅ ᆯᄀ ᅳ ᆨ ᅮ ᅩᄉ ᄉ ᆫᅧ ᅥ ᆼ ᄒᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅳᄅ ᅩ ᄎ ᅮᄌ ᆼᄋ ᅥ ᆯ ᄌ ᅳ ᅦᄋ ᆫᄒ ᅡ ᅡᄋ ᆻᄋ ᅧ ᅳᄆ ᅧ, ᄋ ᅵᄄ ᅢ LIDAR ᄌ ᅡᄅ ᅭᄅ ᆯ ᄒ ᅳ ᆯᄋ ᅪ ᆼᄒ ᅭ ᅡᄋ ᅧ ᄀ ᅳᄃ ᆯᄋ ᅳ ᅵ ᄌ ᅦᄋ ᆫᅡ ᅡ ᆫ ᄒ ᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯ ᄉ ᅳ ᆯᄌ ᅵ ᅦ ᅡᄅ ᄌ ᅭᅦ ᄋᄌ ᆨᄋ ᅥ ᆼᄒ ᅭ ᅡᄋ ᅧᄋ ᆫᄀ ᅧ ᅮᄒ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄇ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄀ ᅡᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᆯᄀ ᅳ ᅡᄌ ᆯᄄ ᅵ ᅢ, Huh (2016b)ᄋ ᅪ Kangᄀ ᅪ Huh (2006)ᄂ ᆫ ᅳ LIDAR ᄌ ᅡᄅ ᅭᄅ ᆯᄋ ᅳ ᅵᄋ ᆼᄒ ᅭ ᅡᄋ ᅧᄀ ᅳᄃ ᆯᄋ ᅳ ᅵᄌ ᅦᄋ ᆫᄒ ᅡ ᆫᄇ ᅡ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄇ ᅩ ᆫᄉ ᅮ ᆫᅡ ᅡ ᆷ ᄒᄉ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄋ ᅥ ᆫᄀ ᅧ ᅮᄋ ᅦᄉ ᆯᄌ ᅵ ᅦᄌ ᅡᄅ ᅭᄅ ᅩᄌ ᆨᄋ ᅥ ᆼᄒ ᅭ ᅡᄋ ᆻᄃ ᅧ ᅡ. Huh.
(7) 763. 0.34. 0.36. 0.38. ISE. 0.40. 0.42. 0.44. Estimation of second moment function with adujusted sample. 0.10. 0.14. 0.18. 0.22. b. Figure 3.2 The ISE as function of b for the case of s2 . The solid line represents the ISE of sˆ(x) and the dotted line represents the ISE of s˜(x). ISE=integrated squared error..
(8) 764. Jib Huh. 0.0. 0.2. 0.4. y. 0.6. 0.8. (2021)ᄂ ᆫᅮ ᅳ ᆫ ᄇᄉ ᆫᄒ ᅡ ᆷᄉ ᅡ ᅮᅪ ᄋᄅ ᅩᄀ ᅳᄇ ᆫᄉ ᅮ ᆫᄒ ᅡ ᆷᄉ ᅡ ᅮᄋ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄉ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᅥ ᅥ ᆸ ᄇᄋ ᆯᄌ ᅳ ᅦᄋ ᆫᄒ ᅡ ᅡᄀ ᅩ LIDAR ᄌ ᅡᄅ ᅭᄋ ᅴᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴ ᅮᄅ ᄉ ᆯᅮ ᅳ ᄎᄌ ᆼᄒ ᅥ ᅡᄋ ᆻᄃ ᅧ ᅡ.. 400. 450. 500. 550. 600. 650. 700. x. Figure 3.3 The squared LIDAR data are represented by the wiggly solid line. The estimated second moment functions of sˆ(x), s˜(x) and sˇ(x) are represented by the solid, the dashed and the dotted line respectively. LIDAR=light detection and range.. Figure 3.3ᄋ ᆫ LIDAR ᄌ ᅳ ᅡᄅ ᅭᄋ ᅴᄎ ᅮᄌ ᆼᄃ ᅥ ᆫᄋ ᅬ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄃ ᆯᅳ ᅳ ᆯ ᄋᄇ ᅩᄋ ᅧᄌ ᅮᄀ ᅩᄋ ᆻᄃ ᅵ ᅡ. ᄁ ᆨᄋ ᅥ ᆫᄉ ᅳ ᆫᄋ ᅥ ᅳᄅ ᅩᄑ ᅭᄒ ᆫᄃ ᅧ ᆫᄀ ᅬ ᆺᄋ ᅥ ᆫᄌ ᅳ ᅡ ᄅᄋ ᅭ ᅴᄉ ᅮᄀ ᅡ 221ᄀ ᅢᄋ ᆫ LIDARᄋ ᅵ ᅴᄇ ᆫᄋ ᅡ ᆼᄇ ᅳ ᆫᄉ ᅧ ᅮᄋ ᅴᄌ ᅡᄅ ᅭᄃ ᆯᅳ ᅳ ᆯ ᄋᄌ ᅦᄀ ᆸᄒ ᅩ ᆫᄀ ᅡ ᆺᄃ ᅥ ᆯᅳ ᅳ ᆯ ᄋᄇ ᅩᄋ ᅧᄌ ᅮᄀ ᅩᄋ ᆻᄀ ᅵ ᅩ, ᄉ ᆯᅧ ᅥ ᆼ 며 ᆫ ᄇᄉ ᅮᄋ ᅴᄀ ᆹ 610 ᅡ ᅵᄒ ᄋ ᅮᄌ ᆼᄃ ᅥ ᅩᄋ ᅦᄉ ᅥᄉ ᆫᄑ ᅡ ᅩᄀ ᅡᄀ ᆸᄌ ᅡ ᆨᄉ ᅡ ᅳᄅ ᆸᄀ ᅥ ᅦᄏ ᅥᄌ ᅵᄀ ᅩᄋ ᆻᄃ ᅵ ᅡᄂ ᆫᄀ ᅳ ᆺᄋ ᅥ ᆯᄋ ᅳ ᆯᄉ ᅡ ᅮᄋ ᆻᄃ ᅵ ᅡ. LIDAR ᄌ ᅡᄅ ᅭᄋ ᅴᄋ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄀ ᅡᄇ ᆯ ᅮ ᆫᄉ ᅧ ᄋ ᆨᅥ ᅩ ᆷ ᄌᄋ ᅵᄋ ᆹᄃ ᅥ ᅡᄀ ᅩᄀ ᅡᄌ ᆼᄒ ᅥ ᆯᅧ ᅡ ᆼ ᄀᄋ ᅮ Nadaraya-Watson ᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅦᄋ ᅴᄒ ᆫᄋ ᅡ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮᄋ ᅴᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆫᄃ ᅳ ᅡᄋ ᆷᄀ ᅳ ᅪᄀ ᇀᄋ ᅡ ᅵ n 1 X Xi − x 2 L Yi nb i=1 b sˇ(x) = n 1 X Xi − x L nb i=1 b. ᄅᄑ ᅩ ᅭᄒ ᆫᄒ ᅧ ᆯᄉ ᅡ ᅮᄋ ᆻᄋ ᅵ ᅳᄆ ᅧ Figure 3.3ᄋ ᅦᄉ ᅥᄀ ᅡᄂ ᆫᄌ ᅳ ᆷᅥ ᅥ ᆫ ᄉᄋ ᅳᄅ ᅩ sˇ(x)ᄅ ᆯᄇ ᅳ ᅩᄋ ᅧᄌ ᅮᄀ ᅩᄋ ᆻᄃ ᅵ ᅡ. ᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅵᄋ ᆻᄃ ᅵ ᅡᄀ ᅩᄀ ᅡᄌ ᆼᄒ ᅥ ᅡᄋ ᅧ ᆷᄑ ᅥ ᄌ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᅦᄋ ᅴᄒ ᅢᄇ ᅩᄌ ᆼᄒ ᅥ ᆫᄑ ᅡ ᅭᄇ ᆫᅳ ᅩ ᆯ ᄋᄐ ᆼᄒ ᅩ ᅢᄎ ᅮᄌ ᆼᄃ ᅥ ᆫᄋ ᅬ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮ sˆ(x)ᄂ ᆫᄉ ᅳ ᆯᄉ ᅵ ᆫᄋ ᅥ ᅳᄅ ᅩᄑ ᅭᄒ ᆫᄒ ᅧ ᅡᄋ ᆻᄀ ᅧ ᅩ, ᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨ ᅩ ᆷᄋ ᅥ ᄌ ᅴᄋ ᅱᄎ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆯᄀ ᅳ ᅵᄌ ᆫᄋ ᅮ ᅳᄅ ᅩᄑ ᅭᄇ ᆫᅳ ᅩ ᆯ ᄋᄌ ᅪᄋ ᅮᄅ ᅩᄇ ᆫᄅ ᅮ ᅵᄒ ᅡᄋ ᅧᄎ ᅮᄌ ᆼᄒ ᅥ ᆫᄋ ᅡ ᅵᄎ ᅡᄌ ᆨᄅ ᅥ ᆯᄒ ᅲ ᆷᄉ ᅡ ᅮ s˜(x)ᄂ ᆫᄀ ᅳ ᆰᄋ ᅮ ᆫᄌ ᅳ ᆷᄉ ᅥ ᆫᄋ ᅥ ᅳᄅ ᅩᄑ ᅭᄒ ᆫᄒ ᅧ ᅡ ᆻᄃ ᅧ ᄋ ᅡ. Figure 3.3ᄋ ᅦᄉ ᅥᄉ ᅡᄋ ᆼᄃ ᅭ ᆫᄄ ᅬ ᅵᄑ ᆨᄃ ᅩ ᆯᄋ ᅳ ᆫ Huh (2016b)ᄋ ᅳ ᅦᄉ ᅥᄀ ᅭᄎ ᅡᄐ ᅡᄃ ᆼᄉ ᅡ ᆼ (cross-validation)ᄋ ᅥ ᅦᄋ ᅴᄒ ᅢᄉ ᆫᅢ ᅥ ᆨ ᄐᄃ ᆫᄀ ᅬ ᆺ ᅥ ᆯᄅ ᅳ ᄃ ᅩ h = 27ᄀ ᅪ b = 43ᄋ ᆯᄉ ᅳ ᅡᄋ ᆼᄒ ᅭ ᅡᄋ ᆻᄃ ᅧ ᅡ. ᄋ ᅵᄄ ᅢᄎ ᅮᄌ ᆼᄃ ᅥ ᆫᄇ ᅬ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᄌ ᅩ ᆷᄋ ᅥ ᅴᄋ ᅱᄎ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄀ ᅣ ᅪᄌ ᆷᄑ ᅥ ᅳᄏ ᅳᄀ ᅵᄎ ᅮᄌ ᆼᄅ ᅥ ᆼᄋ ᅣ ᆫᄀ ᅳ ᆨᄀ ᅡ ᆨ ᅡ.
(9) Estimation of second moment function with adujusted sample. 765. b τ ) = 0.085390ᄋ τb = 636.5ᄋ ᅪ ∆(b ᅵᄃ ᅡ. ᄇ ᆯᄋ ᅮ ᆫᄉ ᅧ ᆨᅳ ᅩ ᆯ ᄋᄀ ᅡᄌ ᆼᄒ ᅥ ᆫᄃ ᅡ ᅮᄎ ᅮᄌ ᆼᄅ ᅥ ᆼ sˆ(x)ᄋ ᅣ ᅪ s˜(x)ᄀ ᅡᄋ ᆫᄉ ᅧ ᆨᄋ ᅩ ᅵᄅ ᅡᄀ ᅩᄀ ᅡᄌ ᆼᄒ ᅥ ᆫᄎ ᅡ ᅮ ᆼᄅ ᅥ ᄌ ᆼ sˇ(x)ᄇ ᅣ ᅩᄃ ᅡ LIDAR ᄌ ᅡᄅ ᅭᄅ ᆯᄃ ᅳ ᅥᄌ ᆯᄉ ᅡ ᆯᄆ ᅥ ᆼᄒ ᅧ ᅡᄀ ᅩᄋ ᆻᄃ ᅵ ᅡᄀ ᅩᄑ ᆫᅡ ᅡ ᆫ ᄃᄃ ᆫᄃ ᅬ ᅡ.. References Chen, L., Chen, M. and Peng, M. (2009). Conditional variance estimation in heteroscedastic regression models. Journal of Statistical Planning and Inference, 139, 236-245. Delgado, M. A. and Hidalgo, J. (2000). Nonparametric inference on structural breaks. Journal of Econometrics, 96, 113-144. Fan, J. and Gijbels, I. (1996). Local polynomial modelling and its applications, Chapman and Halls, London. Gasser, T., Sroka, L. and Jennen-Steinmetz, C. (1986). Residual variance and residual pattern in nonlinear regression. Biometrika, 73, 625-634. Hall, P. and Carroll, R. J. (1989). Variance function estimation in regression: The effect of estimating the mean. Journal of the Royal Statistical Society, Series B, 51, 3-14. H¨ ardle, W. (1990). Applied nonparametric regression, Cambridge University Press, Cambridge. Hong, H. S. and Huh, J. (2017). Discontinuous log-variance function estimation with log-residuals adjusted by an estimator of jump size, The Korean Journal of Statistics, 30, 259-269. Huh, J. (2005). Nonparametric detection of a discontinuity point in the variance function with the second moment function. Journal of the Korean Data & Information Science Society, 16, 591-601. Huh, J. (2016a). Nonparametric estimation of the discontinuous variance function using adjusted residuals. Journal of the Korean Data & Information Science Society, 27, 111-120. Huh, J. (2016b). Estimation of a change point in the variance function based on the χ2 -distribution. Communications in Statistics, 45, 4937-4968. Huh, J. (2020). Nonparametric estimation for motorcycle data in scale-space. Journal of the Korean Data & Information Science Society, 31, 109-121. Huh, J. (2021). Estimation of the number of discontinuity points in the variance function of LIDAR data. Journal of the Korean Data & Information Science Society, 32, 37-47. Huh, J. and Park, B. U. (2004). Detection of change point with local polynomial fits for random design case. Australian and New Zealand Journal of Statistics, 46, 425-441. Kang, K. H. and Huh, J. (2006). Nonparametric estimation of the variance function with a change point. Journal of the Korean Statistical Society, 35, 1-24. Kang, K. H., Koo, J. Y. and Park, C. W. (2000). Kernel estimation of discontinuous regression functions. Statistics and Probability Letters, 47, 277-285. Loader, C. R. (1996). Change point estimation using nonparametric regression. Annals of Statistics, 24, 1667-1678. M¨ uller, H. G. (1992). Change-points in nonparametric regression analysis. Annals of Statistics, 20, 737-761. M¨ uller, H. G. and Stadtm¨ uller, U. (1987). Estimation of heteroscedasticity in regression analysis. Annals of Statistics, 15, 610-625. Rice, J. (1984). Bandwidth choice for nonparametric regression. Annals of Statistics, 12, 12151230. Ruppert, D., Wand, M. P., Holst, U. and H¨ ossjer, O. (1997). Local polynomial variance-function estimation. Technometrics, 39, 262-273. Yu, K. and Jones, M. C. (2004). Likelihood-based local linear estimation of the conditional variance function. Journal of the American Statistical Association, 99, 139-144..
(10) Journal of the Korean Data & Information Science Society 2021, 32(4), 757–766. http://dx.doi.org/10.7465/jkdi.2021.32.4.757 ᆫᄀ ᅡ ᄒ ᆨᄃ ᅮ ᅦᄋ ᅵᄐ ᅥᄌ ᆼᄇ ᅥ ᅩᄀ ᅪᅡ ᆨ ᄒᄒ ᅬᄌ ᅵ. Estimation of second moment function with adujusted sample by an estimator of jump size of discontinuity point Jib Huh1 1. Department of Statistics, Duksung Women’s University. Received 11 June 2021, revised 18 June 2021, accepted 1 July 2021. Abstract. In the case that the regression function is continuous, the discontinuity of the variance function comes from the discontinuous second moment function. In this paper, the estimator of second moment function is proposed by a kernel type estimator using the adjusted squared observations of response variable by an estimator of jump size of the second moment function. After that, the final estimator of the discontinuous second moment function is proposed by reverse adjustment of the kernel type estimator of the second moment function using an estimator of jump size. The estimated second moment function based on the data sets divided by an estimated location has the boundary problem around the location of the discontinuity point like any other kernel type estimators of the statistical functions do. However, the proposed estimator of second moment function does not have the boundary problem near the discontinuity point. Simulation and analysis of real data set demonstrate the performances of the estimators of second moment function. Keywords: Discontinuity point, LIDAR, Nadaraya-Watson estimator, variance function.. 1. Professor, Department of Statistics, Duksung Women’s University, Seoul 01369, Korea. E-mail: [email protected].
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