第1章預(yù)備知識....................................................................................................1
1.1背景介紹...................................................................................................1
1.2收斂方式和極限分布..................................................................................2
1.2.1依概率收斂......................................................................................2
1.2.2幾乎必然收斂..................................................................................3
1.2.3r階收斂.........................................................................................4
1.2.4依分布收斂......................................................................................4
1.2.5收斂方式間的關(guān)系............................................................................4
1.3中心極限定理和幾個(gè)常用的定理..................................................................5
1.3.1中心極限定理..................................................................................5
1.3.2幾個(gè)常用的定理...............................................................................5
1.3.3Delta方法......................................................................................6
1.4記號op(1)和Op(1).....................................................................................6
第2章非參數(shù)核密度估計(jì)......................................................................................9
2.1介紹..........................................................................................................9
2.2單元密度函數(shù)的估計(jì)..................................................................................9
2.2.1核密度估計(jì)的提出...........................................................................9
2.2.2常用的核函數(shù)及其性質(zhì)...................................................................11
2.2.3以f.n(x)作為密度函數(shù)的隨機(jī)變量的一階矩和二階矩........................12
2.2.4f.n(x)的均值、方差和均方誤差........................................................13
2.3單元核密度估計(jì)的帶寬選擇.......................................................................15
2.3.1最優(yōu)帶寬.......................................................................................15
2.3.2拇指法則.......................................................................................16
2.3.3最小二乘交叉驗(yàn)證法則...................................................................17
2.3.4似然交叉驗(yàn)證法則..........................................................................18
2.3.5小結(jié)..............................................................................................19
2.4核函數(shù)的選取...........................................................................................19
2.4.1等價(jià)核函數(shù)....................................................................................19
2.4.2典型帶寬.......................................................................................20
2.4.3最優(yōu)核函數(shù)....................................................................................20