【摘要】：非參數(shù)密度估計(jì)是一類重要的密度估計(jì),它在實(shí)際生活中有著廣泛的應(yīng)用.在自然界中,大多數(shù)總體還是未知分布以及樣本不一定是獨(dú)立的,所以非參數(shù)密度函數(shù)估計(jì)的問題在數(shù)理統(tǒng)計(jì)的研究中備受關(guān)注.非參數(shù)密度函數(shù)的估計(jì)從最初的直方圖密度估計(jì),經(jīng)過不斷地探索逐步有了Rosenblatt密度估計(jì)、Parzen核估計(jì)、核密度估計(jì)、最近鄰密度估計(jì)、移動(dòng)平均直方圖密度估計(jì)和頻率插值密度估計(jì)等等.1985年Scott[5]在直方圖估計(jì)的基礎(chǔ)上提出了頻率插值密度估計(jì),并指出:選擇最優(yōu)窗寬使均方誤差最小下,得到的收斂速度分別為:n-2/3和n-4/5,同時(shí),φ混合序列在時(shí)間序列模型、可靠性理論、生態(tài)系統(tǒng)研究等領(lǐng)域具有廣泛的應(yīng)用,因此統(tǒng)計(jì)學(xué)家對(duì)φ混合序列的研究有著廣泛關(guān)注和興趣.Scott(1985)[5]提出頻率插值密度估計(jì),很多學(xué)者做出深入研究.然而,目前還沒有文獻(xiàn)對(duì)φ混合隨機(jī)域該估計(jì)的性質(zhì)進(jìn)行更多的研究.因此,在φ-混合隨機(jī)域下對(duì)頻率插值密度估計(jì)漸近性質(zhì)的研究是有意義的.本文在φ-混合隨機(jī)域下,主要是對(duì)頻率插值密度估計(jì)漸近性質(zhì)的研究.首先,介紹φ-混合、頻率插值密度估計(jì).其次,混合系數(shù)φ滿足∑i=1∞iN-1(φ(i))β∞,其中0β1.證明出limn→∞(nbnVarfn(x)-[1/2 + 2(k0-x/bn)f(x))= 0.借助Carbona(2010)等對(duì)α-隨機(jī)域里頻率多邊形采用“大小分塊”的思想,對(duì)φ-混合隨機(jī)域大小分塊,來(lái)證明φ-混合樣本下頻率插值的漸近正態(tài)性.
[Abstract]:Nonparametric density estimation is an important class of density estimation, which is widely used in real life. In nature, most of the population is unknown and the samples are not necessarily independent, so the problem of nonparametric density function estimation has attracted much attention in the research of mathematical statistics. The estimation of nonparametric density function from the original histogram density estimation, after continuous exploration, there are gradually Rosenblatt density estimation, Parzen kernel estimation, kernel density estimation, nearest neighbor density estimation. Moving average histogram density estimation and frequency interpolation density estimation, etc. In 1985, Scott [5] proposed a frequency interpolation density estimation based on histogram estimation, and pointed out that when the optimal window width is chosen to minimize the mean square error, The convergence rates obtained are n-2 / 3 and n-4 / 5, respectively. Meanwhile, 蠁 mixed sequences are widely used in time series model, reliability theory, ecosystem research and so on. Therefore, statisticians have a wide range of concerns and interests in the study of 蠁 mixed sequences. [5] [5] Frequency interpolation density estimation has been proposed by many scholars. However, there are no more studies on the properties of this estimator in 蠁 mixed random fields. Therefore, it is significant to study the asymptotic properties of frequency interpolation density estimation in 蠁-mixed random field. In this paper, the asymptotic properties of density estimation of frequency interpolation in 蠁-mixed random domain are studied. Firstly, 蠁-mixing and frequency interpolation density estimation are introduced. Secondly, the mixing coefficient 蠁 satisfies 鈭，

本文編號(hào)：2387476