【摘要】：非參數密度估計是一類重要的密度估計,它在實際生活中有著廣泛的應用.在自然界中,大多數總體還是未知分布以及樣本不一定是獨立的,所以非參數密度函數估計的問題在數理統計的研究中備受關注.非參數密度函數的估計從最初的直方圖密度估計,經過不斷地探索逐步有了Rosenblatt密度估計、Parzen核估計、核密度估計、最近鄰密度估計、移動平均直方圖密度估計和頻率插值密度估計等等.1985年Scott[5]在直方圖估計的基礎上提出了頻率插值密度估計,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,φ混合序列在時間序列模型、可靠性理論、生態(tài)系統研究等領域具有廣泛的應用,因此統計學家對φ混合序列的研究有著廣泛關注和興趣.Scott(1985)[5]提出頻率插值密度估計,很多學者做出深入研究.然而,目前還沒有文獻對φ混合隨機域該估計的性質進行更多的研究.因此,在φ-混合隨機域下對頻率插值密度估計漸近性質的研究是有意義的.本文在φ-混合隨機域下,主要是對頻率插值密度估計漸近性質的研究.首先,介紹φ-混合、頻率插值密度估計.其次,混合系數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α-隨機域里頻率多邊形采用“大小分塊”的思想,對φ-混合隨機域大小分塊,來證明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：2387476