α-混合随机域边缘频率插值估计

发布时间：2018-04-22 16:35

本文选题：随机域 + 边缘频率插值估计　；参考：《广西师范大学》2017年硕士论文

【摘要】：在未知总体分布类型,总体信息已知较少,样本不一定独立的情况下,非参数密度估计则是非常好的选择.在实际数据统计分析中,由于种种原因,不能随意地假定数据的总体分布,所以我们就需要借助非参数模型来估计密度函数f(x).非参数密度估计已经广泛应用在环境科学、电子物理、生物医学、地质学、经济金融、区域经济等领域.非参数密度估计的方法主要有直方图估计、Rosenblatt估计、核密度估计、最近邻密度估计、频率插值估计等等.其中频率插值密度估计应用极为广泛,而且估计效果良好.频率插值密度估计的积分均方误差(IMSE)与非负核密度估计的收敛速度相同,均可达到n-4/5,且快于直方图密度估计的收敛速度n-2/3.但是在数值计算中,频率插值估计的计算量相对少,所以这相对于核密度估计更有计算优势.因此,研究频率插值估计具有很重要的意义.自Scott(1985)提出频率插值密度估计后,吸引了不少学者对其进行研究.后来Jones(1998)对频率插值估计进行了优化,他提出了边缘频率插值估计,在独立样本下,证明其渐近均方误差(AMSE)比频率插值估计的小,并证明了这种新的估计方法(即边缘频率插值密度估计)比传统的频率插值密度估计具有更好的理论性质.因此,本文选择理论性更好的边缘频率插值密度估计的方法.但是迄今为止.在空间数据(即随机域)下对频率插值密度估计的研究却甚少,仅有Carbon等、Bensaid和Dabo-Niang以及EI Machkouri等少数学者在随机域样本下,研究了频率插值密度估计的积分均方误差、最优窗宽、渐近方差性、渐近正态性以及一致强相合性等性质.然而,目前仍未有学者在随机域样本下,研究边缘频率插值密度估计的渐近性质.因此本文将在α-混合随机域样本下研究边缘频率插值密度估计的性质.首先证明α-混合随机域在满足一定条件下,边缘频率插值密度函数具有渐近方差性.其次证明随机域样本在满足一定条件下,当n→∞时,((?)bn)1/2[fn(x)-Efn(x)]σ-1(x)具有渐近标准正态分布,以及证明α-混合随机域边缘频率插值的强相合性.最后用数值模拟的方法分别对不同样本量和窗宽来进行讨论,进一步验证和说明结论的合理性和正确性.
[Abstract]:The nonparametric density estimation is a good choice in the case of unknown population distribution type where the population information is known and the samples are not necessarily independent. In the statistical analysis of actual data, for various reasons, the total distribution of data can not be assumed at will. Therefore, we need to estimate the density function fnx by means of nonparametric model. Nonparametric density estimation has been widely used in environmental science, electronic physics, biomedicine, geology, economics and finance, regional economy and so on. The methods of nonparametric density estimation include histogram estimation Rosenblatt estimation kernel density estimation nearest neighbor density estimation frequency interpolation estimation and so on. The frequency interpolation density estimation is widely used, and the effect is good. The integral mean square error (IMSEE) of frequency interpolation density estimation is the same as that of non-negative kernel density estimation, which can reach n-4 / 5, and is faster than that of histogram density estimation n-2 / 3. But in the numerical calculation, the frequency interpolation estimation has less computation, so it has more advantages than the kernel density estimation. Therefore, it is of great significance to study the frequency interpolation estimation. Since Scottt proposed frequency interpolation density estimation in 1985, it has attracted many scholars to study it. Later, Jones-1998) optimized the frequency interpolation estimation. He proposed the edge frequency interpolation estimation. Under independent samples, it is proved that the asymptotic mean square error (AMSE) is smaller than the frequency interpolation estimation. It is proved that this new method (i.e. edge frequency interpolation density estimation) has better theoretical properties than traditional frequency interpolation density estimation. Therefore, this paper chooses a better theoretical method of edge frequency interpolation density estimation. But so far. Only a few scholars, such as Carbon et al. Bensaid, Dabo-Niang and ei Machkouri, have studied the integral mean square error and the optimal window width of frequency interpolation density estimation in random domain samples. Asymptotic variance, asymptotic normality and uniform strong consistency. However, no scholars have studied the asymptotic properties of edge frequency interpolation density estimation in random domain samples. Therefore, in this paper, we will study the properties of edge frequency interpolation density estimation in 伪-mixed random field samples. Firstly, it is proved that the edge frequency interpolation density function has asymptotic variance under certain conditions in 伪 -mixed random fields. Secondly, it is proved that the random domain samples have asymptotically standard normal distribution and strong consistency of edge frequency interpolation in 伪 -mixed random fields under certain conditions. Finally, different sample sizes and window widths are discussed by numerical simulation to verify and explain the rationality and correctness of the conclusions.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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