本文關(guān)鍵詞： 左截斷右刪失 剩余壽命分位數(shù) 置信區(qū)間 Bootstrap-t Jackknife-d　出處：《蘭州財經(jīng)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：在醫(yī)學(xué)的臨床研究中,數(shù)據(jù)往往同時存在刪失和截斷。近年來刪失和截斷數(shù)據(jù)在剩余壽命分位數(shù)的研究中已經(jīng)變得越來越普遍。本文主要針對左截斷右刪失數(shù)據(jù)討論了剩余壽命分位數(shù)的置信區(qū)間構(gòu)造問題。在截斷和刪失數(shù)據(jù)下或樣本量很小時,傳統(tǒng)的置信區(qū)間構(gòu)造方法通常是不理想的,而且涉及到參數(shù)估計的漸近方差計算相當(dāng)繁瑣。本文從重抽樣的角度出發(fā),構(gòu)造剩余壽命函數(shù)分位數(shù)的置信區(qū)間。Jackknife-d方法是實際中最常用的一種重抽樣方法,與傳統(tǒng)的置信區(qū)間構(gòu)造方法相比,可以充分地利用感興趣變量之外的輔助信息。同時,在非平滑函數(shù)下得到的方差估計也具有無偏性等優(yōu)點。另一方面,Bootstrap-t方法可以直接從數(shù)據(jù)中獲得的信息來構(gòu)造置信區(qū)間,不包括任何理論假設(shè),并且在小樣本情況下也表現(xiàn)出較好的覆蓋誤差。因此,本文分別利用Jackknife-d方法和Bootstrap-t方法構(gòu)造了左截斷右刪失數(shù)據(jù)下剩余壽命函數(shù)分位數(shù)的置信區(qū)間并分別給出了估計量相應(yīng)的漸近性質(zhì)。同時,通過Monte Carlo模擬和實例分析對兩種重抽樣方法和傳統(tǒng)的四種方法進行評價。模擬結(jié)果表明:小樣本情況下,本文提出的兩種重抽樣方法在區(qū)間長度較傳統(tǒng)方法有明顯的優(yōu)勢。其中,Jackknife-d方法構(gòu)造的區(qū)間區(qū)間長度最短,是小樣本下一種理想的區(qū)間構(gòu)造方法。
[Abstract]:In the clinical research of medicine, In recent years, censored and truncated data have become more and more common in the study of residual life quantiles. In this paper, the residual life quantiles are mainly discussed for left truncated and right censored data. With truncated and censored data or small sample sizes, The traditional method of constructing confidence interval is usually not ideal, and the calculation of asymptotic variance involving parameter estimation is rather complicated. The Jackknife-d method for constructing the quantile of residual life function is one of the most commonly used resampling methods in practice. Compared with the traditional confidence interval construction method, it can make full use of the auxiliary information other than the variables of interest. On the other hand, the Bootstrap-t method can construct confidence intervals directly from the information obtained from the data, and does not include any theoretical assumptions. And it also shows good coverage error in the case of small sample. In this paper, Jackknife-d method and Bootstrap-t method are used to construct the confidence interval of the quantile of the residual life function under the left truncation and the right censored data, and the asymptotic properties of the estimator are given respectively. Two resampling methods and four traditional methods are evaluated by Monte Carlo simulation and case analysis. The simulation results show that: in the case of small sample, The two resampling methods proposed in this paper have obvious advantages over the traditional method in interval length. Jackknife-d method is the shortest interval length and is an ideal interval construction method for small samples.
【學(xué)位授予單位】：蘭州財經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212

【參考文獻】

相關(guān)期刊論文 前4條

1 ZHANG Li;LIU Peng;ZHOU Yong;;Smoothed Estimator of Quantile Residual Lifetime for Right Censored Data[J];Journal of Systems Science & Complexity;2015年06期

2 WANG YiXin;LIU Peng;ZHOU Yong;;Quantile residual lifetime for left-truncated and right-censored data[J];Science China(Mathematics);2015年06期

3 劉玉濤;劉鵬;周勇;;競爭風(fēng)險下剩余壽命分位數(shù)的光滑非參數(shù)估計[J];應(yīng)用數(shù)學(xué)學(xué)報;2015年01期

4 劉煥彬;左截斷右刪失數(shù)據(jù)下百分剩余壽命函數(shù)的非參數(shù)估計[J];數(shù)學(xué)雜志;1996年04期

，

本文編號：1524733