论文检索

依赖性右删失下生长曲线的两样本检验AI 解读

In many tumour growth inhibition studies, tumour sizes are recorded over a period of time, forming a growth curve for each experimental animal. A frequently asked question in these studies is whether or not different treatment agents/inhibitors result in different growth rates. To compare tumour growth rates under two treatments, either the t‐test or the Wilcoxon–Mann–Whitney test could be used under suitable assumptions, provided that a one‐dimensional variable, such as the…

从图像去模糊到最优投资：正性线性逆问题的极大似然解法AI 解读

SUMMARY The problem of recovering an input signal from a blurred output, in an input-output system with linear distortion, is ubiquitous in science and technology. When the blurred output is not degraded by statistical noise the problem is entirely deterministic and amounts to a mathematical inversion of a linear system with positive parameters, subject to positivity constraints on the solution. We show that all such linear inverse problems with positivity restrictions…

随机乘法删失模型中经验分布的大样本研究AI 解读

Consider an incomplete data problem with the following specifications. There are three independent samples $(X_1, \ldots, X_m), (Z_1, \ldots, Z_n)$ and $(U_1, \ldots, U_n)$. The first two samples are drawn from a common lifetime distribution function $G$, while the third sample is drawn from the uniform distribution over the interval $(0,1)$. In this paper we derive the large sample properties of $\hat{G}_{m,n}$, the nonparametric maximum likelihood estimate of $G$ based on…

摘要暂缺

摘要暂缺

摘要暂缺

选择偏差模型中的经验分布AI 解读

The following problem is treated: Given $s$ not-necessarily-random samples from an unknown distribution $F$, and assuming that we know the sampling rule of each sample, is it possible to combine the samples in order to estimate $F$, and if so what is the natural way of doing it? More formally, this translates to the problem of determining whether there exists a nonparametric maximum likelihood estimate (NPMLE) of $F$ on the basis of $s$ samples from weighted versions of $F$,…

正电子发射断层成像的统计模型AI 解读

Positron emission tomography (PET)—still in its research stages—is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner. Much as in X-ray transmission tomography and other modes of computerized tomography, the quality of the reconstructed image in PET is very sensitive to the mathematical algorithm to be used for reconstruction. In this article, we tailor a mathematical model to the…

更新过程中的非参数估计AI 解读

Data collected from many independent identically distributed renewal processes, each of which is observed for an arbitrary period of time, is usually affected by censoring coupled with length biased sampling. In this paper we derive an algorithm that produces the nonparametric maximum likelihood estimator (i.e., the analog of the single-sample empirical distribution function) of the common lifetime distribution, based on such data.

基于重叠数据的估计效率界AI 解读

If we have several estimates of the same quantity, based on partially overlapping sets of data, we can contemplate combining them, linearly, to give a single estimate. We give bounds, which depend only on the degrees of overlap but not on the individual variances, for the efficiency of the best linear unbiased combination of these estimates. with and without covariance information, relative to the overall best linear unbiased estimate. In particular, if the sets have no more…

存在长度偏倚时的非参数估计AI 解读

We derive the nonparametric maximum likelihood estimate, $\hat{F}$ say, of a lifetime distribution $F$ on the basis of two independent samples, one a sample of size $m$ from $F$ and the other a sample of size $n$ from the length-biased distribution of $F$, i.e. from $G_F(x) = \int^x_0 u dF(u)/\mu, \mu = \int^\infty_0 x dF(x)$. We further show that $(m + n)^{1/2}(\hat{F} - F)$ converges weakly to a pinned Gaussian process with a simple covariance function, when $m + n \rightarrow \infty$…

基于重叠数据的估计效率界AI 解读

If we have several estimates of the same quantity, based on partially overlapping sets of data, we can contemplate combining them, linearly, to give a single estimate. We give bounds, which depend only on the degrees of overlap but not on the individual variances, for the efficiency of the best linear unbiased combination of these estimates. with and without covariance information, relative to the overall best linear unbiased estimate. In particular, if the sets have no more…

渐近最优序贯估计：泊松情形AI 解读

The problems of estimating sequentially the intensity parameter of a homogeneous Poisson process and of estimating sequentially the mean of a sequence of i.i.d. Poisson rv's, are considered. The procedures suggested are shown to perform well for large values of the parameter and/or for small sampling cost. Having bounded regret, the procedure for estimating the mean of the Poisson sequence is asymptotically Bayes w.r.t. any sequence of a priori densities, which spread mass…

某些序贯估计量的渐近最优性AI 解读

We give a decision-theoretic justification of a heuristic principle suggested by Robbins. Suppose a sequence $X_1, X_2, \cdots$ of independent random variables can be observed; they are known to be identically distributed with unknown mean and variance $u, \sigma^2(u)$ respectively. We assume further that the common distribution is of exponential type, so that the sample mean $\bar{X}$ is a sufficient statistic. The problem is to estimate $u$ taking into account the cost of…