Ester Mariucci
We recall the main concepts of the Le Cam theory of statistical experiments , especially the notion of Le Cam distance and its properties. We also review classical tools for bounding such a distance before presenting some examples. A proof of the classical equivalence result between density estimation problems and Gaussian white noise models will be analyzed.
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The paper contains some musings about the abstractions introduced by Lucien Le Cam into the asymptotic theory of statistical inference and decision theory. A short, self-contained proof of a key result (existence of randomizations via convergence in distribution of likelihood ratios), and an outline of a proof of a local asymptotic minimax theorem, are presented as an illustration of how Le Cam's approach leads to conceptual simplifications of asymptotic theory.
Statistical inference for pairwise comparison models
本文研究了成对比较模型中最大似然估计的渐近正态性，通过图拉普拉斯算子的谱分析提供了理论基础，并通过模拟和实验证实了结果。
General linear models (GLM) are often constructed and used in statistical inference at the voxel level in brain imaging. In this paper, we explore the basics of random fields and the multiple comparisons on the random fields, which are necessary to properly threshold statistical maps for the whole image at specific statistical significance level. The multiple comparisons are crucial in determining overall statistical significance in correlated test statistics over the whole brain. In practice, t- or F-statistics in adjacent voxels are correlated. So there is the problem of multiple comparisons…
Indirect comparisons of treatment-specific outcomes across separate studies often inform decision-making in the absence of head-to-head randomized comparisons. Differences in baseline characteristics between study populations may introduce confounding bias in such comparisons. Matching-adjusted indirect comparison (MAIC) (Signorovitch et al., 2010) has been used to adjust for differences in observed baseline covariates when the individual patient-level data (IPD) are available for only one study and aggregate data (AGD) are available for the other study. The approach weights outcomes from the …
We show how the classic Cramer-Rao bound limits how accurately one can simultaneously estimate values of a large number of Google Ad campaigns (or similarly limit the measurement rate of many confounding A/B tests).
There are various parametric models for analyzing pairwise comparison data, including the Bradley-Terry-Luce (BTL) and Thurstone models, but their reliance on strong parametric assumptions is limiting. In this work, we study a flexible model for pairwise comparisons, under which the probabilities of outcomes are required only to satisfy a natural form of stochastic transitivity. This class includes parametric models including the BTL and Thurstone models as special cases, but is considerably more general. We provide various examples of models in this broader stochastically transitive class for…
Diagnostic accuracy studies assess sensitivity and specificity of a new index test in relation to an established comparator or the reference standard. The development and selection of the index test is usually assumed to be conducted prior to the accuracy study. In practice, this is often violated, for instance if the choice of the (apparently) best biomarker, model or cutpoint is based on the same data that is used later for validation purposes. In this work, we investigate several multiple comparison procedures which provide family-wise error rate control for the emerging multiple testing pr…
Motivated by population studies of Diffusion Tensor Imaging, the paper investigates the use of mean-based and dispersion-based permutation tests to define and compute the significance of a statistical test for data taking values on nonlinear manifolds. The paper proposes statistical tests that are computationally tractable and geometrically sound for Diffusion Tensor Imaging.
Different network structures are compiared with respect to degree of robustnes of identification statistical procedures. It is shown that threshold (market) graph, cliques and independent sets in the threshold (market) graphs are preferable network structure from this point of view.
A comparison of statistical models for short categorical or ordinal time series with applications in ecology
本文研究了两种短长度分类（或有序）时间序列的统计模型。第一种是基于广义线性模型的回归模型。第二种是参数化马尔可夫模型，将离散自回归模型具体化到分类数据的情形。这些模型被用来分析两个数据集：每年的落叶松球果生产量和每周的针叶树丰度。
Geometric mean-based pairwise comparison method with the reference values -- statistical approach
本文从统计视角出发，利用参考值和几何平均提出成对比较方法，可捕捉不一致现象与偏好距离，还定义了衡量权重向量质量的指标，为涉及专家的决策提供新方法和指标。
Statistical Evidence Measured on a Properly Calibrated Scale Across Nested and Non-nested Hypothesis Comparisons
本文将信息动力学统计证据框架从单侧二项比较推广到嵌套与非嵌套假设比较，借助范德瓦尔斯方程扩展并引入与自由度相关的校准常数，推动构建可通用的适当校准证据度量。
Image fusion produces a single fused image from a set of input images. A new method for image fusion is proposed based on Weighted Average Merging Method (WAMM) in the NonSubsampled Contourlet Transform (NSCT) domain. A performance analysis on various statistical fusion rules are also analysed both in NSCT and Wavelet domain. Analysis has been made on medical images, remote sensing images and multi focus images. Experimental results shows that the proposed method, WAMM obtained better results in NSCT domain than the wavelet domain as it preserves more edges and keeps the visual quality intact …
A family of probability distributions (i.e. a statistical model) is said to be sufficient for another, if there exists a transition matrix transforming the probability distributions in the former to the probability distributions in the latter. The Blackwell-Sherman-Stein (BSS) theorem provides necessary and sufficient conditions for one statistical model to be sufficient for another, by comparing their information values in statistical decision problems. In this paper we extend the BSS theorem to quantum statistical decision theory, where statistical models are replaced by families of density …
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is, the number of variables. Inspired by the spike models used in random matrix theory, we concentrate on the largest eigenvalues of the matrices in order to determine significance. To avoid false rejections we must guard against residual spikes and need a sufficiently precise description of the behaviour of the largest eigenvalues under the null hypothesis. In t…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is, the number of variables. Inspired by the spike models used in random matrix theory, we concentrate on the largest eigenvalues of the matrices in order to determine significance. To avoid false rejections we must guard against residual spikes and need a sufficiently precise description of the behaviour of the largest eigenvalues under the null hypothesis. In t…
Quantitative comparisons between finitary posterior distributions and Bayesian posterior distributions
贝叶斯统计推断的主要目的是确定后验分布。有时，这些定律是为缺乏经验值的量给出的。当我们只考虑有限视界框架时，这个严重的缺点就消失了。然而，假设无限的交换率会产生相当容易处理的{ \it a posteriori}量，这在应用中是非常有吸引力的。因此，为了调和这两个方面的贝叶斯推理方式，在本文中，我们提供了定量比较后验分布的有限参数和后验分布的盟军参数出现在通常的统计模型。
Approximate Computation via Le Cam Simulability
通过Le Cam可模拟性框架，研究计算复杂性从语法精确性到语义近似性的转变，定义计算缺陷并提出LeCam-P复杂性类，揭示决策鲁棒性与近似计算的关系。
Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement
本文针对局部变化测量尺度空间中随机变量的信息利用问题，提出广义随机占优序，并构建经线性优化实现、由不精确概率稳健化的正则化统计检验。
E-values as statistical evidence: A comparison to Bayes factors, likelihoods, and p-values
本文比较了e值和e过程与p值、似然比和贝叶斯因子在证据测量中的特性，指出e值具有自然组合、处理复合假设、长期误差率等优势，且e过程能处理选择停止和继续，值得作为可解释的证据测量方法考虑。
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