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模式识别中的相关性与高维一致性AI 解读

Classical discriminant analysis breaks down when the feature vectors are of extremely high dimension; for example, when the basic observation is a random function observed over a fine grid. Alternative methods have been developed assuming a simplified form for the covariance structure. We analyze the high-dimensional asymptotics of some of these methods, emphasizing the effects of correlations such as occur when the baseline is random. For instance, the Euclidean distance…

模式识别中的相关性与高维一致性AI 解读

Classical discriminant analysis breaks down when the feature vectors are of extremely high dimension; for example, when the basic observation is a random function observed over a fine grid. Alternative methods have been developed assuming a simplified form for the covariance structure. We analyze the high-dimensional asymptotics of some of these methods, emphasizing the effects of correlations such as occur when the baseline is random. For instance, the Euclidean distance…

近似线性回归中一步 GM 估计量的泛函稳定性AI 解读

This paper provides a comparative sensitivity analysis of one-step Newton–Raphson estimators for linear regression. Such estimators have been proposed as a way to combine the global stability of high breakdown estimators with the local stability of generalized maximum likelihood estimators. We analyze this strategy, obtaining upper bounds for the maximum bias induced by $\varepsilon$-contamination of the model. These bounds yield break-down points and local rates of…

L1 统计分析及相关方法AI 解读

Prologue. Thoughts on Real Data and Statistics (Y. Dodge). Some Statistical Tools for the Analysis of Complex Molecular Spectra (A.F. Ruckstuhl). Estimation, Testing and Property Characterization. The Gauss Markov Property for the Median (G.W. Basset, Jr.,). A Class of Estimators Based on Adaptative Convex Combinations of Two Estimation Procedures (Y. Dodge, J. Jureckova). Robustness of L1 Regression in the Light of Linear Programming (J. Dupacova). A Linear Model with a…

污染偏差的下界：全局极小极大与局部线性估计AI 解读

We study how robust estimators can be in parametric families, obtaining a lower bound on the contamination bias of an estimator that holds for a wide class of parametric families. This lower bound includes as a special case the bound used to establish that the median is bias minimax among location equivariant estimators, and it is tight or nearly tight in a variety of other settings such as scale estimation, discrete exponential families and multiple linear regression. The…

统计检验的崩溃稳健性AI 解读

Power and level breakdown functions of a test statistic are introduced to obtain a unified analysis of local stability (as typified by the influence function) and global stability (as illustrated by the breakdown point). The power breakdown function gives the amount of contamination of each alternative distribution that can carry the test statistic to a null value. The level breakdown function gives the amount of contamination of a null distribution that can carry the test…

允许高剂量响应下降的剂量反应曲线非参数检验：渐近功效AI 解读

Dose-response experiments are widely used in scientific research and nonmonotone dose-response curves are commonly observed. A class of nonparametric tests for dose-response curves subject to downturns at high doses is examined via its asymptotic properties. This class includes the well-known Jonckheere-Terpstra test as a limiting case. The analysis indicates that the Jonckheere-Terpstra test lacks robustness to a downturn in the dose-response, and that other members of the…

Hellinger 偏差检验：效率、崩溃点与实例AI 解读

Hellinger distance analogs of likelihood ratio tests are proposed for parametric inference. The proposed tests are based on minimized Hellinger distances between nonparametric density estimates and densities corresponding to null and unconstrained parametric models. If the parametric model is correct, the Hellinger deviance test is asymptotically equivalent to the likelihood ratio test. A simulation study examines the relative performance of these tests in finite samples.…

计数数据分析中的最小 Hellinger 距离估计AI 解读

Minimum Hellinger distance (MHD) estimation is studied in the context of discrete data. The MHD estimator is shown to provide an effective treatment of anomalous data points, and its properties are illustrated using short-term mutagenicity test data. Asymptotic normality for a discrete distribution with countable support is derived under a readily verified condition on the model. Breakdown properties of the MHD estimator and an outlier screen are compared. Count data occur…

离散数据的 M 估计：渐近分布理论及其含义AI 解读

The asymptotic distribution of an $M$-estimator is studied when the underlying distribution is discrete. Asymptotic normality is shown to hold quite generally within the assumed parametric family. When the specification of the model is inexact, however, it is demonstrated that an $M$-estimator whose score function is not everywhere differentiable, e.g., a Huber estimator, has a nonnormal limiting distribution at certain distributions, resulting in unstable inference in the…

摘要暂缺

允许高剂量响应下降的剂量反应关系递归非参数检验AI 解读

A general recursive strategy is introduced to test nonparametrically for an increasing dose-response relationship when a downturn in response at high doses is possible. A specific implementation involving a test of Jonckheere (1954) and Terpstra (1952) is considered, and its size and power properties are investigated via Monte Carlo methods. Data from mutation research illustrate the phenomenon of concern.