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- Volume 5, 2018
Annual Review of Statistics and Its Application - Volume 5, 2018
Volume 5, 2018
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Robust Nonparametric Inference
Vol. 5 (2018), pp. 473–500More LessIn this article, we provide a personal review of the literature on nonparametric and robust tools in the standard univariate and multivariate location and scatter, as well as linear regression problems, with a special focus on sign and rank methods, their equivariance and invariance properties, and their robustness and efficiency. Beyond parametric models, the population quantities of interest are often formulated as location, scatter, skewness, kurtosis and other functionals. Some old and recent tools for model checking, dimension reduction, and subspace estimation in wide semiparametric models are discussed. We also discuss recent extensions of procedures in certain nonstandard semiparametric cases including clustered and matrix-valued data. Our personal list of important unsolved and future issues is provided.
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Topological Data Analysis
Vol. 5 (2018), pp. 501–532More LessTopological data analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. These methods include clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation and persistent homology. This paper reviews some of these methods.
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Principal Components, Sufficient Dimension Reduction, and Envelopes
Vol. 5 (2018), pp. 533–559More LessWe review probabilistic principal components, principal fitted components, sufficient dimension reduction, and envelopes, arguing that at their core they are all based on variations of the conditional independence argument that Fisher used to develop his fundamental concept of sufficiency. We emphasize the foundations of the methods. Methodological details, derivations, and examples are included when they convey the flavor and implications of basic concepts. In addition to the main topics, this review covers extensions of probabilistic principal components, the central subspace and central mean subspace, sliced inverse regression, sliced average variance estimation, dimension reduction for covariance matrices, and response and predictor envelopes.
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