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This paper considers the problem of inferring the causal effect of a variable Z on a dependently censored survival time T. We allow for unobserved confounding variables, such that the error term of the regression model for T is dependent on the confounded variable Z. Moreover, T is subject to dependent censoring. This means that T is right censored by a censoring time C, which is dependent on T (even after conditioning out the effects of the measured covariates). A control function approach, relying on an instrumental variable, is leveraged to tackle the confounding issue. Further, it is assumed that T and C follow a joint regression model with bivariate Gaussian error terms and an unspecified covariance matrix, such that the dependent censoring can be handled in a flexible manner. Conditions under which the model is identifiable are given, a two-step estimation procedure is proposed, and it is shown that the resulting estimator is consistent and asymptotically normal. Simulations are used to confirm the validity and finite-sample performance of the estimation procedure. Finally, the proposed method is used to estimate the causal effect of job training programs on unemployment duration.

The discussion focuses on the different choices that are made by the user in carrying out shape-based functional data analysis. First, there is the choice of an additional warping penalty that can be included in the procedure. An object-oriented data analysis approach can be useful for selecting such a warping penalty, and an example from monitoring peatland is given. Also, there is a choice to be made about whether the analysis is in a quotient manifold or an ambient space. There are advantages and disadvantages to either strategy, but in many examples, the results are similar due to a Laplace approximation. The final comment states that the authors provide plenty of convincing approaches with many useful insights. It is clear that the square root velocity function (SRVF) and transported SRVF methods will give solutions to many more problems in the future.

Correlation matrices are an essential tool for investigating the dependency structures of random vectors or comparing them. We introduce an approach for testing a variety of null hypotheses that can be formulated based upon the correlation matrix. Examples cover MANOVA-type hypothesis of equal correlation matrices as well as testing for special correlation structures such as sphericity. Apart from existing fourth moments, our approach requires no other assumptions, allowing applications in various settings. To improve the small sample performance, a bootstrap technique is proposed and theoretically justified. Based on this, we also present a procedure to simultaneously test the hypotheses of equal correlation and equal covariance matrices. The performance of all new test statistics is compared with existing procedures through extensive simulations.

Tensor eigenvectors naturally generalize matrix eigenvectors to multi-way arrays: eigenvectors of symmetric tensors of order k and dimension p are stationary points of polynomials of degree k in p variables on the unit sphere. Dominant eigenvectors of symmetric tensors maximize polynomials in several variables on the unit sphere, while base eigenvectors are roots of polynomials in several variables. In this paper, we focus on skewness-based projection pursuit and on third-order tensor eigenvectors, which provide the simplest, yet relevant connections between tensor eigenvectors and projection pursuit. Skewness-based projection pursuit finds interesting data projections using the dominant eigenvector of the sample third standardized cumulant to maximize skewness. Skewness-based projection pursuit also uses base eigenvectors of the sample third cumulant to remove skewness and facilitate the search for interesting data features other than skewness. Our contribution to the literature on tensor eigenvectors and on projection pursuit is twofold. Firstly, we show how skewness-based projection pursuit might be helpful in sequential cluster detection. Secondly, we show some asymptotic results regarding both dominant and base tensor eigenvectors of sample third cumulants. The practical relevance of the theoretical results is assessed with six well-known data sets.

For (d ge 2), let X be a random vector having a Bingham distribution on ({mathcal {S}}^{d-1}), the unit sphere centered at the origin in ({mathbb {R}}^d), and let (Sigma ) denote the symmetric matrix parameter of the distribution. Let (Psi (Sigma )) be the normalizing constant of the distribution and let (nabla Psi _d(Sigma )) be the matrix of first-order partial derivatives of (Psi (Sigma )) with respect to the entries of (Sigma ). We derive complete asymptotic expansions for (Psi (Sigma )) and (nabla Psi _d(Sigma )), as (d rightarrow infty ); these expansions are obtained subject to the growth condition that (Vert Sigma Vert ), the Frobenius norm of (Sigma ), satisfies (Vert Sigma Vert le gamma _0 d^{r/2}) for all d, where (gamma _0 > 0) and (r in [0,1)). Consequently, we obtain for the covariance matrix of X an asymptotic expansion up to terms of arbitrary degree in (Sigma ). Using a range of values of d that have appeared in a variety of applications of high-dimensional spherical data analysis, we tabulate the bounds on the remainder terms in the expansions of (Psi (Sigma )) and (nabla Psi _d(Sigma )) and we demonstrate the rapid convergence of the bounds to zero as r decreases.

We consider the problem of detecting distributional changes in a sequence of high dimensional data. Our approach combines two separate statistics stemming from (L_p) norms whose behavior is similar under (H_0) but potentially different under (H_A), leading to a testing procedure that that is flexible against a variety of alternatives. We establish the asymptotic distribution of our proposed test statistics separately in cases of weakly dependent and strongly dependent coordinates as (min {N,d}rightarrow infty ), where N denotes sample size and d is the dimension, and establish consistency of testing and estimation procedures in high dimensions under one-change alternative settings. Computational studies in single and multiple change point scenarios demonstrate our method can outperform other nonparametric approaches in the literature for certain alternatives in high dimensions. We illustrate our approach through an application to Twitter data concerning the mentions of U.S. governors.

In the Big Data era, with the ubiquity of geolocation sensors in particular, massive datasets exhibiting a possibly complex spatial dependence structure are becoming increasingly available. In this context, the standard probabilistic theory of statistical learning does not apply directly and guarantees of the generalization capacity of predictive rules learned from such data are left to establish. We analyze here the simple Kriging task, the flagship problem in Geostatistics, from a statistical learning perspective, i.e., by carrying out a nonparametric finite-sample predictive analysis. Given (dge 1) values taken by a realization of a square integrable random field (X={X_s}_{sin S}), (Ssubset {mathbb {R}}^2), with unknown covariance structure, at sites (s_1,; ldots ,; s_d) in S, the goal is to predict the unknown values it takes at any other location (sin S) with minimum quadratic risk. The prediction rule being derived from a training spatial dataset: a single realization (X') of X, is independent from those to be predicted, observed at (nge 1) locations (sigma _1,; ldots ,; sigma _n) in S. Despite the connection of this minimization problem with kernel ridge regression, establishing the generalization capacity of empirical risk minimizers is far from straightforward, due to the non-independent and identically distributed nature of the training data (X'_{sigma _1},; ldots ,; X'_{sigma _n}) involved in the learning procedure. In this article, non-asymptotic bounds of order (O_{{mathbb {P}}}(1/sqrt{n})) are proved for the excess risk of a plug-in predictive rule mimicking the true minimizer in the case of isotropic stationary Gaussian processes, observed at locations forming a regular grid in the learning stage. These theoretical results, as well as the role played by the technical conditions required to establish them, are illustrated by various numerical experiments, on simulated data and on real-world datasets, and hopefully pave the way for further developments in statistical learning based on spatial data.

We address the problem of testing for the invariance of a probability measure under the action of a group of linear transformations. We propose a procedure based on consideration of one-dimensional projections, justified using a variant of the Cramér–Wold theorem. Our test procedure is powerful, computationally efficient, and dimension-independent, extending even to the case of infinite-dimensional spaces (multivariate functional data). It includes, as special cases, tests for exchangeability and sign-invariant exchangeability. We compare our procedure with some previous proposals in these cases, in a small simulation study. The paper concludes with two real-data examples.