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Abstract We address the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure. The difficulty of forecasting high-dimensional functional time series lies in the curse of dimensionality. In this paper, we propose a novel method to solve this problem. Dynamic functional principal component analysis is first applied to reduce each functional time series to a vector. We then use the factor model as a further dimension reduction technique so that only a small number of latent factors are preserved. Classic time series models can be used to forecast the factors and conditional forecasts of the functions can be constructed. Asymptotic properties of the approximated functions are established, including both estimation error and forecast error. The proposed method is easy to implement, especially when the dimension of the functional time series is large. We show the superiority of our approach by both simulation studies and an application to Japanese age-specific mortality rates. [ABSTRACT FROM AUTHOR]

Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized and represented in a number of different ways. Moreover, generalized Pareto distributions enjoy a number of interesting stability properties. An overview of the main features of such distributions is given, expressed compactly in several parametrizations, giving the potential user of these distributions a convenient catalogue of ways to handle and work with generalized Pareto distributions. [ABSTRACT FROM AUTHOR]

This paper studies vector quantile regression (VQR), which models the dependence of a random vector with respect to a vector of explanatory variables with enough flexibility to capture the whole conditional distribution, and not only the conditional mean. The problem of vector quantile regression is formulated as an optimal transport problem subject to an additional mean-independence condition. This paper provides results on VQR beyond the specified case which had been the focus of previous work. We show that even beyond the specified case, the VQR problem still has a solution which provides a general representation of the conditional dependence between random vectors. [ABSTRACT FROM AUTHOR]

The multivariate one-sample location problem is well studied in the literature, and several tests are available for it. But most of the existing one-sample tests perform poorly for high-dimensional data, and many of them are not even applicable when the dimension of the data exceeds the sample size. In this article, we develop and investigate some nonparametric one-sample tests based on functions of interpoint distances. These proposed tests can be conveniently used in high dimension, low sample size (HDLSS) situations, and good power properties of these tests for HDLSS data have been established using theoretical as well as numerical results. [ABSTRACT FROM AUTHOR]

In this paper we present a treatment for the estimation of variance components and estimable vectors in linear mixed models in which the relation matrices may not commute. To overcome this difficulty, we partition the mixed model in sub-models using orthogonal matrices. In addition, we obtain confidence regions and derive tests of hypothesis for the variance components. A numerical example is included. There we illustrate the estimation of the variance components using our treatment and compare the obtained estimates with the ones obtained by the ANOVA method. Besides this, we also present the restricted and unrestricted maximum likelihood estimates. [ABSTRACT FROM AUTHOR]

The multivariate Bayesian hierarchical model with independent means has been studied extensively and is widely used in practice. In contrast, the case of dependent means has received scant attention, even though multivariate observations are often correlated. In this paper, we investigate a multivariate heteroscedastic Bayesian hierarchical model in which an informative prior with equicorrelated means is assumed. We estimate the mean vector by the shrinkage estimator based on Stein’s unbiased risk estimation (SURE). It is shown that the squared error loss of the SURE estimator is close to that of an oracle estimator as the number of means grows. Our SURE estimator includes the SURE estimator under independence considered by Xie et al. (2012) as a special case. The finite-sample performance of our estimator is explored via simulations and two real data sets are used for illustration purposes. [ABSTRACT FROM AUTHOR]

Many inference techniques for multivariate data analysis assume that the rows of the data matrix are realizations of independent and identically distributed random vectors. Such an assumption will be met, for example, if the rows of the data matrix are multivariate measurements on a set of independently sampled units. In the absence of an independent random sample, a relevant question is whether or not a statistical model that assumes such row exchangeability is plausible. One method for assessing this plausibility is a statistical test of row covariation. Maintenance of a constant type I error rate regardless of the column covariance or matrix mean can be accomplished with a test that is invariant under an appropriate group of transformations. In the context of a class of elliptically contoured matrix-variate regression models (such as matrix normal models), it is shown that there are no non-trivial invariant tests if the number of rows is not sufficiently larger than the number of columns. Furthermore, even if the number of rows is large, there are no non-trivial invariant tests that have power to detect arbitrary row covariance in the presence of arbitrary column covariance. However, biased tests can be constructed that have power to detect certain types of row covariance that may be encountered in practice. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some conditions to compare multivariate mixture models with respect to some well-known multivariate stochastic orders. We also utilize the established results in reliability theory to compare the vectors of residual life-lengths of live components of ( n − k + 1 ) -out-of- n systems in both one sample and two samples situations. [ABSTRACT FROM AUTHOR]

Canonical correlation analysis (CCA) is a dimension-reduction technique in which two random vectors from high dimensional spaces are reduced to a new pair of low dimensional vectors after applying linear transformations to each of them, retaining as much information as possible. The components of the transformed vectors are called canonical variables. One seeks linear combinations of the original vectors maximizing the correlation subject to the constraint that they are to be uncorrelated with the previous canonical variables within each vector. By these means one actually gets two transformed random vectors of lower dimension whose expected square distance has been minimized subject to have uncorrelated components of unit variance within each vector. Since the closeness between the two transformed vectors is evaluated through a highly sensitive measure to outlying observations as the mean square loss, the linear transformations we are seeking are also affected. In this paper we use a robust univariate dispersion measure (like an M-scale) based on the distance of the transformed vectors to derive robust S-estimators for canonical vectors and correlations. An iterative algorithm is performed by exploiting the existence of efficient algorithms for S-estimation in the context of Principal Component Analysis. Some convergence properties are analyzed for the iterative algorithm. A simulation study is conducted to compare the new procedure with some other robust competitors available in the literature, showing a remarkable performance. We also prove that the proposal is Fisher consistent. [ABSTRACT FROM AUTHOR]

This paper considers testing the equality of multiple high-dimensional mean vectors under dependency. We propose a test that is based on a linear transformation of the data by the precision matrix which incorporates the dependence structure of the variables. The limiting null distribution of the test statistic is derived and is shown to be the extreme value distribution of type I. The convergence to the limiting distribution is, however, slow when the number of groups is relatively large. An intermediate correction factor is introduced which significantly improves the accuracy of the test. It is shown that the test is particularly powerful against sparse alternatives and enjoys certain optimality. A simulation study is carried out to examine the numerical performance of the test and compare with other tests given in the literature. The numerical results show that the proposed test significantly outperforms those tests against sparse alternatives. [ABSTRACT FROM AUTHOR]

In this paper we define distributions on the moment spaces corresponding to p × p real or complex matrix measures on the real line with an unbounded support. For random vectors on the unbounded matricial moment spaces we prove the convergence in distribution to the Gaussian orthogonal ensemble or the Gaussian unitary ensemble, respectively. [ABSTRACT FROM AUTHOR]

A new method is proposed for estimating the difference between the high-dimensional mean vectors of two multivariate normal populations with equal covariance matrix based on an ł1 penalized normal likelihood. It is well known that the normal likelihood involves the covariance matrix which is usually unknown. We substitute the adaptive thresholding estimator given by Cai and Liu (2011) of the covariance matrix, and then estimate the difference between the mean vectors by maximizing the ł1 penalized normal likelihood. Under the high-dimensional framework where both the sample size and the dimension tend to infinity, we show that the proposed estimator has sign recovery and also derive its mean squared error. We also compare the proposed estimator with the soft-thresholding and the adaptive soft-thresholding estimators which give simple thresholdings for the sample mean vector. [ABSTRACT FROM AUTHOR]

Abstract: We obtain random vectors with null third-order cumulants by projecting the data onto appropriate subspaces. Statistical applications include, but are not limited to, the robustification of Hotelling’s test against nonnormality. Our approach only requires the existence of the third-order moments and leads to normal transformed variables when the parent distribution belongs to well-known classes of sample selection models. [Copyright &y& Elsevier]

Abstract: Different concepts of neutrality have been studied in the literature in context of independence properties of vectors of random probabilities, in particular, for Dirichlet random vectors. Some neutrality conditions led to characterizations of the Dirichlet distribution. In this paper we provide a new characterization in terms of neutrality with respect to two partitions, which generalizes previous results. In particular, no restrictions on the size of the vector of random probabilities are imposed. In the proof we enhance the moments method approach proposed in Bobecka and Wesołowski (2009) [2] by combining it with some graph theoretic techniques. [Copyright &y& Elsevier]