查看更多>>摘要：We propose computationally efficient methods for estimating stationary multivariate spatial and spatial-temporal spectra from incomplete gridded data. The methods are iterative and rely on successive imputation of data and updating of model estimates. Imputations are done according to a periodic model on an expanded domain. The periodicity of the imputations is a key feature that reduces edge effects in the periodogram and is facilitated by efficient circulant embedding techniques. In addition, we describe efficient methods for decomposing the estimated cross spectral density function into a linear model of coregionalization plus a residual process. The methods are applied to two storm datasets, one of which is from Hurricane Florence, which struck the southeastern United States in September 2018. The application demonstrates how fitted models from different datasets can be compared, and how the methods are computationally feasible on datasets with more than 200,000 total observations. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Improving estimation efficiency for regression coefficients is an important issue in the analysis of longitudinal data, which involves estimating the covariance matrix of the within-subject errors. In the balanced or nearly balanced setting, we can also regard the covariance matrix of the dependent errors as the bivariate covariance function evaluated at specific time points. In this paper, we compare the performance of the proposed regularized-covariance-function-based estimator and the conventional high-dimensional covariance matrix estimator of the within-subject errors. It shows that when the number p of the time points in each subject is large enough compared to the number n of the subjects, i.e., p >> n(1/4) log n, the estimation errors of the high-dimensional covariance matrix will be accumulated, therefore the error bound of the proposed regularized covariance-function-based estimator will be smaller than that of the high-dimensional covariance matrix estimator in Frobenius norm. We also assess the performance of these two estimators for the incomplete longitudinal data. All the comparisons and theoretical results are illustrated using both simulated and real data. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In recent years, shrinkage priors have received much attention in high-dimensional data analysis from a Bayesian perspective. Compared with widely used spike-and-slab priors, shrinkage priors have better computational efficiency. But the theoretical properties, especially posterior contraction rate, which is important in uncertainty quantification, are not established in many cases. In this paper, we apply global-local shrinkage priors to high-dimensional multivariate linear regression with unknown covariance matrix. We show that when the prior is highly concentrated near zero and has heavy tail, the posterior contraction rates for both coefficients matrix and covariance matrix are nearly optimal. Our results hold when number of features p grows much faster than the sample size n, which is of great interest in modern data analysis. We show that a class of readily implementable scale mixture of normal priors satisfies the conditions of the main theorem. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In a varying means model, the temporary evolution of a p-vector system is determined by p deterministic nonparametric functions superimposed by error terms, possibly dependent cross sectionally. The basic interest is in linear combinations across the p dimensions that make the deterministic functions constant over time. The number of such linearly independent linear combinations is referred to as a cotrending dimension, and their spanned space as a cotrending space. This work puts forward a framework to test statistically for cotrending dimension and space. Connections to principal component analysis and cointegration are also considered. Finally, a simulation study to assess the finite-sample performance of the proposed tests, and applications to several real data sets are also provided. (c) 2021 Elsevier Inc. All rights reserved.
Nasri, Bouchra R.Remillard, Bruno N.Bahraoui, Tarik
18页
查看更多>>摘要：In this article we show that under weak assumptions, the change-point tests designed for independent random vectors can also be used with pseudo-observations for testing change-point in the joint distribution of non-observable random vectors, the associated copula, or the margins, without modifying the limiting distributions. In particular, change-point tests can be applied to the residuals of stochastic volatility models or conditional distribution functions applied to the observations, which are prime examples of pseudo-observations. Since the limiting distribution of test statistics depends on the unknown joint distribution function or its associated unknown copula when the dimension is greater than one, we also show that iid multipliers and traditional bootstrap can be used with pseudo-observations to approximate P-values for the test statistics. Numerical experiments are performed in order to compare the different statistics and bootstrapping methods. Examples of applications to change-point problems are given. The R package changepointTests (Nasri and Remillard, 2021) includes all the methodologies proposed in this article. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Multiply robust estimation with missing data is considered as an important field in statistics, which incorporates information by weighting multiply candidate models and loosens the requirement of the model specification. Nevertheless, in high-dimensional cases one more flexible hypothesis is the "true structure"beyond the correct model. In this paper, we study the parametric estimation for high-order autoregressive processes with a lagged-dependent binary explanatory variable that is missing at random (MAR). Based on the "true structure"specification, we propose a penalized multiply robust estimation equation in the presence of multiply candidate model sets. The selecting criterion for optimal tuning parameters is modified for the model identification with incomplete data. We validate that our tuning criterion can correctly distinguish the true autoregressive coefficients from zero asymptotically, the estimators of population parameters enjoy the oracle properties as well. Some simulations are carried out and we apply the method to fit the model for the U.S. Industrial Production Index data and produce out-of-sample forecasts to confirm the rationality of results. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The Birnbaum-Saunders distribution has been generalized in various ways, for parametric or nonparametric statistical inference. In this paper, as a remedy for the boundary bias problem of nonparametric density estimation, a family of deformed multivariate elliptical-based non-central Birnbaum-Saunders kernel density estimators is introduced, and its asymptotic mean integrated squared error is discussed. The simulation results reveal that a novel log-elliptical density estimator has a good performance in small sample size. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Conventional linear mixed-effects modeling is routinely challenging when the validity of necessary assumptions is suspicious. In particular, robustifying model fitting is appealing in the presence of potential outlying points. This paper introduces a robust regression methodology in a parametric setting by constructing a novel multivariate skew-Huber distribution for longitudinal data with heavy-tails and skewed structures. Unlike preceding studies, our model allows for jointly estimating the tuning parameter, which controls the impact of outliers, with all other parameters using an undemanding computational algorithm. Moreover, by promoting an unconstrained parameterization through the modified Cholesky decomposition, the estimate of variance-covariance components can be merely accessible. We also present a spline mixed model to account for the covariate effect. To highlight the usefulness of our methodology, we conducted a simulation study and analyzed a data set collected on type 2 diabetic patients with microalbuminuria over a 6-year prospective cohort study. Findings show that our proposed robust model leads to convincing conclusions in empirical studies. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：New inference methods for the multivariate coefficient of variation and its reciprocal, the standardized mean, are presented. While there are various testing procedures for both parameters in the univariate case, it is less known how to do inference in the multivariate setting appropriately. There are some existing procedures but they rely on restrictive assumptions on the underlying distributions. We tackle this problem by applying Wald-type statistics in the context of general, potentially heteroscedastic factorial designs. In addition to the k-sample case, higher-way layouts can be incorporated into this framework allowing the discussion of main and interaction effects. The resulting procedures are shown to be asymptotically valid under the null hypothesis and consistent under general alternatives. To improve the finite sample performance, we suggest permutation versions of the tests and show that the tests' asymptotic properties can be transferred to them. An exhaustive simulation study compares the new tests, their permutation counterparts and existing methods. To further analyze the differences between the tests, we conduct two illustrative real data examples. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Multivariate sample spaces may be incomplete Cartesian products, when certain combi-nations of the categories of the variables are not possible. Traditional log-linear models, which generalize independence and conditional independence, do not apply in such cases, as they may associate positive probabilities with the non-existing cells. To describe the association structure in incomplete sample spaces, this paper develops a class of hi-erarchical multiplicative models which are defined by setting certain non-homogeneous generalized odds ratios equal to one and are named after Aitchison and Silvey who were among the first to consider such ratios. These models are curved exponential families that do not contain an overall effect and, from an algebraic perspective, are non-homogeneous toric ideals. The relationship of this model class with log-linear models and quasi log-linear models is studied in detail in terms of both statistics and algebraic geometry. The existence of maximum likelihood estimates and their properties, as well as the relevant algorithms are also discussed. (c) 2021 Elsevier Inc. All rights reserved.
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