Richard A. Davis, Mikkel Slot Nielsen, Victor Rohde.

Source: Bernoulli, Volume 26, Number 2, 799--827.

Abstract:
In this paper, we introduce a model, the stochastic fractional delay differential equation (SFDDE), which is based on the linear stochastic delay differential equation and produces stationary processes with hyperbolically decaying autocovariance functions. The model departs from the usual way of incorporating this type of long-range dependence into a short-memory model as it is obtained by applying a fractional filter to the drift term rather than to the noise term. The advantages of this approach are that the corresponding long-range dependent solutions are semimartingales and the local behavior of the sample paths is unaffected by the degree of long memory. We prove existence and uniqueness of solutions to the SFDDEs and study their spectral densities and autocovariance functions. Moreover, we define a subclass of SFDDEs which we study in detail and relate to the well-known fractionally integrated CARMA processes. Finally, we consider the task of simulating from the defining SFDDEs.

Elena Issoglio, Francesco Russo.

Source: Bernoulli, Volume 26, Number 1, 728--766.

Abstract:
In this paper, we investigate BSDEs where the driver contains a distributional term (in the sense of generalised functions) and derive general Feynman–Kac formulae related to these BSDEs. We introduce an integral operator to give sense to the equation and then we show the existence of a strong solution employing results on a related PDE. Due to the irregularity of the driver, the $Y$-component of a couple $(Y,Z)$ solving the BSDE is not necessarily a semimartingale but a weak Dirichlet process.

Stanislav Minsker, Xiaohan Wei.

Source: Bernoulli, Volume 26, Number 1, 694--727.

Abstract:
Let $Y$ be a $d$-dimensional random vector with unknown mean $mu $ and covariance matrix $Sigma $. This paper is motivated by the problem of designing an estimator of $Sigma $ that admits exponential deviation bounds in the operator norm under minimal assumptions on the underlying distribution, such as existence of only 4th moments of the coordinates of $Y$. To address this problem, we propose robust modifications of the operator-valued U-statistics, obtain non-asymptotic guarantees for their performance, and demonstrate the implications of these results to the covariance estimation problem under various structural assumptions.

Alexander Schnurr.

Source: Bernoulli, Volume 26, Number 1, 642--663.

Abstract:
We extend the class of semimartingales in a natural way. This allows us to incorporate processes having paths that leave the state space $mathbb{R}^{d}$. In particular, Markov processes related to sub-Markovian kernels, but also non-Markovian processes with path-dependent behavior. By carefully distinguishing between two killing states, we are able to introduce a fourth semimartingale characteristic which generalizes the fourth part of the Lévy quadruple. Using the probabilistic symbol, we analyze the close relationship between the generators of certain Markov processes with killing and their (now four) semimartingale characteristics.

Nicolas Privault, Grzegorz Serafin.

Source: Bernoulli, Volume 26, Number 1, 587--615.

Abstract:
We derive normal approximation bounds in the Kolmogorov distance for sums of discrete multiple integrals and weighted $U$-statistics made of independent Bernoulli random variables. Such bounds are applied to normal approximation for the renormalized subgraph counts in the Erdős–Rényi random graph. This approach completely solves a long-standing conjecture in the general setting of arbitrary graph counting, while recovering recent results obtained for triangles and improving other bounds in the Wasserstein distance.

Eric Beutner, Laurent Bordes, Laurent Doyen.

Source: Bernoulli, Volume 26, Number 1, 557--586.

Abstract:
Virtual age models are very useful to analyse recurrent events. Among the strengths of these models is their ability to account for treatment (or intervention) effects after an event occurrence. Despite their flexibility for modeling recurrent events, the number of applications is limited. This seems to be a result of the fact that in the semiparametric setting all the existing results assume the virtual age function that describes the treatment (or intervention) effects to be known. This shortcoming can be overcome by considering semiparametric virtual age models with parametrically specified virtual age functions. Yet, fitting such a model is a difficult task. Indeed, it has recently been shown that for these models the standard profile likelihood method fails to lead to consistent estimators. Here we show that consistent estimators can be constructed by smoothing the profile log-likelihood function appropriately. We show that our general result can be applied to most of the relevant virtual age models of the literature. Our approach shows that empirical process techniques may be a worthwhile alternative to martingale methods for studying asymptotic properties of these inference methods. A simulation study is provided to illustrate our consistency results together with an application to real data.

Zhuang Ma, Xiaodong Li.

Source: Bernoulli, Volume 26, Number 1, 432--470.

Abstract:
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by the recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose two losses based on the principal angles between the model spaces spanned by the sample canonical variates and their population correspondents, respectively. We further characterize the non-asymptotic error bounds for the estimation risks under the proposed error metrics, which reveal how the performance of sample CCA depends adaptively on key quantities including the dimensions, the sample size, the condition number of the covariance matrices and particularly the population canonical correlation coefficients. The optimality of our uniform upper bounds is also justified by lower-bound analysis based on stringent and localized parameter spaces. To the best of our knowledge, for the first time our paper separates $p_{1}$ and $p_{2}$ for the first order term in the upper bounds without assuming the residual correlations are zeros. More significantly, our paper derives $(1-lambda_{k}^{2})(1-lambda_{k+1}^{2})/(lambda_{k}-lambda_{k+1})^{2}$ for the first time in the non-asymptotic CCA estimation convergence rates, which is essential to understand the behavior of CCA when the leading canonical correlation coefficients are close to $1$.

Xiucai Ding.

Source: Bernoulli, Volume 26, Number 1, 387--417.

Abstract:
We consider the recovery of a low rank $M imes N$ matrix $S$ from its noisy observation $ ilde{S}$ in the high dimensional framework when $M$ is comparable to $N$. We propose two efficient estimators for $S$ under two different regimes. Our analysis relies on the local asymptotics of the eigenstructure of large dimensional rectangular matrices with finite rank perturbation. We derive the convergent limits and rates for the singular values and vectors for such matrices.

Irina Gaynanova.

Source: Bernoulli, Volume 26, Number 1, 286--322.

Abstract:
Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the corresponding prediction and estimation consistency results have been lacking. We bridge this gap by providing probabilistic bounds on out-of-sample prediction error and estimation error of multi-class penalized optimal scoring allowing for diverging number of classes.

Stepan Mazur, Dmitry Otryakhin, Mark Podolskij.

Source: Bernoulli, Volume 26, Number 1, 226--252.

Abstract:
In this paper, we investigate the parametric inference for the linear fractional stable motion in high and low frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural non-Gaussian analogue of the scaled fractional Brownian motion. It is fully characterised by the scaling parameter $sigma>0$, the self-similarity parameter $Hin(0,1)$ and the stability index $alphain(0,2)$ of the driving stable motion. The parametric estimation of the model is inspired by the limit theory for stationary increments Lévy moving average processes that has been recently studied in ( Ann. Probab. 45 (2017) 4477–4528). More specifically, we combine (negative) power variation statistics and empirical characteristic functions to obtain consistent estimates of $(sigma,alpha,H)$. We present the law of large numbers and some fully feasible weak limit theorems.

Michael V. Boutsikas, Eutichia Vaggelatou

Source: Bernoulli, Volume 16, Number 2, 301--330.

Abstract:
Let X 1 , X 2 , …, X n be a sequence of independent or locally dependent random variables taking values in ℤ + . In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the distribution of the sum ∑ i =1 n X i and an appropriate Poisson or compound Poisson distribution. These bounds include a factor which depends on the smoothness of the approximating Poisson or compound Poisson distribution. This “smoothness factor” is of order O( σ −2 ), according to a heuristic argument, where σ 2 denotes the variance of the approximating distribution. In this way, we offer sharp error estimates for a large range of values of the parameters. Finally, specific examples concerning appearances of rare runs in sequences of Bernoulli trials are presented by way of illustration.

Thomson (Family)

Fuhlbohm (Family)

Siekmann, Francis Heinrich Ernst, 1830-1917.

Hewish Henry -- Family.

Grant (Family)

Hicks (Family)

Klemm (Family)

King's Orphan Schools (New Town, Tas.)

Genetic genealogy -- Handbooks, manuals, etc.

Germans -- South Australia.

Cheesman, John -- Family.

Traeger, Ernst Wilhelm, 1805-1874.

Fuhlbohm (Family)

Huppatz (Family).

Nixon, Geoffrey Owen, 1921-2011.

Three weeks before he was shot dead, Miguel Calderon, an inmate in the lawless Los Llanos jail on Venezuela's central plains, sent a voice message to his father. Like many of the prisoners in Venezuela's overcrowded and violent penitentiaries, Los Llanos's 4,000 inmates normally subsist on food relatives bring them. The guards, desperate themselves amid national shortages, began stealing the little food getting behind bars, inmates said, forcing some prisoners to turn to eating stray animals.

Vice President Pence’s trip to Iowa shows how the Trump administration’s aims to move past coronavirus are sometimes complicated by the virus itself.

U.S. Chief Justice John Roberts on Friday put a temporary hold on the disclosure to a Democratic-led House of Representatives committee of grand jury material redacted from former Special Counsel Robert Mueller's report on Russian interference in the 2016 election. The U.S. Court of Appeals for the District of Columbia Circuit ruled in March that the materials had to be disclosed to the House Judiciary Committee and refused to put that decision on hold. The appeals court said the materials had to be handed over by May 11 if the Supreme Court did not intervene.

Boeing CEO Dave Calhoun said the company was aiming to resume production this month, despite the ongoing grounding and coronavirus pandemic.

Barack Obama said the “rule of law is at risk” following the justice department’s decision to drop charges against former Trump advisor Mike Flynn, as he issued a stark warning about the long-term impact on the American way of life by his successor.

The military is preparing to deploy to the region to try to stop illegal logging and mining.

Georgia is one of four states that doesn't have a hate crime law. Arbery's killing has reignited calls for legislation.

The ongoing investigation of the fatal shooting in Brunswick, Georgia, will also look at a neighbor of suspects Gregory and Travis McMichael who recorded video of the incident, authorities said.

Jami J. Mulgrave, Subhashis Ghosal.

Source: Bayesian Analysis, Volume 15, Number 2, 449--475.

Abstract:
Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for continuous variables where it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformations on each of them. We consider a Bayesian approach in the nonparanormal graphical model by putting priors on the unknown transformations through a random series based on B-splines where the coefficients are ordered to induce monotonicity. A truncated normal prior leads to partial conjugacy in the model and is useful for posterior simulation using Gibbs sampling. On the underlying precision matrix of the transformed variables, we consider a spike-and-slab prior and use an efficient posterior Gibbs sampling scheme. We use the Bayesian Information Criterion to choose the hyperparameters for the spike-and-slab prior. We present a posterior consistency result on the underlying transformation and the precision matrix. We study the numerical performance of the proposed method through an extensive simulation study and finally apply the proposed method on a real data set.

Andrés F. Barrientos, Víctor Peña.

Source: Bayesian Analysis, Volume 15, Number 2, 363--388.

Abstract:
In this article, we present data-subsetting algorithms that allow for the approximate and scalable implementation of the Bayesian bootstrap. They are analogous to two existing algorithms in the frequentist literature: the bag of little bootstraps (Kleiner et al., 2014) and the subsampled double bootstrap (Sengupta et al., 2016). Our algorithms have appealing theoretical and computational properties that are comparable to those of their frequentist counterparts. Additionally, we provide a strategy for performing lossless inference for a class of functionals of the Bayesian bootstrap and briefly introduce extensions to the Dirichlet Process.

Qingpo Cai, Jian Kang, Tianwei Yu.

Source: Bayesian Analysis, Volume 15, Number 1, 79--102.

Abstract:
Selecting informative nodes over large-scale networks becomes increasingly important in many research areas. Most existing methods focus on the local network structure and incur heavy computational costs for the large-scale problem. In this work, we propose a novel prior model for Bayesian network marker selection in the generalized linear model (GLM) framework: the Thresholded Graph Laplacian Gaussian (TGLG) prior, which adopts the graph Laplacian matrix to characterize the conditional dependence between neighboring markers accounting for the global network structure. Under mild conditions, we show the proposed model enjoys the posterior consistency with a diverging number of edges and nodes in the network. We also develop a Metropolis-adjusted Langevin algorithm (MALA) for efficient posterior computation, which is scalable to large-scale networks. We illustrate the superiorities of the proposed method compared with existing alternatives via extensive simulation studies and an analysis of the breast cancer gene expression dataset in the Cancer Genome Atlas (TCGA).