Miracle-dz/UniFAR-FTUs huggingface dataset:
Grouped Variable Selection via Nested Spike and Slab Priors

In this paper we study grouped variable selection problems by proposing a specified prior, called the nested spike and slab prior, to model collective behavior of regression coefficients. At the group level, the nested spike and slab prior puts positive mass on the event that the l2-norm of the grouped coefficients is equal to zero. At the individual level, each coefficient is assumed to follow a spike and slab prior. We carry out maximum a posteriori estimation for the model by applying blockwise coordinate descent algorithms to solve an optimization problem involving an approximate objective modified by majorization-minimization techniques. Simulation studies show that the proposed estimator performs relatively well in the situations in which the true and redundant covariates are both covered by the same group. Asymptotic analysis under a frequentist's framework further shows that the l2 estimation error of the proposed estimator can have a better upper bound if the group that covers the true covariates does not cover too many redundant covariates. In addition, given some regular conditions hold, the proposed estimator is asymptotically invariant to group structures, and its model selection consistency can be established without imposing irrepresentable-type conditions.
Multiple Testing for Exploratory Research

Motivated by the practice of exploratory research, we formulate an approach to multiple testing that reverses the conventional roles of the user and the multiple testing procedure. Traditionally, the user chooses the error criterion, and the procedure the resulting rejected set. Instead, we propose to let the user choose the rejected set freely, and to let the multiple testing procedure return a confidence statement on the number of false rejections incurred. In our approach, such confidence statements are simultaneous for all choices of the rejected set, so that post hoc selection of the rejected set does not compromise their validity. The proposed reversal of roles requires nothing more than a review of the familiar closed testing procedure, but with a focus on the non-consonant rejections that this procedure makes. We suggest several shortcuts to avoid the computational problems associated with closed testing.
Coupled MCMC with a randomized acceptance probability

We consider Metropolis Hastings MCMC with tar- get �(�) in cases where the log of the ratio of target distributions D = log(�(� ' )/�(�)) is replaced by an estimator ˆ D(W). The esti- mator is based on m samples W = (W1,W2,.,Wm) from an inde- pendent online Monte Carlo simulation. Under some conditions on the distribution of ˆ D(W) the process resembles Metropolis Hast- ings MCMC with a randomized transition kernel. When this is the case there is a correction to the estimated acceptance proba- bility which ensures that the target distribution remains the equi- librium distribution. The simplest versions of the penalty method of Ceperley and Dewing 1999 (6), the universal algorithm of Ball et al. 2003 (3) and the single variable exchange algorithm of Murray et al. 2006 (15) are special cases. In many applications of interest the correction terms cannot be computed. We consider approxi- mate versions of the algorithms. We show that on average O(m) of the samples realized by a simulation approximating a randomized chain of length n are exactly the same as those of a coupled (exact) randomized chain. Approximation biases Monte Carlo estimates with terms O(1/m) or smaller. This should be compared to the Monte Carlo error which is O(1/ √ n). Monte Carlo simulation offers a direct route to statistical inference for many otherwise awkward fitting problems. The class of problems which may be treated using Markov chain Monte Carlo (MCMC) and Sequential Monte Carlo has grown a great deal since the core algorithms were proposed (12, 7). One of the most important recent advances (11, 4, 2, 1) has given us pseudo-marginal MCMC algorithms which are useful for some doubly intractable distributions. Such distributions are hard to simulate as we cannot readily compute the ratio of densities at two values of the target variable. Algorithms with a pseudo-marginal target distribution put an estimate for the target distribution in the Monte Carlo state along with the target variable. In this paper we give a class of MCMC algorithms characterized by a pseudo-marginal transition probability kernel. In these algorithms the Monte Carlo state 1
Edge universality of correlation matrices

xij = 0 and E e 2 = 1 M , N,M → ∞. These entries have a sub-exponential decay at the tails. We will be working in the regime N/M = dN,limN! 1 dN 6 0,1,∞. In this paper we prove the edge universality of correlation matrices X † X, where the rectangular matrix X (called the standardized matrix) is obtained by normalizing each column of the data matrix e X by its Euclidean norm. Our main result states that, asymptotically the k-point (k > 1) correlation functions of the extreme eigenvalues (at both edges of the spectrum) of the correlation matrix X † X converge to those of the Gaussian correlation matrix, i.e., Tracy-Widom law, and thus in particular, the largest and the smallest eigenvalues of X † X after appropriate centering and rescaling converge to the Tracy-Widom distribution. The asymptotic distribution of extreme eigenvalues of the Gaussian correlation matrix has been worked out only recently. As a corollary of the main result in this paper, we also obtain that the extreme eigenvalues of Gaussian correlation matrices are asymptotically distributed according to the TracyWidom law. The proof is based on the comparison of Green functions, but the key obstacle to be surmounted is the strong dependence of the entries of the correlation matrix. We achieve this via a novel argument which involves comparing the moments of product of the entries of the standardized data matrix to those of the raw data matrix. Our proof strategy may be extended for proving the edge universality of other random matrix ensembles with dependent entries and hence is of independent interest.
Survival-supervised latent Dirichlet allocation models for genomic analysis of time-to-event outcomes

Two challenging problems in the clinical study of cancer are the characterization of cancer subtypes and the classification of individual patients according to those subtypes. Statistical approaches addressing these problems are hampered by population heterogeneity and challenges inherent in data integration across high-dimensional, diverse covariates. We have developed a survival-supervised latent Dirichlet allocation (survLDA) modeling framework to address these concerns. LDA models have proven extremely effective at identifying themes common across large collections of text, but applications to genomics have been limited. Our framework extends LDA to the genome by considering each patient as a `document' with `text' constructed from clinical and high-dimensional genomic measurements. We then further extend the framework to allow for supervision by a time-to-event response. The model enables the efficient identification of collections of clinical and genomic features that co-occur within patient subgroups, and then characterizes each patient by those features. An application of survLDA to The Cancer Genome Atlas (TCGA) ovarian project identifies informative patient subgroups that are characterized by different propensities for exhibiting abnormal mRNA expression and methylations, corresponding to differential rates of survival from primary therapy.
Confidence intervals for low dimensional parameters in high dimensional linear models

The purpose of this paper is to propose methodologies for statistical inference of low dimensional parameters with high dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of several of them in a linear regression model, although our ideas are applicable in a much broader context. The theoretical results that are presented provide sufficient conditions for the asymptotic normality of the proposed estimators along with a consistent estimator for their finite dimensional covariance matrices. These sufficient conditions allow the number of variables to exceed the sample size and the presence of many small non‐zero coefficients. Our methods and theory apply to interval estimation of a preconceived regression coefficient or contrast as well as simultaneous interval estimation of many regression coefficients. Moreover, the method proposed turns the regression data into an approximate Gaussian sequence of point estimators of individual regression coefficients, which can be used to select variables after proper thresholding. The simulation results that are presented demonstrate the accuracy of the coverage probability of the confidence intervals proposed as well as other desirable properties, strongly supporting the theoretical results.
Third-order Asymptotic Optimality of the Generalized Shiryaev-Roberts Changepoint Detection Procedures

Several variations of the Shiryaev-Roberts detection procedure in the context of the simple changepoint problem are considered: starting the procedure at $R_0=0$ (the original Shiryaev-Roberts procedure), at $R_0=r$ for fixed $r>0$, and at $R_0$ that has a quasi-stationary distribution. Comparisons of operating characteristics are made. The differences fade as the average run length to false alarm tends to infinity. It is shown that the Shiryaev-Roberts procedures that start either from a specially designed point $r$ or from the random "quasi-stationary" point are order-3 asymptotically optimal.
Spectral covolatility estimation from noisy observations using local weights

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an appropriate estimation for time-varying volatilities stems from an asymptotic equivalence of the underlying statistical model to a white noise model with correlation and volatility processes being constant over small intervals. The asymptotic equivalence of the continuous-time and the discrete-time experiments are proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier nonparametric approaches in the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between the various proposed methods.
Dependency and false discovery rate: Asymptotics

Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing n hypotheses when test statistics are dependent. In this paper we investigate the expected error rate (EER) and the false discovery rate (FDR) in some extreme parameter configurations when n tends to infinity for test statistics being exchangeable under null hypotheses. All results are derived in terms of p-values. In a general setup we present a series of results concerning the interrelation of Simes' rejection curve and the (limiting) empirical distribution function of the p-values. Main objects under investigation are largest (limiting) crossing points between these functions, which play a key role in deriving explicit formulas for EER and FDR. As specific examples we investigate equi-correlated normal and t-variables in more detail and compute the limiting EER and FDR theoretically and numerically. A surprising limit behavior occurs if these models tend to independence.
On prediction with the LASSO when the design is not incoherent

The LASSO estimator is an $\ell_1$-norm penalized least-squares estimator, which was introduced for variable selection in the linear model. When the design matrix satisfies, e.g. the Restricted Isometry Property, or has a small coherence index, the LASSO estimator has been proved to recover, with high probability, the support and sign pattern of sufficiently sparse regression vectors. Under similar assumptions, the LASSO satisfies adaptive prediction bounds in various norms. The present note provides a prediction bound based on a new index for measuring how favorable is a design matrix for the LASSO estimator. We study the behavior of our new index for matrices with independent random columns uniformly drawn on the unit sphere. Using the simple trick of appending such a random matrix (with the right number of columns) to a given design matrix, we show that a prediction bound similar to \cite[Theorem 2.1]{CandesPlan:AnnStat09} holds without any constraint on the design matrix, other than restricted non-singularity.
AN EFFICIENT ESTIMATOR FOR LOCALLY STATIONARY GAUSSIAN LONG-MEMORY PROCESSES

This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying parametric formulation of these models is introduced and a Whittle likelihood technique is proposed for estimating the parameters involved. Large sample properties of these Whittle estimates such as consistency, normality and efficiency are established in this work. Furthermore, the finite sample behavior of the estimators is investigated through Monte Carlo experiments. As a result from these simulations, we show that the estimates behave well even for relatively small sample sizes.
Minimax bounds for estimation of normal mixtures

This paper deals with minimax rates of convergence for estimation of density functions on the real line. The densities are assumed to be location mixtures of normals, a global regularity requirement that creates subtle difficulties for the application of standard minimax lower bound methods. Using novel Fourier and Hermite polynomial techniques, we determine the mini max optimal rate - slightly larger than the parametric rate - under squared error loss. For Hellinger loss, we provide a minimax lower bound using ideas modified from the squared error loss case.
On universal oracle inequalities related to high-dimensional linear models

This paper deals with recovering an unknown vector θ from the noisy data Y = Aθ + σξ, where A is a known (m x n)-matrix and is a white Gaussian noise. It is assumed that n is large and A may be severely ill-posed. Therefore, in order to estimate θ, a spectral regularization method is used, and our goal is to choose its regularization parameter with the help of the data Y. For spectral regularization methods related to the so-called ordered smoothers [see Kneip Ann. Statist. 22 (1994) 835―866], we propose new penalties in the principle of empirical risk minimization. The heuristical idea behind these penalties is related to balancing excess risks. Based on this approach, we derive a sharp oracle inequality controlling the mean square risks of data-driven spectral regularization methods.
Likelihood Ratio Type Two‐Sample Tests for Current Status Data

Abstract. We introduce fully non‐parametric two‐sample tests for testing the null hypothesis that the samples come from the same distribution if the values are only indirectly given via current status censoring. The tests are based on the likelihood ratio principle and allow the observation distributions to be different for the two samples, in contrast with earlier proposals for this situation. A bootstrap method is given for determining critical values and asymptotic theory is developed. A simulation study, using Weibull distributions, is presented to compare the power behaviour of the tests with the power of other non‐parametric tests in this situation.
Unit roots in moving averages beyond first order

The asymptotic theory of various estimators based on Gaussian likelihood has been developed for the unit root and near unit root cases of a first-order moving average model. Previous studies of the MA(1) unit root problem rely on the special autocovariance structure of the MA(1) process, in which case, the eigenvalues and eigenvectors of the covariance matrix of the data vector have known analytical forms. In this paper, we take a different approach to first consider the joint likelihood by including an augmented initial value as a parameter and then recover the exact likelihood by integrating out the initial value. This approach by-passes the difficulty of computing an explicit decomposition of the covariance matrix and can be used to study unit root behavior in moving averages beyond first order. The asymptotics of the generalized likelihood ratio (GLR) statistic for testing unit roots are also studied. The GLR test has operating characteristics that are competitive with the locally best invariant unbiased (LBIU) test of Tanaka for some local alternatives and dominates for all other alternatives.
Adaptive Bayesian multivariate density estimation with Dirichlet mixtures

We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient conditions on the prior specification that guarantee convergence to a true density at a rate that is minimax optimal for the smoothness class to which the true density belongs. No prior knowledge of smoothness is assumed. The sufficient conditions are shown to hold for the Dirichlet location mixture-of-normals prior with a Gaussian base measure and an inverse Wishart prior on the covariance matrix parameter. Locally Holder smoothness classes and their anisotropic extensions are considered. Our study involves several technical novelties, including sharp approximation of finitely differentiable multivariate densities by normal mixtures and a new sieve on the space of such densities. Copyright 2013, Oxford University Press.
Plugin procedure in segmentation and application to hyperspectral image segmentation

In this article we give our contribution to the problem of segmentation with plug-in procedures. We give general sufficient conditions under which plug in procedure are efficient. We also give an algorithm that satisfy these conditions. We give an application of the used algorithm to hyperspectral images segmentation. Hyperspectral images are images that have both spatial and spectral coherence with thousands of spectral bands on each pixel. In the proposed procedure we combine a reduction dimension technique and a spatial regularisation technique. This regularisation is based on the mixlet modelisation of Kolaczyck and Al.
The 2004 Venezuelan Presidential Recall Referendum: Discrepancies Between Two Exit Polls and Official Results

We present a simulation-based study in which the results of two major exit polls conducted during the recall referendum that took place in Venezuela on August 15, 2004, are compared to the official results of the Venezuelan National Electoral Council "Consejo Nacional Electoral" (CNE). The two exit polls considered here were conducted independently by S\'{u}mate, a nongovernmental organization, and Primero Justicia, a political party. We find significant discrepancies between the exit poll data and the official CNE results in about 60% of the voting centers that were sampled in these polls. We show that discrepancies between exit polls and official results are not due to a biased selection of the voting centers or to problems related to the size of the samples taken at each center. We found discrepancies in all the states where the polls were conducted. We do not have enough information on the exit poll data to determine whether the observed discrepancies are the consequence of systematic biases in the selection of the people interviewed by the pollsters around the country. Neither do we have information to study the possibility of a high number of false or nonrespondents. We have limited data suggesting that the discrepancies are not due to a drastic change in the voting patterns that occurred after the exit polls were conducted. We notice that the two exit polls were done independently and had few centers in common, yet their overall results were very similar.
Quasi-estimation as a Basis for Two-stage Solving of Regression Problem

An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, produces two alternative estimates. It is proved that, in comparison to the least squares estimate, one alternative has a significantly smaller quadratic risk, retaining at the same time unbiasedness and consistency. These properties hold true for one-dimensional, multi-dimensional, orthogonal and non-orthogonal problems. Moreover, a Monte-Carlo simulation confirms high robustness of the quasi-estimator to violations of the initial assumptions. Therefore, at the first stage of the estimation we calculate mentioned two alternative estimates. At the second stage we choose the better estimate out of these alternatives. In order to do so we use additional information, among it but not exclusively of a priori nature. In case of two alternatives the volume of such information should be minimal. Furthermore, the additional information is not built-in into the quasi-estimator structure, so that any kind of information, even intuitive one, can be used. These features, in combination with decrease of the quadratic risk, provide a great advantage of our method. A variety of types of the additional information for choosing the better estimate is considered. One example is the successful processing of the famous experiment conducted by astronomers in 1919 to verify the General The-ory of Relativity of A. Einstein.
Correction note: Poisson point process models solve the “pseudo-absence problem” for presence-only data in ecology

Presence-only data, point locations where a species has beenrecorded as being present, are often used in modeling the distribu-tion of a species as a function of a set of explanatory variables—whether to map species occurrence, to understand its associationwith the environment, or to predict its response to environmentalchange. Currently, ecologists most commonly analyze presence-onlydata by adding randomly chosen “pseudo-absences” to the data suchthat it can be analyzed using logistic regression, an approach whichhas weaknesses in model speciﬁcation, in interpretation, and in imple-mentation. To address these issues, we propose Poisson point processmodeling of the intensity of presences. We also derive a link betweenthe proposed approach and logistic regression—speciﬁcally, we showthat as the number of pseudo-absences increases (in a regular or uni-form random arrangement), logistic regression slope parameters andtheir standard errors converge to those of the corresponding Poissonpoint process model. We discuss the practical implications of theseresults. In particular, point process modeling oﬀers a framework forchoice of the number and location of pseudo-absences, both of whichare currently chosen by ad hoc and sometimes ineﬀective methods inecology, a point which we illustrate by example.
The effect of differential recruitment, non-response and non-recruitment on estimators for respondent-driven sampling

Respondent-driven sampling is a widely-used network sampling technique, designed to sample from hard-to-reach populations. Estimation from the resulting samples is an area of active research, with software available to compute at least four estimators of a population proportion. Each estimator is claimed to address deficiencies in previous estimators, however those claims are often unsubstantiated. In this study we provide a simulation-based comparison of five existing estimators, focussing on sampling conditions which a recent estimator is designed to address. We find no estimator consistently out-performs all others, and highlight sampling conditions in which each is to be preferred.