Miracle-dz/UniFAR-FTUs huggingface dataset:
Significance level and positivity bias as causes for high rate of non-reproducible scientific results?

The high fraction of published results that turn out to be incorrect is a major concern of today's science. This paper contributes to the understanding of this problem in two independent directions. First, Johnson's recent claim that hypothesis testing with a significance level of 0.05 can alone lead to an unacceptably large proportion of false positives among all results is shown to be unfounded. Second, a way to quantify the effect of "positivity bias" (the tendency to consider only positive results as worthwhile) is introduced. We estimate the proportion of false positives among positive results in terms of the significance level used and the positivity ratio. The latter quantity is the fraction of positive results over all results, be they positive or not, published or not. In particular, if one uses a significance level of 0.05, and produces 4 (possibly unpublished) negative results for every positive result, then the proportion of false positives among positive results can climb to a high 21%.
The importance of distinct modeling strategies for gene and gene-specific treatment effects in hierarchical models for microarray data

When analyzing microarray data, hierarchical models are often used to share information across genes when estimating means and variances or identifying differential expression. Many methods utilize some form of the two-level hierarchical model structure suggested by Kendziorski et al. [Stat. Med. (2003) 22 3899-3914] in which the first level describes the distribution of latent mean expression levels among genes and among differentially expressed treatments within a gene. The second level describes the conditional distribution, given a latent mean, of repeated observations for a single gene and treatment. Many of these models, including those used in Kendziorski's et al. [Stat. Med. (2003) 22 3899-3914] EBarrays package, assume that expression level changes due to treatment effects have the same distribution as expression level changes from gene to gene. We present empirical evidence that this assumption is often inadequate and propose three-level hierarchical models as extensions to the two-level log-normal based EBarrays models to address this inadequacy. We demonstrate that use of our three-level models dramatically changes analysis results for a variety of microarray data sets and verify the validity and improved performance of our suggested method in a series of simulation studies. We also illustrate the importance of accounting for the uncertainty of gene-specific error variance estimates when using hierarchical models to identify differentially expressed genes.
A structural analysis on Gravity of Trade: on removing distance from the model

The Gravity Model is the workhorse for empirical studies in International Economies for its empirical power and it is commonly used in explaining the trade flow between countries; it relies on a function that relates the trade with the masses of the two countries and the distance (as a proxy of the trasport costs) between them. However, the notion that using of distance functions in conventional interaction models effectively captures spatial dependence in international flows has long been challenged. It has been recently fully recognized that a spatial interaction effect exists essentially due to the spatial spillover and the third country effect. This motivates the introduction of the spatial autoregressive components in the so-called spatial gravity model of trade. A so-called weight matrix is used in order to define the set of the spatial neighbors and it is traditionally based on the inverse of the distance. Two issues follow from this standard procedure: the first regards the biasness of the distance if it is used as a proxy of the transport costs in a panel data, the second is related to the collinearity emerging if we use distance twice. So, several attempt were made in the recent literature having the scope of remove the distance. We propose a theoretically consistent procedure based on Anderson, Van Wincoop derivation model, and some ad-hoc tests, relating to this attempt. The empirical results based on a 22-years panel of OECD countries are conforting, and they allow us to estimate the model without the distance, if properly replaced by a set of fixed effects. This article, in addition, fits in the dispute about how to estimate the multilateral resistance terms.
Monotone Function Estimation for Computer Experiments

In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all inputs. We develop a Bayesian approach to Gaussian process modelling capable of incorporating monotonicity information for computer model emulation. Markov chain Monte Carlo methods are used to sample from the posterior distribution of the process given the simulator output and monotonicity information. The performance of the proposed approach in terms of predictive accuracy and uncertainty quantification is demonstrated in a number of simulated examples as well as a real queueing system application.
Graph connection Laplacian and random matrices with random blocks

Graph connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones appearing in the null case of GCL, i.e the case where there is no structure in the dataset under investigation. Developing this understanding is important in making sense of the output of the algorithms based on GCL. We hence develop a theory explaining the behavior of the spectral distribution of a large class of random matrices, in particular random matrices with random block entries of fixed size. Part of the theory covers the case where there is significant dependence between the blocks. Numerical work shows that the agreement between our theoretical predictions and numerical simulations is generally very good.
Sensitivity analysis for multidimensional and functional outputs

Let $X:=(X_1, \ldots, X_p)$ be random objects (the inputs), defined on some probability space $(\Omega,{\mathcal{F}}, \mathbb P)$ and valued in some measurable space $E=E_1\times\ldots \times E_p$. Further, let $Y:=Y = f(X_1, \ldots, X_p)$ be the output. Here, $f$ is a measurable function from $E$ to some Hilbert space $\mathbb{H}$ ($\mathbb{H}$ could be either of finite or infinite dimension). In this work, we give a natural generalization of the Sobol indices (that are classically defined when $Y\in\mathbb R$ ), when the output belongs to $\mathbb{H}$. These indices have very nice properties. First, they are invariant. under isometry and scaling. Further they can be, as in dimension $1$, easily estimated by using the so-called Pick and Freeze method. We investigate the asymptotic behaviour of such estimation scheme.
Incorporation of Sparsity Information in Large-scale Multiple Two-sample $t$ Tests

Large-scale multiple two-sample Student’s t testing problems often arise from the statistical analysis of scientic data. To detect components with dierent values between two mean vectors, a well-known procedure is to apply the Benjamini and Hochberg (B-H) method and two-sample Student’s t statistics to control the false discovery rate (FDR). In many applications, mean vectors are expected to be sparse or asymptotically sparse. When dealing with such type of data, can we gain more power than the standard procedure such as the B-H method with Student’s t statistics while keeping the FDR under control? The answer is positive. By exploiting the possible sparsity information in mean vectors, we present an uncorrelated screening-based (US) FDR control procedure, which is shown to be more powerful than the B-H method. The US testing procedure depends on a novel construction of screening statistics, which are asymptotically uncorrelated with two-sample Student’s t statistics. The US testing procedure is dierent
Weak Convergence to Stochastic Integrals Driven by $\alpha-$Stable Lévy Processes

We use the martingale convergence method to get the weak convergence theorem on general functionals of partial sums of independent heavy-tailed random variables. The limiting process is the stochastic integral driven by $\alpha-$stable L\'evy process. Our method is very powerful to obtain the limit behavior of heavy-tailed random variables.
Adjusting for Misclassification: A Three-Phase Sampling Approach

Abstract The United States Department of Agriculture’s National Agricultural Statistics Service (NASS) conducts the June Agricultural Survey (JAS) annually. Substantial misclassification occurs during the prescreening process and from field-estimating farm status for nonresponse and inaccessible records, resulting in a biased estimate of the number of US farms from the JAS. Here, the Annual Land Utilization Survey (ALUS) is proposed as a follow-on survey to the JAS to adjust the estimates of the number of US farms and other important variables. A three-phase survey design-based estimator is developed for the JAS-ALUS with nonresponse adjustment for the second phase (ALUS). A design-unbiased estimator of the variance is provided in explicit form.
What Is Meant by "Missing at Random"?

The concept of missing at random is central in the literature on statistical analysis with missing data. In general, inference using incomplete data should be based not only on observed data values but should also take account of the pattern of missing values. However, it is often said that if data are missing at random, valid inference using likelihood approaches (including Bayesian) can be obtained ignoring the missingness mechanism. Unfortunately, the term "missing at random" has been used inconsistently and not always clearly; there has also been a lack of clarity around the meaning of "valid inference using likelihood". These issues have created potential for confusion about the exact conditions under which the missingness mechanism can be ignored, and perhaps fed confusion around the meaning of "analysis ignoring the missingness mechanism". Here we provide standardised precise definitions of "missing at random" and "missing completely at random", in order to promote unification of the theory. Using these definitions we clarify the conditions that suffice for "valid inference" to be obtained under a variety of inferential paradigms.
Comparisons of penalized least squares methods by simulations

Penalized least squares methods are commonly used for simultaneous estimation and variable selection in high-dimensional linear models. In this paper we compare several prevailing methods including the lasso, nonnegative garrote, and SCAD in this area through Monte Carlo simulations. Criterion for evaluating these methods in terms of variable selection and estimation are presented. This paper focuses on the traditional n > p cases. For larger p, our results are still helpful to practitioners after the dimensionality is reduced by a screening method. K
Sparsistent Estimation of Time-Varying Discrete Markov Random Fields

Network models have been popular for modeling and representing complex relationships and dependencies between observed variables. When data comes from a dynamic stochastic process, a single static network model cannot adequately capture transient dependencies, such as, gene regulatory dependencies throughout a developmental cycle of an organism. Kolar et al (2010b) proposed a method based on kernel-smoothing l1-penalized logistic regression for estimating time-varying networks from nodal observations collected from a time-series of observational data. In this paper, we establish conditions under which the proposed method consistently recovers the structure of a time-varying network. This work complements previous empirical findings by providing sound theoretical guarantees for the proposed estimation procedure. For completeness, we include numerical simulations in the paper.
Testing against a linear regression model using ideas from shape‐restricted estimation

A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large dimensional, non‐parametric double‐cone alternative. For example, the test against a constant function uses the alternative of increasing or decreasing regression functions, and the test against a linear function uses the convex or concave alternative. The test proposed is exact and unbiased and the critical value is easily computed. The power of the test increases to 1 as the sample size increases, under very mild assumptions—even when the alternative is misspecified, i.e. the power of the test converges to 1 for any true regression function that deviates (in a non‐degenerate way) from the parametric null hypothesis. We also formulate tests for the linear versus partial linear model and consider the special case of the additive model. Simulations show that our procedure behaves well consistently when compared with other methods. Although the alternative fit is non‐parametric, no tuning parameters are involved. Supplementary materials with proofs and technical details are available on line.
Adaptation in a class of linear inverse problems

Author(s): Johnstone, Iain M. ; Paul, Debashis | Abstract: We consider the linear inverse problem of estimating an unknown signal $f$ from noisy measurements on $Kf$ where the linear operator $K$ admits a wavelet-vaguelette decomposition (WVD). We formulate the problem in the Gaussian sequence model and propose estimation based on complexity penalized regression on a level-by-level basis. We adopt squared error loss and show that the estimator achieves exact rate-adaptive optimality as $f$ varies over a wide range of Besov function classes.
TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES

In this article, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a unified framework, with a number of possible applications in auction models, game theoretic models, wage inequality, and revealed preferences. Our test involves a one-sided version of Lp functionals of kernel-type estimators (1 ≤ p < ∞) and is easy to implement in general, mainly due to its recourse to the bootstrap method. The bootstrap procedure is based on the nonparametric bootstrap applied to kernel-based test statistics, with an option of estimating “contact sets. ” We provide regularity conditions under which the bootstrap test is asymptotically valid uniformly over a large class of distributions, including cases where the limiting distribution of the test statistic is degenerate. Our bootstrap test is shown to exhibit good power properties in Monte Carlo experiments, and we provide a general form of the local power function. As an illustration, we consider testing implications from auction theory, provide primitive conditions for our test, and demonstrate its usefulness by applying our test to real data. We supplement this example with the second empirical illustration in the context of wage inequality.
Hierarchical sparsity priors for regression models

Sparse regression problems, where it is usually assumed that there are many variables and that the effects of a large subset of variables are negligible, have become increasingly important. This paper describes the construction of hierarchical prior distributions when the effects are considered related. These priors allow dependence between the regression coefficients and the shrinkage to zero of different regression coefficients to be related. The properties of these priors are discussed and applications to linear models with interactions and generalized additive models are used as illustrations.
Fisher information and asymptotic normality in system identification for quantum Markov chains

This paper deals with the problem of estimating the coupling constant {theta} of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of {theta} whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolute bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of {theta}=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.
Kernel density estimation with Berkson error

Given a sample {Xi}i=1n from fX we construct kernel density estimators for fY , the convolution of fX with a known error density fε . This problem is known as density estimation with Berkson error and has applications in epidemiology and astronomy. Little is understood about bandwidth selection for Berkson density estimation. We compare three approaches to selecting the bandwidth both asymptotically, using large‐sample approximations to the MISE , and at finite samples, using simulations. Our results highlight the relationship between the structure of the error fε and the optimal bandwidth. In particular the results demonstrate the importance of smoothing when the error term fε is concentrated near 0. We propose a data‐driven bandwidth estimator and test its performance on NO 2 exposure data. The Canadian Journal of Statistics 44: 142–160; 2016 © 2016 Statistical Society of Canada
Accelerating Metropolis-Hastings algorithms: Delayed acceptance with prefetching

MCMC algorithms such as Metropolis-Hastings algorithms are slowed down by the computation of complex target distributions as exemplified by huge datasets. We offer in this paper an approach to reduce the computational costs of such algorithms by a simple and universal divide-and-conquer strategy. The idea behind the generic acceleration is to divide the acceptance step into several parts, aiming at a major reduction in computing time that outranks the corresponding reduction in acceptance probability. The division decomposes the "prior x likelihood" term into a product such that some of its components are much cheaper to compute than others. Each of the components can be sequentially compared with a uniform variate, the first rejection signalling that the proposed value is considered no further, This approach can in turn be accelerated as part of a prefetching algorithm taking advantage of the parallel abilities of the computer at hand. We illustrate those accelerating features on a series of toy and realistic examples.
Semiparametric posterior limits under local asymptotic exponentiality

Consider a nonparametric model of densities that display discontinuities; estimation of only the location of discontinuity is an example of an irregular semiparametric question in which likelihoods are approximated using Ibragimov and Has’minskii’s local asymptotic exponentiality (LAE). It is shown that, under certain conditions on model and prior, the marginal posterior for an LAE parameter of interest displays Bernstein{von Mises-type asymptotic behaviour with exponential distributions forming the limiting sequence. The main result is applied to examples of semiparametric estimation of LAE location and scaling parameters. Although the ML and MAP estimators are inecient under this form of irregularity due to bias, posterior means attain minimax risk bounds. This suggests that with regard to asymptotic optimality, the posterior is more informative than the maximum of its density alone, and it urges focus on eciency of Bayesian methods in their own right, rather than on comparison with frequentist procedures like the MLE.
Optimal two-step prediction in regression

High-dimensional prediction typically comprises two steps: variable selection and subsequent least-squares refitting on the selected variables. However, the standard variable selection procedures, such as the lasso, hinge on tuning parameters that need to be calibrated. Cross-validation, the most popular calibration scheme, is computationally costly and lacks finite sample guarantees. In this paper, we introduce an alternative scheme, easy to implement and both computationally and theoretically efficient.
Asymptotic inferences for an AR(1) model with a change point: stationary and nearly non-stationary cases

This paper examines the asymptotic inference for AR(1) models with a possible structural break in the AR parameter $\beta $ near the unity at an unknown time $k_{0}$. Consider the model $y_{t}=\beta_{1}y_{t-1}I\{t\leq k_{0}\}+\beta _{2}y_{t-1}I\{t>k_{0}\}+\varepsilon_{t},~t=1,2,\cdots ,T,$ where $I\{\cdot \}$ denotes the indicator function. We examine two cases: Case (I) $|\beta_{1}|<1,\beta_{2}=\beta_{2T}=1-c/T$; and case (II)~$\beta_{1}=\beta_{1T}=1-c/T,|\beta _{2}|<1$, where $c$\ is a fixed constant, and $\{\varepsilon_{t},t\geq 1\}$\ is a sequence of i.i. d. random variables which are in the domain of attraction of the normal law with zero means and possibly infinite variances. We derive the limiting distributions of the least squares estimators of $\beta_{1}$ and $\beta_{2} $, and that of the break-point estimator for shrinking break for the aforementioned cases. Monte Carlo simulations are conducted to demonstrate the finite sample properties of the estimators. Our theoretical results are supported by Monte Carlo simulations. \newline
Rates of convergence of the Adaptive LASSO estimators to the Oracle distribution and higher order refinements by the bootstrap

Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] proposed the Adaptive LASSO (ALASSO) method for simultaneous variable selection and estimation of the regression parameters, and established its oracle property. In this paper, we investigate the rate of convergence of the ALASSO estimator to the oracle distribution when the dimension of the regression parameters may grow to infinity with the sample size. It is shown that the rate critically depends on the choices of the penalty parameter and the initial estimator, among other factors, and that confidence intervals (CIs) based on the oracle limit law often have poor coverage accuracy. As an alternative, we consider the residual bootstrap method for the ALASSO estimators that has been recently shown to be consistent; cf. Chatterjee and Lahiri [J. Amer. Statist. Assoc. 106 (2011a) 608-625]. We show that the bootstrap applied to a suitable studentized version of the ALASSO estimator achieves second-order correctness, even when the dimension of the regression parameters is unbounded. Results from a moderately large simulation study show marked improvement in coverage accuracy for the bootstrap CIs over the oracle based CIs.
Network inference in matrix-variate Gaussian models with non-independent noise

Inferring a graphical model or network from observational data from a large number of variables is a well studied problem in machine learning and computational statistics. In this paper we consider a version of this problem that is relevant to the analysis of multiple phenotypes collected in genetic studies. In such datasets we expect correlations between phenotypes and between individuals. We model observations as a sum of two matrix normal variates such that the joint covariance function is a sum of Kronecker products. This model, which generalizes the Graphical Lasso, assumes observations are correlated due to known genetic relationships and corrupted with non-independent noise. We have developed a computationally efficient EM algorithm to fit this model. On simulated datasets we illustrate substantially improved performance in network reconstruction by allowing for a general noise distribution.