The stable tail dependence function provides a full characterization of the extremal dependence structures. Unfortunately, the estimation of the stable tail dependence function often suffers from significant bias, whose scale relates to the Peaks-Over-Threshold (POT) second-order parameter. For this second-order parameter, this paper introduces a penalized estimator that discourages it from being too close to zero. This paper then establishes this estimator's asymptotic consistency, uses it to correct the bias in the estimation of the stable tail dependence function, and illustrates its desirable empirical properties in the estimation of the extremal dependence structures.
The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. We rigorously derive the EL prior, a Jeffreys-type prior, which asymptotically maximizes the Shannon mutual information between data and the parameters of interest. The focus of our approach is on an integrated Kullback-Leibler distance between the EL-based posterior and prior density functions. The EL prior density is the density function for which the corresponding posterior for…
In this paper, we present a generalized estimating equations based estimation approach and a variable selection procedure for single-index models when the observed data are clustered. Unlike the case of independent observations, bias-correction is necessary when general working correlation matrices are used in the estimating equations. Our variable selection procedure based on smooth-threshold estimating equations \citep{Ueki-2009} can automatically eliminate irrelevant parameters by setting them as zeros and is computationally simpler than alternative approaches based on shrinkage penalty. Th…
This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator. We derive the asymptotic covariance matrices and second-order biases under general estimating equations without assuming the normality of the underlying distributions and identify a class of second-order unbiased estimators of variance components. It is also shown that the asymptotic covariance matrices and second-order biases do not depend on whether the re…
Capture-recapture methods aim to estimate the size of a closed population on the basis of multiple incomplete enumerations of individuals. In many applications, the individual probability of being recorded is heterogeneous in the population. Previous studies have suggested that it is not possible to reliably estimate the total population size when capture heterogeneity exists. Here we approach population estimation in the presence of capture heterogeneity as a latent length biased nonparametric density estimation problem on the unit interval. We show that in this setting it is generally imposs…
With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes. Generally there is particular interest in those effects estimated to be most extreme. Unfortunately naive estimates of these effect-sizes (even after potentially accounting for multiplicity in a testing procedure) can be severely biased. In this manuscript we explore this bias from a frequentist perspective: we give a formal definition, and show that an oracle estimator using this bias dominates the naive …
Institute for Analytical Sociology（分析社会学研究所）；Linköping University（林雪平大学）；Chalmers University of Technology（查尔姆斯理工大学）
Observational studies of causal effects require adjustment for confounding factors. In the tabular setting, where these factors are well-defined, separate random variables, the effect of confounding is well understood. However, in public policy, ecology, and in medicine, decisions are often made in non-tabular settings, informed by patterns or objects detected in images (e.g., maps, satellite or tomography imagery). Using such imagery for causal inference presents an opportunity because objects in the image may be related to the treatment and outcome of interest. In these cases, we rely on the…
State-level policy evaluations commonly employ a difference-in-differences (DID) study design; yet within this framework, statistical model specification varies notably across studies. Motivated by applied state-level opioid policy evaluations, this simulation study compares statistical performance of multiple variations of two-way fixed effect models traditionally used for DID under a range of simulation conditions. While most linear models resulted in minimal bias, non-linear models and population-weighted versions of classic linear two-way fixed effect and linear GEE models yielded consider…
It is difficult to accurately estimate the rates of rape and domestic violence due to the sensitive nature of these crimes. There is evidence that bias in estimating the crime rates from survey data may arise because some women respondents are "gagged" in reporting some types of crimes by the use of a telephone rather than a personal interview, and by the presence of a spouse during the interview. On the other hand, as data on these crimes are collected every year, it would be more efficient in data analysis if we could identify and make use of information from previous data. In this paper we …
We investigate the accuracy of the two most common estimators for the maximum expected value of a general set of random variables: a generalization of the maximum sample average, and cross validation. No unbiased estimator exists and we show that it is non-trivial to select a good estimator without knowledge about the distributions of the random variables. We investigate and bound the bias and variance of the aforementioned estimators and prove consistency. The variance of cross validation can be significantly reduced, but not without risking a large bias. The bias and variance of different va…
Finite-sample bias-variance tradeoff with variables related to trial participation inserted into causal forest models for ensuring generalizability
Division of Preventive Medicine, Department of Medicine, Brigham and Women’s Hospital and Harvard Medical School（预防医学系，内科，布莱根妇女医院和哈佛医学院）；Department of Epidemiology, Graduate School of Medicine, Dentistry and Pharmaceutical Sciences, Okayama University（流行病学科，医药齿学研究院，冈山大学）；Harris School of Public Policy, University of Chicago（哈里斯公共政策学院，芝加哥大学）
In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an exponential regression model that was introduced in Diebolt et al. (2008). The asymptotic normality of the extreme quantile estimator is established. We also introduce an adaptive selection procedure to determine the number of upper order statistics to be used. A simulation study as well as an application to a real data set are provided in order to prove th…
Estimating the number of signals embedded in noise is a fundamental problem in signal processing. As a classic estimator based on random matrix theory (RMT), the RMT estimator estimates the number of signals via sequentially testing the likelihood of an eigenvalue as arising from a signal or noise for a given over-detection probability. However, it tends to under-estimate the number of signals as weak signal eigenvalues may be immersed in the non-negligible bias term among eigenvalues for finite sample size. In order to solve this problem, we propose an RMT estimator with adaptive decision cri…
The Receiver Operating Characteristic (ROC) surface is a generalization of ROC curve and is widely used for assessment of the accuracy of diagnostic tests on three categories. A complication called the verification bias, meaning that not all subjects have their true disease status verified often occur in real application of ROC analysis. This is a common problem since the gold standard test, which is used to generate true disease status, can be invasive and expensive. In this paper, we will propose a Bayesian approach for estimating the ROC surface based on continuous data under a semi-paramet…
Respondent-driven sampling (RDS) is a popular approach to study marginalized or hard-to-reach populations. It collects samples from a networked population by incentivizing participants to refer their friends into the study. One major challenge in analyzing RDS samples is seed bias. Seed bias refers to the fact that when the social network is divided into multiple communities (or blocks), the RDS sample might not provide a balanced representation of the different communities in the population, and such unbalance is correlated with the initial participant (or the seed). In this case, the distrib…
Lag windows are commonly used in time series, econometrics, steady-state simulation, and Markov chain Monte Carlo to estimate time-average covariance matrices. In the presence of positive correlation of the underlying process, estimators of this matrix almost always exhibit significant negative bias, leading to undesirable finite-sample properties. We propose a new family of lag windows specifically designed to improve finite-sample performance by offsetting this negative bias. Any existing lag window can be adapted into a lugsail equivalent with no additional assumptions. We use these lag win…
The inverse probability weighting approach is popular for evaluating treatment effects in observational studies, but extreme propensity scores could bias the estimator and induce excessive variance. Recently, the overlap weighting approach has been proposed to alleviate this problem, which smoothly down-weighs the subjects with extreme propensity scores. Although advantages of overlap weighting have been extensively demonstrated in literature with continuous and binary outcomes, research on its performance with time-to-event or survival outcomes is limited. In this article, we propose two weig…
Databases derived from electronic health records (EHRs) are commonly subject to left truncation, a type of selection bias induced due to patients needing to survive long enough to satisfy certain entry criteria. Standard methods to adjust for left truncation bias rely on an assumption of marginal independence between entry and survival times, which may not always be satisfied in practice. In this work, we examine how a weaker assumption of conditional independence can result in unbiased estimation of common statistical parameters. In particular, we show the estimability of conditional paramete…
Wind-generated waves are often treated as stochastic processes. There is particular interest in their spectral density functions, which are often expressed in some parametric form. Such spectral density functions are used as inputs when modelling structural response or other engineering concerns. Therefore, accurate and precise recovery of the parameters of such a form, from observed wave records, is important. Current techniques are known to struggle with recovering certain parameters, especially the peak enhancement factor and spectral tail decay. We introduce an approach from the statistica…
Although the interest in the the use of social and information networks has grown, most inferences on networks assume the data collected represents the complete. However, when ignoring missing data, even when missing completely at random, this results in bias for estimators regarding inference network related parameters. In this paper, we focus on constructing estimators for the probability that a randomly selected node has node has at least one edge under the assumption that nodes are missing completely at random along with their corresponding edges. In addition, issues also arise in obtainin…
This paper addresses the problem of estimating the Potts parameter B jointly with the unknown parameters of a Bayesian model within a Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because performing inference on B requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method the estimation of B is conducted using a likelihood-free Metropolis-Hastings algorithm. Experimental results obtained for synthetic data show that estimating B jointly with the other unknown parameters leads to estimation results…
This paper explores bias in the estimation of sampling variance in Respondent Driven Sampling (RDS). Prior methodological work on RDS has focused on its problematic assumptions and the biases and inefficiencies of its estimators of the population mean. Nonetheless, researchers have given only slight attention to the topic of estimating sampling variance in RDS, despite the importance of variance estimation for the construction of confidence intervals and hypothesis tests. In this paper, we show that the estimators of RDS sampling variance rely on a critical assumption that the network is First…
