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Register a new userTransformed Fay-Herriot Model with Measurement Error in Covariates
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Added by
Sepideh Mosaferi
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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Statistical agencies are often asked to produce small area estimates (SAEs) for positively skewed variables. When domain sample sizes are too small to support direct estimators, effects of skewness of the response variable can be large. As such, it is important to appropriately account for the distribution of the response variable given available auxiliary information. Motivated by this issue and in order to stabilize the skewness and achieve normality in the response variable, we propose an area-level log-measurement error model on the response variable. Then, under our proposed modeling framework, we derive an empirical Bayes (EB) predictor of positive small area quantities subject to the covariates containing measurement error. We propose a corresponding mean squared prediction error (MSPE) of EB predictor using both a jackknife and a bootstrap method. We show that the order of the bias is $O(m^{-1})$, where $m$ is the number of small areas. Finally, we investigate the performance of our methodology using both design-based and model-based simulation studies.
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Count data are collected in many scientific and engineering tasks including image processing, single-cell RNA sequencing and ecological studies. Such data sets often contain missing values, for example because some ecological sites cannot be reached in a certain year. In addition, in many instances, side information is also available, for example covariates about ecological sites or species. Low-rank methods are popular to denoise and impute count data, and benefit from a substantial theoretical background. Extensions accounting for covariates have been proposed, but to the best of our knowledge their theoretical and empirical properties have not been thoroughly studied, and few softwares are available for practitioners. We propose a complete methodology called LORI (Low-Rank Interaction), including a Poisson model, an algorithm, and automatic selection of the regularization parameter, to analyze count tables with covariates. We also derive an upper bound on the estimation error. We provide a simulation study with synthetic data, revealing empirically that LORI improves on state of the art methods in terms of estimation and imputation of the missing values. We illustrate how the method can be interpreted through visual displays with the analysis of a well-know plant abundance data set, and show that the LORI outputs are consistent with known results. Finally we demonstrate the relevance of the methodology by analyzing a water-birds abundance table from the French national agency for wildlife and hunting management (ONCFS). The method is available in the R package lori on the Comprehensive Archive Network (CRAN).
Causal inference has been increasingly reliant on observational studies with rich covariate information. To build tractable causal models, including the propensity score models, it is imperative to first extract important features from high dimensional data. Unlike the familiar task of variable selection for prediction modeling, our feature selection procedure aims to control for confounding while maintaining efficiency in the resulting causal effect estimate. Previous empirical studies imply that one should aim to include all predictors of the outcome, rather than the treatment, in the propensity score model. In this paper, we formalize this intuition through rigorous proofs, and propose the causal ball screening for selecting these variables from modern ultra-high dimensional data sets. A distinctive feature of our proposal is that we do not require any modeling on the outcome regression, thus providing robustness against misspecification of the functional form or violation of smoothness conditions. Our theoretical analyses show that the proposed procedure enjoys a number of oracle properties including model selection consistency, normality and efficiency. Synthetic and real data analyses show that our proposal performs favorably with existing methods in a range of realistic settings.
Statistical modeling of animal movement is of critical importance. The continuous trajectory of an animals movements is only observed at discrete, often irregularly spaced time points. Most existing models cannot handle the unequal sampling interval naturally and/or do not allow inactivity periods such as resting or sleeping. The recently proposed moving-resting (MR) model is a Brownian motion governed by a telegraph process, which allows periods of inactivity in one state of the telegraph process. The MR model shows promise in modeling the movements of predators with long inactive periods such as many felids, but the lack of accommodation of measurement errors seriously prohibits its application in practice. Here we incorporate measurement errors in the MR model and derive basic properties of the model. Inferences are based on a composite likelihood using the Markov property of the chain composed by every other observed increments. The performance of the method is validated in finite sample simulation studies. Application to the movement data of a mountain lion in Wyoming illustrates the utility of the method.
The purpose of this paper is to construct confidence intervals for the regression coefficients in the Fine-Gray model for competing risks data with random censoring, where the number of covariates can be larger than the sample size. Despite strong motivation from biomedical applications, a high-dimensional Fine-Gray model has attracted relatively little attention among the methodological or theoretical literature. We fill in this gap by developing confidence intervals based on a one-step bias-correction for a regularized estimation. We develop a theoretical framework for the partial likelihood, which does not have independent and identically distributed entries and therefore presents many technical challenges. We also study the approximation error from the weighting scheme under random censoring for competing risks and establish new concentration results for time-dependent processes. In addition to the theoretical results and algorithms, we present extensive numerical experiments and an application to a study of non-cancer mortality among prostate cancer patients using the linked Medicare-SEER data.
We focus on the problem of generalizing a causal effect estimated on a randomized controlled trial (RCT) to a target population described by a set of covariates from observational data. Available methods such as inverse propensity weighting are not designed to handle missing values, which are however common in both data sources. In addition to coupling the assumptions for causal effect identifiability and for the missing values mechanism and to defining appropriate estimation strategies, one difficulty is to consider the specific structure of the data with two sources and treatment and outcome only available in the RCT. We propose and compare three multiple imputation strategies (separate imputation, joint imputation with fixed effect, joint imputation without source information), as well as a technique that uses estimators that can handle missing values directly without imputing them. These methods are assessed in an extensive simulation study, showing the empirical superiority of fixed effect multiple imputation followed with any complete data generalizing estimators. This work is motivated by the analysis of a large registry of over 20,000 major trauma patients and a RCT studying the effect of tranexamic acid administration on mortality. The analysis illustrates how the missing values handling can impact the conclusion about the effect generalized from the RCT to the target population.
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