Strong Distributional Assumptions Research Articles

Bayesian Empirical Likelihood Regression for Semiparametric Estimation of Optimal Dynamic Treatment Regimes.

We propose a semiparametric approach to Bayesian modeling of dynamic treatment regimes that is built on a Bayesian likelihood-based regression estimation framework. Methods based on this framework exhibit a probabilistic coherence property that leads to accurate estimation of the optimal dynamic treatment regime. Unlike most Bayesian estimation methods, our proposed method avoids strong distributional assumptions for the intermediate and final outcomes by utilizing empirical likelihoods. Our proposed method allows for either linear, or more flexible forms of mean functions for the stagewise outcomes. A variational Bayes approximation is used for computation to avoid common pitfalls associated with Markov Chain Monte Carlo approaches coupled with empirical likelihood. Through simulations and analysis of the STAR*D sequential randomized trial data, our proposed method demonstrates superior accuracy over Q-learning and parametric Bayesian likelihood-based regression estimation, particularly when the parametric assumptions of regression error distributions may be potentially violated.

Systemic risk measurement: A Quantile Long Short-Term Memory network approach

In finance, systemic risk is the risk that the crisis of an institution could trigger instability or bring down an entire system or market. The Delta Conditional Value-at-Risk is a market-based measure proposed by the recent literature to quantify the systematicity of some financial institutions. Several methods have been proposed to estimate this measure, and the choice of the best method is still an open question. The bivariate constant conditional correlation GARCH model represents one of the most preferred approaches since it allows the computation of the Delta Conditional Value-at-Risk in a closed form. Nevertheless, it requires strong distributional assumptions that are often considered unrealistic. We develop a Quantile Long Short-Term Memory network approach that allows the estimation of the Delta Conditional Value-at-Risk of several financial institutions simultaneously. The model consists of a multi-output neural network able to provide, at the same time, the log-return quantiles of different institutions useful to measure the systemic risk. Furthermore, the proposed model does not need any particular assumption, and it is specifically designed to avoid quantile crossing issues affecting the traditional quantile regression-based approach. Numerical experiments on data of some global systemically important banks reported in the Financial Stability Board validated our approach. We obtain Delta Conditional Value-at-Risk estimates that accurately capture market dynamics and produce a ranking of systemic banks that meets the desired properties of stability and persistence.

Learning With Proper Partial Labels.

Partial-label learning is a kind of weakly supervised learning with inexact labels, where for each training example, we are given a set of candidate labels instead of only one true label. Recently, various approaches on partial-label learning have been proposed under different generation models of candidate label sets. However, these methods require relatively strong distributional assumptions on the generation models. When the assumptions do not hold, the performance of the methods is not guaranteed theoretically. In this letter, we propose the notion of properness on partial labels. We show that this proper partial-label learning framework requires a weaker distributional assumption and includes many previous partial-label learning settings as special cases. We then derive a unified unbiased estimator of the classification risk. We prove that our estimator is risk consistent, and we also establish an estimation error bound. Finally, we validate the effectiveness of our algorithm through experiments.

Model-free prediction test with application to genomics data

Testing the significance of predictors in a regression model is one of the most important topics in statistics. This problem is especially difficult without any parametric assumptions on the data. This paper aims to test the null hypothesis that given confounding variables Z, X does not significantly contribute to the prediction of Y under the model-free setting, where X and Z are possibly high dimensional. We propose a general framework that first fits nonparametric machine learning regression algorithms on [Formula: see text] and [Formula: see text], then compares the prediction power of the two models. The proposed method allows us to leverage the strength of the most powerful regression algorithms developed in the modern machine learning community. The P value for the test can be easily obtained by permutation. In simulations, we find that the proposed method is more powerful compared to existing methods. The proposed method allows us to draw biologically meaningful conclusions from two gene expression data analyses without strong distributional assumptions: 1) testing the prediction power of sequencing RNA for the proteins in cellular indexing of transcriptomes and epitopes by sequencing data and 2) identification of spatially variable genes in spatially resolved transcriptomics data.

A universal deep neural network for in-depth cleaning of single-cell RNA-Seq data

Single cell RNA sequencing (scRNA-Seq) is being widely used in biomedical research and generated enormous volume and diversity of data. The raw data contain multiple types of noise and technical artifacts, which need thorough cleaning. Existing denoising and imputation methods largely focus on a single type of noise (i.e., dropouts) and have strong distribution assumptions which greatly limit their performance and application. Here we design and develop the AutoClass model, integrating two deep neural network components, an autoencoder, and a classifier, as to maximize both noise removal and signal retention. AutoClass is distribution agnostic as it makes no assumption on specific data distributions, hence can effectively clean a wide range of noise and artifacts. AutoClass outperforms the state-of-art methods in multiple types of scRNA-Seq data analyses, including data recovery, differential expression analysis, clustering analysis, and batch effect removal. Importantly, AutoClass is robust on key hyperparameter settings including bottleneck layer size, pre-clustering number and classifier weight. We have made AutoClass open source at: https://github.com/datapplab/AutoClass.

Toward Causal Inference for Spatio-Temporal Data: Conflict and Forest Loss in Colombia

How does armed conflict influence tropical forest loss? For Colombia, both enhancing and reducing effect estimates have been reported. However, a lack of causal methodology has prevented establishing clear causal links between these two variables. In this work, we propose a class of causal models for spatio-temporal stochastic processes which allows us to formally define and quantify the causal effect of a vector of covariates X on a real-valued response Y. We introduce a procedure for estimating causal effects and a nonparametric hypothesis test for these effects being zero. Our application is based on geospatial information on conflict events and remote-sensing-based data on forest loss between 2000 and 2018 in Colombia. Across the entire country, we estimate the effect to be slightly negative (conflict reduces forest loss) but insignificant (P = 0.578), while at the provincial level, we find both positive effects (e.g., La Guajira, P = 0.047) and negative effects (e.g., Magdalena, P = 0.004). The proposed methods do not make strong distributional assumptions, and allow for arbitrarily many latent confounders, given that these confounders do not vary across time. Our theoretical findings are supported by simulations, and code is available online.

Statistical data harmonization for neuropsychological test battery conversion

AbstractBackgroundA current problem scientists and clinicians face when studying cognitive impairment is how to harmonize scores across neuropsychological tests evaluating the same cognitive domains in a longitudinal analysis. Prior point conversion methods typically do not allow quantification of uncertainty and may be based on strong distributional assumptions. Our framework was motivated by an interest in assessing the uncertainty when converting scores.MethodWe established new statistical methodology for converting C1 and C2 neuropsychological batteries of the National Alzheimer’s Coordinating Center Uniform Data Set collected by the NIA Alzheimer’s Disease Research Centers Program. We adapted methodology from the measurement error and latent variable statistical modeling techniques and proposed an algorithm to give point and interval conversions. We developed parametric and non‐parametric models to achieve this task, allowing one to control for important traits such as age, education level and sex at birth. Additionally, we developed variational inference and functional Expectation Maximization algorithms to fit these models and implemented them in R. This method was compared to existing methodology using Z‐score conversions or quantile matching.ResultWe assessed our model by converting C1 scores (e.g. Mini‐Mental State Examination) to C2 scores (e.g. Montreal Cognitive Assessment). We trained our method on 18092 cognitively normal individuals with either a C1 or C2 score observed. The method was validated on a set 420 individuals with both scores observed using the Hellinger and Total Variation probability metrics to compare conversion distributions. Both methods outperformed prior methods in describing intrinsic variability (Table 1), which is the difference of scores from subsequent visits. Additionally, the non‐parametric model outperformed the others in matching the extrinsic variability, which is the difference of scores for individuals with multiple same day tests used to verify a model is capturing the conversion uncertainty (Table 1; Figures 1,2,3).ConclusionOur framework provides a statistically grounded approach to convert scores with uncertainty, a significant step towards understanding cognitive progression in settings where different neuropsychological batteries are used over time. This work establishes groundwork for future study including detection of Mild Cognitive Impairment when multiple testing batteries are used during an individual’s lifetime.

Real-time accurate detection of wind turbine downtime - An Irish perspective

Wind turbines are complex systems that are susceptible to frequent anomalies, faults, and abnormal behaviour. These are caused mainly due to off-nominal conditions, catastrophic events, and major failures, resulting in downtime conditions. An accurate and timely detection of downtime events provides crucial information for planning and decision-making. This study investigates the utility of wind power and wind speed as potential parameters for real-time downtime detection. Early and accurate detection of these anomalies using system outputs collected from monitoring stations is challenging and involved, especially when attempted in real-time. In this article, a real-time downtime detection framework is proposed that maps system outputs to turbine events - faults, scheduled, and unplanned maintenance - through online condition indicators. Without imposing strong distributional assumptions, using available training samples, an optimal, cost-sensitive real-time anomaly detection framework is proposed to determine whether a sample is anomalous. Considering the trade-off between misclassification errors and detection rates, detection studies are performed using wind power and speed - calibrated against available alarm classifiers - obtained from two Irish wind farms. The data cleaning and formatting for analysis was automated and subjected to classification with several levels of complexity. Recursive condition indicators (RCIs) such as Recursive Mahalanobis distance (RMD) and Recursive Residual Error (RRE) are chosen as features for classification. The real-time detection model becomes particularly useful when it is prohibitive to identify in advance the anomalies without a baseline of the system behaviour under such conditions. Case studies involving Irish wind Supervisory Control And Data Acquisition (SCADA) data demonstrate the successful application of the proposed work for early and accurate downtime detection with comparison to a reference machine learning approach.

Data Pooling in Stochastic Optimization

Managing large-scale systems often involves simultaneously solving thousands of unrelated stochastic optimization problems, each with limited data. Intuition suggests that one can decouple these unrelated problems and solve them separately without loss of generality. We propose a novel data-pooling algorithm called Shrunken-SAA that disproves this intuition. In particular, we prove that combining data across problems can outperform decoupling, even when there is no a priori structure linking the problems and data are drawn independently. Our approach does not require strong distributional assumptions and applies to constrained, possibly nonconvex, nonsmooth optimization problems such as vehicle-routing, economic lot-sizing, or facility location. We compare and contrast our results to a similar phenomenon in statistics (Stein’s phenomenon), highlighting unique features that arise in the optimization setting that are not present in estimation. We further prove that, as the number of problems grows large, Shrunken-SAA learns if pooling can improve upon decoupling and the optimal amount to pool, even if the average amount of data per problem is fixed and bounded. Importantly, we highlight a simple intuition based on stability that highlights when and why data pooling offers a benefit, elucidating this perhaps surprising phenomenon. This intuition further suggests that data pooling offers the most benefits when there are many problems, each of which has a small amount of relevant data. Finally, we demonstrate the practical benefits of data pooling using real data from a chain of retail drug stores in the context of inventory management. This paper was accepted by Chung Piaw Teo, Management Science Special Section on Data-Driven Prescriptive Analytics.

Cross-Validation for Correlated Data

–K-fold cross-validation (CV) with squared error loss is widely used for evaluating predictive models, especially when strong distributional assumptions cannot be taken. However, CV with squared error loss is not free from distributional assumptions, in particular in cases involving non-iid data. This article analyzes CV for correlated data. We present a criterion for suitability of standard CV in presence of correlations. When this criterion does not hold, we introduce a bias corrected CV estimator which we term that yields an unbiased estimate of prediction error in many settings where standard CV is invalid. We also demonstrate our results numerically, and find that introducing our correction substantially improves both, model evaluation and model selection in simulations and real data studies. Supplementary materials for this article are available online.

Spatial Disaggregation of Social Indicators: An Info-Metrics Approach

In this paper we propose a methodology to obtain social indicators at a detailed spatial scale by combining the information contained in census and sample surveys. Similarly to previous proposals, the method proposed here estimates a model at the sample level to later project it to the census scale. The main novelties of the technique presented are that (i) the small-scale mapping produced is perfectly consistent with the aggregates -regional or national- observed in the sample, and (ii) it does not require imposing strong distributional assumptions. The methodology suggested here follows the basics presented on Golan (2018) by adapting a cross-moment constrained Generalized Maximum Entropy (GME) estimator to the spatial disaggregation problem. This procedure is compared with the equivalent methodology of Tarozzi and Deaton (2009) by means of numerical experiments, providing a comparatively better performance. Additionally, the practical implementation of the methodology proposed is illustrated by estimating poverty rates for small areas for the region of Andalusia (Spain).

Making the Output of Seasonal Climate Models More Palatable to Agriculture: A Copula-Based Postprocessing Method

AbstractSeasonal climate forecasts from raw climate models at coarse grids are often biased and statistically unreliable for credible crop prediction at the farm scale. We develop a copula-based postprocessing (CPP) method to overcome this mismatch problem. The CPP forecasts are ensemble based and are generated from the predictive distribution conditioned on raw climate forecasts. CPP performs univariate postprocessing procedures at each station, lead time, and variable separately and then applies the Schaake shuffle to reorder ensemble sequence for a more realistic spatial, temporal, and cross-variable dependence structure. The use of copulas makes CPP free of strong distributional assumptions and flexible enough to describe complex dependence structures. In a case study, we apply CPP to postprocess rainfall, minimum temperature, maximum temperature, and radiation forecasts at a monthly level from the Australian Community Climate and Earth-System Simulator Seasonal model (ACCESS-S) to three representative stations in Australia. We evaluate forecast skill at lead times of 0–5 months on a cross-validation theme in the context of both univariate and multivariate forecast verification. When compared with forecasts that use climatological values as the predictor, the CPP forecast has positive skills, although the skills diminish with increasing lead times and finally become comparable at long lead times. When compared with the bias-corrected forecasts and the quantile-mapped forecasts, the CPP forecast is the overall best, with the smallest bias and greatest univariate forecast skill. As a result of the skill gain from univariate forecasts and the effect of the Schaake shuffle, CPP leads to the most skillful multivariate forecast as well. Further results investigate whether using ensemble mean or additional predictors can enhance forecast skill for CPP.

A Gaussian copula approach for dynamic prediction of survival with a longitudinal biomarker.

Dynamic prediction uses patient information collected during follow-up to produce individualized survival predictions at given time points beyond treatment or diagnosis. This allows clinicians to obtain updated predictions of a patient's prognosis that can be used in making personalized treatment decisions. Two commonly used approaches for dynamic prediction are landmarking and joint modeling. Landmarking does not constitute a comprehensive probability model, and joint modeling often requires strong distributional assumptions and computationally intensive methods for estimation. We introduce an alternative approximate approach for dynamic prediction that aims to overcome the limitations of both methods while achieving good predictive performance. We separately specify the marker and failure time distributions conditional on surviving up to a prediction time of interest and use standard variable selection and goodness-of-fit techniques to identify the best-fitting models. Taking advantage of its analytic tractability and easy two-stage estimation, we use a Gaussian copula to link the marginal distributions smoothly at each prediction time with an association function. With simulation studies, we examine the proposed method's performance. We illustrate its use for dynamic prediction in an application to predicting death for heart valve transplant patients using longitudinal left ventricular mass index information.

Data-Pooling in Stochastic Optimization

Managing large-scale systems often involves simultaneously solving thousands of unrelated stochastic optimization problems, each with limited data. Intuition suggests one can decouple these unrelated problems and solve them separately without loss of generality. We propose a novel data-pooling algorithm called Shrunken-SAA that disproves this intuition. In particular, we prove that combining data across problems can outperform decoupling, even when there is no a priori structure linking the problems and data are drawn independently. Our approach does not require strong distributional assumptions and applies to constrained, possibly non-convex, non-smooth optimization problems such as vehicle-routing, economic lot-sizing or facility location. We compare and contrast our results to a similar phenomenon in statistics (Stein's Phenomenon), highlighting unique features that arise in the optimization setting that are not present in estimation. We further prove that as the number of problems grows large, Shrunken-SAA learns if pooling can improve upon decoupling and the optimal amount to pool, even if the average amount of data per problem is fixed and bounded. Importantly, we highlight a simple intuition based on stability that highlights when and why data-pooling offers a benefit, elucidating this perhaps surprising phenomenon. This intuition further suggests that data-pooling offers the most benefits when there are many problems, each of which has a small amount of relevant data. Finally, we demonstrate the practical benefits of data-pooling using real data from a chain of retail drug stores in the context of inventory management.

Substantial Bias in the Tobit Estimator: Making a Case for Alternatives

Censored outcome data are commonly encountered in criminology. Criminologists sometimes use the tobit model to address these censored data. While tobit models make more realistic demands of censored outcome data than ordinary least squares (OLS) regression, they require the researcher to make strong distributional assumptions. When these assumptions are not met, as is often the case in criminological data, tobit models yield biased and inconsistent estimates. We seek to demonstrate this substantial bias in simulation analyses and present easily applied alternative methods. The tobit model and semiparametric alternatives for censored outcome data are applied with simulated data under varying conditions. These simulations are followed with an empirical example using sentencing data. The bias from tobit can be corrected through application of semiparametric alternatives. Criminologists should begin their analyses of censored outcome data with the least restrictive of the available models (CLAD) before progressing to more efficient, but potentially biased, estimators.

Randomization Inference for Outcomes with Clumping at Zero

ABSTRACTWhile randomization inference is well developed for continuous and binary outcomes, there has been comparatively little work for outcomes with nonnegative support and clumping at zero. Typically, outcomes of this type have been modeled using parametric models that impose strong distributional assumptions. This article proposes new randomization inference procedures for nonnegative outcomes with clumping at zero. Instead of making distributional assumptions, we propose various assumptions about the nature of the response to treatment and use permutation inference for both testing and estimation. This approach allows for some natural goodness-of-fit tests for model assessment, as well as flexibility in selecting test statistics sensitive to different potential alternatives. We illustrate our approach using two randomized trials, where job training interventions were designed to increase earnings of participants.

Nonparametric Resampling Methods for Testing Multiplicative Terms in AMMI and GGE Models for Multienvironment Trials

The additive main effects and multiplicative interaction (AMMI) and genotype and genotype × environment interaction (GGE) models have been extensively used for the analysis of genotype × environment experiments in plant breeding and variety testing. Since their introduction, several tests have been proposed for testing the significance of the multiplicative terms, including a parametric bootstrap procedure. However, all of these tests are based on the assumptions of normality and homogeneity variance of the errors. In this paper, we propose tests based on nonparametric bootstrap and permutation methods. The proposed tests do not require any strong distributional assumptions. We also propose a test that can handle heterogeneity of variance between environments. The robustness of the proposed tests is compared with the robustness of other competing tests. The simulation study shows that the proposed tests always perform better than the parametric bootstrap method when the distributional assumptions of normality and homogeneity of variance are violated. The stratified permutation test can be recommended in case of heterogeneity of variance between environments.

Semi-supervised AUC optimization based on positive-unlabeled learning

Maximizing the area under the receiver operating characteristic curve (AUC) is a standard approach to imbalanced classification. So far, various supervised AUC optimization methods have been developed and they are also extended to semi-supervised scenarios to cope with small sample problems. However, existing semi-supervised AUC optimization methods rely on strong distributional assumptions, which are rarely satisfied in real-world problems. In this paper, we propose a novel semi-supervised AUC optimization method that does not require such restrictive assumptions. We first develop an AUC optimization method based only on positive and unlabeled data (PU-AUC) and then extend it to semi-supervised learning by combining it with a supervised AUC optimization method. We theoretically prove that, without the restrictive distributional assumptions, unlabeled data contribute to improving the generalization performance in PU and semi-supervised AUC optimization methods. Finally, we demonstrate the practical usefulness of the proposed methods through experiments.

A Weighting Method for Assessing Between-Site Heterogeneity in Causal Mediation Mechanism

When a multisite randomized trial reveals between-site variation in program impact, methods are needed for further investigating heterogeneous mediation mechanisms across the sites. We conceptualize and identify a joint distribution of site-specific direct and indirect effects under the potential outcomes framework. A method-of-moments procedure incorporating ratio-of-mediator-probability weighting (RMPW) consistently estimates the causal parameters. This strategy conveniently relaxes the assumption of no Treatment × Mediator interaction while greatly simplifying the outcome model specification without invoking strong distributional assumptions. We derive asymptotic standard errors that reflect the sampling variability of the estimated weight. We also offer an easy-to-use R package, MultisiteMediation, that implements the proposed method. It is freely available at the Comprehensive R Archive Network ( http://cran.r-project.org/web/packages/MultisiteMediation ).

Standard Errors and Confidence Intervals of Norm Statistics for Educational and Psychological Tests.

Norm statistics allow for the interpretation of scores on psychological and educational tests, by relating the test score of an individual test taker to the test scores of individuals belonging to the same gender, age, or education groups, et cetera. Given the uncertainty due to sampling error, one would expect researchers to report standard errors for norm statistics. In practice, standard errors are seldom reported; they are either unavailable or derived under strong distributional assumptions that may not be realistic for test scores. We derived standard errors for four norm statistics (standard deviation, percentile ranks, stanine boundaries and Z-scores) under the mild assumption that the test scores are multinomially distributed. A simulation study showed that the standard errors were unbiased and that corresponding Wald-based confidence intervals had good coverage. Finally, we discuss the possibilities for applying the standard errors in practical test use in education and psychology. The procedure is provided via the R function check.norms, which is available in the mokken package.