Shorter Confidence Intervals Research Articles

Dissecting the colocalized GWAS and eQTLs with mediation analysis for high-dimensional exposures and confounders.

To leverage the advancements in genome-wide association studies (GWAS) and quantitative trait loci (QTL) mapping for traits and molecular phenotypes to gain mechanistic understanding of the genetic regulation, biological researchers often investigate the expression QTLs (eQTLs) that colocalize with QTL or GWAS peaks. Our research is inspired by 2 such studies. One aims to identify the causal single nucleotide polymorphisms that are responsible for the phenotypic variation and whose effects can be explained by their impacts at the transcriptomic level in maize. The other study in mouse focuses on uncovering the cis-driver genes that induce phenotypic changes by regulating trans-regulated genes. Both studies can be formulated as mediation problems with potentially high-dimensional exposures, confounders, and mediators that seek to estimate the overall indirect effect (IE) for each exposure. In this paper, we propose MedDiC, a novel procedure to estimate the overall IE based on difference-in-coefficients approach. Our simulation studies find that MedDiC offers valid inference for the IE with higher power, shorter confidence intervals, and faster computing time than competing methods. We apply MedDiC to the 2 aforementioned motivating datasets and find that MedDiC yields reproducible outputs across the analysis of closely related traits, with results supported by external biological evidence. The code and additional information are available on our GitHub page (https://github.com/QiZhangStat/MedDiC).

A Generalized Bootstrap Procedure of the Standard Error and Confidence Interval Estimation for Inverse Probability of Treatment Weighting

The inverse probability of treatment weighting (IPTW) approach is commonly used in propensity score analysis to infer causal effects in regression models. Due to oversized IPTW weights and errors associated with propensity score estimation, the IPTW approach can underestimate the standard error of causal effect. To remediate this, bootstrap standard errors have been recommended to replace the IPTW standard error, but the ordinary bootstrap (OB) procedure might still result in underestimation of the standard error because of its inefficient resampling scheme and untreated oversized weights. In this paper, we develop a generalized bootstrap (GB) procedure for estimating the standard error and confidence intervals of the IPTW approach. Compared with the OB procedure and other three procedures in comparison, the GB procedure has the highest precision and yields conservative standard error estimates. As a result, the GB procedure produces short confidence intervals with highest coverage rates. We demonstrate the effectiveness of the GB procedure via two simulation studies and a dataset from the National Educational Longitudinal Study-1988 (NELS-88).

An interval water demand prediction method to reduce uncertainty: A case study of Sichuan Province, China

Effective prediction of water demand is a prerequisite for decision makers to achieve reliable management of water supply. Currently, the research on water demand prediction focuses on point prediction method. In this study, we constructed a GA-BP-KDE hybrid interval water demand prediction model by combining non-parametric estimation and point prediction. Multiple metaheuristic algorithms were used to optimize the Back-Propagation Neural Network (BP) and Kernel Extreme Learning Machine (KELM) network structures. The performance of the water demand point prediction models was compared by the Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), Kling-Gupta Efficiency (KGE), computation time, and fitness convergence curves. The kernel density estimation method (KDE) and the normal distribution method were used to fit the distribution of errors. The probability density function with the best fitting degree was selected based on the index G. The shortest confidence interval under 95% confidence was calculated according to the asymmetry of the error distribution. We predicted the impact indicator values for 2025 using the exponential smoothing method, and obtained water demand prediction intervals for various water use sectors. The results showed that the GA-BP model was the optimal model as it exhibited the highest computational efficiency, algorithmic stability, and prediction accuracy. The three prediction intervals estimated after adjusting the KDE bandwidth parameter covered most of the sample points in the test set. The prediction intervals of the four water use sectors were evaluated as F values of 1.6845, 1.3294, 1.6237, and 1.3600, which indicates high accuracy and quality of the prediction intervals. The mixed water demand interval prediction based on GA-BP-KDE reduces the uncertainty of the point prediction results and can provide a basis for water resource management by decision makers.

Uncertainty Quantification for Nonconvex Tensor Completion: Confidence Intervals, Heteroscedasticity and Optimality

We study the distribution and uncertainty of nonconvex optimization for noisy tensor completion—the problem of estimating a low-rank tensor given incomplete and corrupted observations of its entries. Focusing on a two-stage estimation algorithm proposed by Cai <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , we characterize the distribution of this nonconvex estimator down to fine scales. This distributional theory in turn allows one to construct valid and short confidence intervals for both the unseen tensor entries and the unknown tensor factors. The proposed inferential procedure enjoys several important features: (1) it is fully adaptive to noise heteroscedasticity, and (2) it is data-driven and automatically adapts to unknown noise distributions. Furthermore, our findings unveil the statistical optimality of nonconvex tensor completion: it attains un-improvable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math></inline-formula> accuracy—including both the rates and the pre-constants—when estimating both the unknown tensor and the underlying tensor factors.

Propagating uncertainty about molecular evolution models and prior distributions to phylogenetic trees

Phylogenetic trees constructed from molecular sequence data rely on largely arbitrary assumptions about the substitution model, the distribution of substitution rates across sites, the version of the molecular clock, and, in the case of Bayesian inference, the prior distribution. Those assumptions affect results reported in the form of clade probabilities and error bars on divergence times and substitution rates. Overlooking the uncertainty in the assumptions leads to overly confident conclusions in the form of inflated clade probabilities and short confidence intervals or credible intervals.This paper demonstrates how to propagate that uncertainty by combining the models considered along with all of their assumptions, including their prior distributions. The combined models incorporate much more of the uncertainty than Bayesian model averages since the latter tend to settle on a single model due to the higher-level assumption that one of the models is true. Nucleotide sequence data illustrates the proposed model combination method.

Empirical Investigation on the Effect of the Number of Resamplings on the Distribution of Bootstrap Standard Error Using Response Time Data

Aims: To investigate how the number of bootstrapping B affects the values returned by the bootstrap standard error of the arithmetic mean and the α-trimmed mean of response data using bootstrap confidence intervals (CI) at 95% level; carried out to fill up observed gap for study on standard error, the tool generally employed in assessing the long run accuracy of a given statistical estimator of θ.&#x0D; Study Design: This was a parametric, empirical bootstrap simulation study.&#x0D; Place and Duration of the Study: Departments of Computer Science and Statistics, Federal Polytechnic Oko, 2020/2021 session.&#x0D; Methodology: Response time data were generated with student customers of mobile telephone network (mtn) Nigeria and stored in SPSS. A sample n = 51 responses was selected using “Select Cases” command to increase precision and minimize bias. Bootstrap simulation study was carried out using R programming language. Four approaches for estimating bootstrap confidence intervals were used. The interval coverage and the interval lengths were determined and compared for B = 20, 50, 100, 500, 1000, 5000, and 10000.&#x0D; Results: The 95% CI for 0.2266338 (the estimated sample standard error of 10% trimmed mean) returned the best interval for our skewed data set; when B = 20; the CI for returned (0.2051, 0.2343) for the normal approach, (0.2082, 0.2371) for the basic, (0.2071, 0.2360) for the percentile and (0.2071, 0.2360) for the BCa method. As B increased to 5000, it returned (0.2259, 0.2277) for the normal approach, (0.2259, 0.2277) for the basic, (0.2260, 0.2277) for the percentile and (0.2261, 0.2279) for the BCa showing a shorter interval yet covering the estimate.&#x0D; Conclusion: Thus for our response data study, increasing B in estimating standard error increases the chances of more precise and shorter confidence intervals rather than the chances for coverage.

Fast estimation and choice of confidence interval methods for step regression

In this paper we propose a new fast grid search algorithm for finding the least square estimators of a step regression model. This algorithm makes it practical to compute resampling-based confidence intervals for step regression models. We introduce five data generating models, including one where the mean model is a step model (model correctly specified) and four where the mean models are not step models (model misspecified), and use them to study the coverage probabilities of two new types of resampling-based confidence intervals for step regression: symmetric percentile bootstrap confidence intervals and subsampling confidence intervals using a new set of rules-of-thumb to select block size. Our results show that when the model is correctly specified, the symmetric percentile Efron bootstrap confidence intervals provide close-to-nominal coverage and have shorter intervals than the subsampling methods; when the model is misspecified, the subsampling method using the rules-of-thumb provides good coverage and shorter confidence intervals than the symmetric percentile Efron bootstrap method and the subsampling method using a double bootstrap-like procedure for block size selection. Finally, we apply the proposed methods to a real world environmental dataset on the relationship between grassland productivity, soil moisture anomalies and other hydro-climatic and land use variables to provide inference for the threshold in soil moisture anomalies, across which there is a jump in grassland productivity.

Semiparametric empirical likelihood inference with estimating equations under density ratio models

The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or additional auxiliary information expressed as estimating equations. We examine the asymptotic properties of the maximum empirical likelihood estimators (MELEs) of the unknown parameters in the DRMs and/or defined through estimating equations, and establish the chi-square limiting distributions for the empirical likelihood ratio (ELR) statistics. We show that the asymptotic variance of the MELEs of the unknown parameters does not decrease if one estimating equation is dropped. Similar properties are obtained for inferences on the cumulative distribution function and quantiles of each of the populations involved. We also propose an ELR test for the validity and usefulness of the auxiliary information. Simulation studies show that correctly specified estimating equations for the auxiliary information result in more efficient estimators and shorter confidence intervals. Two real examples are used for illustrations.

Efficacy of aqua-based plyometric exercises in the rehabilitation of patients with juvenile dermatomyositis: A randomized crossover pilot study.

Patients with juvenile dermatomyositis (JDM) experience muscle weakness, tiredness, and loss of energy, which restrict their abilities in performance of their daily living activities. To explore the effect of aquatic-based plyometric (Aqua-PLYO) exercises on muscle strength, fatigue, and functional ability in patients with JDM. This was a randomized, single-blind, crossover pilot study that included 16 patients with JDM (age 13.44±2.85years). They were assigned randomly to receive either the Aqua-PLYO exercises (n=8) or the standard outpatient care (SoC ; n=8) first. After a 1-month washout, the treatment was reversed. Lower limb muscle strength, fatigue perception, functional ability, and disease activity were evaluated before and after each treatment period. Irrespective of the treatment order, the Aqua-PLYO treatment yielded greater improvement in muscle strength (hip flexors and abductors [P<0.001] or knee flexors [P<0.001] and extensors [P=0.0008]), fatigue perception (P<0.001), functional ability (P=0.009), and disease activity (P=0.0001) than the SoC treatment. By using the shortest confidence intervals (100[1-2α]%) of the difference, the average bioequivalence of the Aqua-PLYO and SoC has not been established at P=0.05, because the upper and lower confidence bounds of all outcomes were not between the acceptance limits. No period or carryover effects were detected in all outcomes. The Aqua-PLYO exercise protocol as implemented in this study is safe, feasible, and well-tolerated in patients with JDM and seemingly useful to help increase muscle strength, reduce fatigue, and enhance functional ability in such a patient population.

Constructing a confidence interval for the ratio of normal distribution quantiles

Abstract In this paper, to construct a confidence interval (general and shortest) for quantiles of normal distribution in one population, we present a pivotal quantity that has non-central t distribution. In the case of two independent normal populations, we propose a confidence interval for the ratio of quantiles based on the generalized pivotal quantity, and we introduce a simple method for extracting its percentiles, based on which a shorter confidence interval can be created. Also, we provide general and shorter confidence intervals using the method of variance estimate recovery. The performance of five proposed methods will be examined by using simulation and examples.

A Robust Statistical method to Estimate the Intervention Effect with Longitudinal Data

Segmented regression is a standard statistical procedure used to estimate the effect of a policy intervention on time series outcomes. This statistical method assumes the normality of the outcome variable, a large sample size, no autocorrelation in the observations, and a linear trend over time. Also, segmented regression is very sensitive to outliers. In a small sample study, if the outcome variable does not follow a Gaussian distribution, then using segmented regression to estimate the intervention effect leads to incorrect inferences. To address the small sample problem and non-normality in the outcome variable, including outliers, we describe and develop a robust statistical method to estimate the policy intervention effect in a series of longitudinal data. A simulation study is conducted to demonstrate the effect of outliers and non-normality in the outcomes by calculating the power of the test statistics with the segmented regression and the proposed robust statistical methods. Moreover, since finding the sampling distribution of the proposed robust statistic is analytically difficult, we use a nonparametric bootstrap technique to study the properties of the sampling distribution and make statistical inferences. Simulation studies show that the proposed method has more power than the standard t-test used in segmented regression analysis under the non-normality error distribution. Finally, we use the developed technique to estimate the intervention effect of the Istanbul Declaration on illegal organ activities. The robust method detected more significant effects compared to the standard method and provided shorter confidence intervals.

On the Shortest Pivotal Confidence Intervals: An Entropy Measure Technique

For the important role of confidence intervals in statistical inference, we present in this article the shortest pivotal confidence interval using an entropy measure called the Resistor-Average distance, two examples are used to show the application of the proposed technique which include a simulation study.

Ratio- and product-based estimators using known coefficient of variation of the auxiliary variable via modified maximum likelihood

In this paper, we improve ratio- and product-based estimators for population mean using known coefficient of variation of the auxiliary variable through modified maximum likelihood. The expressions for biases and mean square errors of the proposed estimators have been obtained theoretically. We obtain some conditions under which the proposed estimators have minimum mean square errors than other existing estimators. For the support of the theoretical outcomes, simulations studies have been made under several super-population models. One real life application for the support of the properties of the proposed estimator has also been given. We also study the robustness properties of the proposed estimators. We show that the use of modified maximum likelihood estimates in estimating finite population mean results to robust estimates under non-normality and outliers. Confidence intervals show that the proposed estimator has shorter confidence intervals and more coverage of estimates than those of the existing estimators.

Feasible generalized least squares using support vector regression

We investigate semiparametric Feasible Generalized Least Squares using Support Vector Regression to estimate the conditional variance function. Monte Carlo results indicate the resulting estimator and an accompanying standard error correction offer substantially improved precision, nominal coverage rates, and shorter confidence intervals than Ordinary Least Squares with heteroskedasticity-consistent standard errors. Reductions in root mean squared error can be over 90% of those achievable when the form of heteroskedasticity is known.

Feasible Generalized Least Squares Using Machine Learning

In the presence of heteroskedastic errors, regression using Feasible Generalized Least Squares (FGLS) offers potential efficiency gains over Ordinary Least Squares (OLS). However, FGLS adoption remains limited, in part because the form of heteroskedasticity may be misspecified. We investigate machine learning methods to address this concern, focusing on Support Vector Regression. Monte Carlo results indicate the resulting estimator and an accompanying standard error correction offer substantially improved precision, nominal coverage rates, and shorter confidence intervals than OLS with heteroskedasticity-consistent (HC3) standard errors. Reductions in root mean squared error are over 90% of those achievable when the form of heteroskedasticity is known.

A novel nonparametric confidence interval for differences of proportions for correlated binary data.

Various confidence interval estimators have been developed for differences in proportions resulted from correlated binary data. However, the width of the mostly recommended Tango's score confidence interval tends to be wide, and the computing burden of exact methods recommended for small-sample data is intensive. The recently proposed rank-based nonparametric method by treating proportion as special areas under receiver operating characteristic provided a new way to construct the confidence interval for proportion difference on paired data, while the complex computation limits its application in practice. In this article, we develop a new nonparametric method utilizing the U-statistics approach for comparing two or more correlated areas under receiver operating characteristics. The new confidence interval has a simple analytic form with a new estimate of the degrees of freedom of n - 1. It demonstrates good coverage properties and has shorter confidence interval widths than that of Tango. This new confidence interval with the new estimate of degrees of freedom also leads to coverage probabilities that are an improvement on the rank-based nonparametric confidence interval. Comparing with the approximate exact unconditional method, the nonparametric confidence interval demonstrates good coverage properties even in small samples, and yet they are very easy to implement computationally. This nonparametric procedure is evaluated using simulation studies and illustrated with three real examples. The simplified nonparametric confidence interval is an appealing choice in practice for its ease of use and good performance.

The use of chained two-point clusters for the examination of associations of air pollution with health conditions

There are a few accepted and intensively applied statistical methods used to study associations of ambient air pollution with health conditions. Among the most popular methods applied to assess short term air health effects are case-crossover (using events) and time-series methodologies (using counts). A few other techniques for studying counts of events have been proposed, including the Generalized Linear Mixed Models (GLMM). One suggested GLMM technique uses cluster structures based on natural embedded hierarchies: days are nested in the days of a week (dow), which, in turn, are nested in months and months in years (< dow, month, years >). In this study the authors considered clusters with hierarchical structures in a form of < dow, 14-days, year >, where the 14-days hierarchy determines 7 clusters composed of 2 days (the same days) of a week (2 Mondays, 2 Tuesdays, etc.), in 1 year. In this work the authors proposed hierarchical chained clusters in which 2 days of a week are grouped as follows: (first, second), (second, third), (third, fourth) and so on. Such an approach allows determination of an additional series of the slopes on the clusters (second, third), (fourth, fifth), etc., i.e., estimation of the coefficients for other configurations of air pollutant levels. The authors considered a series of 2 point chained clusters covering a year. In such a construction each cluster has one common data point (day) with another one. The authors estimated coefficients (slopes) related to the ambient ozone exposure (mortality) and to 3 selected air pollutants (particulate matter, nitrogen dioxide and ozone) combined into index and considered as health risk exposure (emergency department (ED) visits). The generated results were compared to the estimations obtained from the time-series method and the time-stratified case-crossover method applied to the same data. The proposed statistical method, based on the chained hierarchical clusters (< dow, 14-days, year >), generated results with shorter confidence intervals than the other methods.

Length minimization for Poisson confidence procedures

ABSTRACTWe study Poisson confidence procedures that potentially lead to short confidence intervals, investigating the class of all minimal cardinality procedures. We consider how length minimization should be properly defined, and show that Casella and Robert's (1989) criterion for comparing Poisson confidence procedures leads to a contradiction. We provide an alternative criterion for comparing length performance, identify the unique length optimal minimal cardinality procedure by this criterion, and propose a modification that eliminates an important drawback it possesses. We focus on procedures whose coverage never falls below the nominal level and discuss the case in which the nominal level represents mean coverage.

Sample Selection Model with Bootstrap (BPSSM) Approach: Case Study of the Malaysian Population and Family Survey

Heckman Sampel Selection Model (PSSM) has been adopted widely in the study of labour work. This model contains exogenous, endogenous and standard error variables. However, this model is constantly exposed to high inaccuracy of estimation result. Therefore, to obtain an accurate and precise estimation, the bootstrap approach is introduced. The bootstrap approach will be hybrid with PSSM model known as BPSSM to achieve estimation result that is more precise. Then, the BPSSM is applied to Malaysian Population and Family Survey 1994 (MPFS-1994) data. The results showed that BPSSM provide a smaller standard error and shorter confidence intervals.

Confidence Intervals for Quantiles of a Two-parameter Exponential Distribution under Progressive Type-II Censoring

Confidence intervals for the pth-quantile Q of a two-parameter exponential distribution provide useful information on the plausible range of Q, and only inefficient equal-tail confidence intervals have been discussed in the statistical literature so far. In this article, the construction of the shortest possible confidence interval within a family of two-sided confidence intervals is addressed. This shortest confidence interval is always shorter, and can be substantially shorter, than the corresponding equal-tail confidence interval. Furthermore, the computational intensity of both methodologies is similar, and therefore it is advantageous to use the shortest confidence interval. It is shown how the results provided in this paper can apply to data obtained from progressive Type II censoring, with standard Type II censoring as a special case. The applications of more complex confidence interval constructions through acceptance set inversions that can employ prior information are also discussed.