Confidence Interval Estimation Method Research Articles

Optimal Cut-Point Selection Methods Under Binary Classification When Subclasses Are Involved.

In practice, we often encounter binary classification problems where both main classes consist of multiple subclasses. For example, in an ovarian cancer study where biomarkers were evaluated for their accuracy of distinguishing noncancer cases from cancer cases, the noncancer class consists of healthy subjects and benign cases, while the cancer class consists of subjects at both early and late stages. This article aims to provide a large number of optimal cut-point selection methods for such setting. Furthermore, we also study confidence interval estimation of the optimal cut-points. Simulation studies are carried out to explore the performance of the proposed cut-point selection methods as well as confidence interval estimation methods. A real ovarian cancer data set is analyzed using the proposed methods.

Stress Prediction Model of Super-High Arch Dams during Their Initial Operation Stages

It is of great significance to identify the spatiotemporal stress distribution characteristics to ensure the safety of a super-high arch dam during the initial operation stage. Taking the 285.5 m-high Xiluodu Dam as an example, the spatiotemporal distribution characteristics were analyzed based on the five-year observation data after impoundment. Statistical and boosted-regression-tree-based prediction models for the dam stress were established. The boosted-regression-tree-based prediction model is more accurate than the statistical model. The monitoring indicators for the measuring points of focused locations were determined using the confidence interval estimation method. The results show that the dam was in a compression state, and the arching effect was obvious. The arch direction compressive stress gradually increased and stabilized, and the maximum appeared in the middle of the upstream face of the crown cantilever monolith. For the crown cantilever, the cantilever direction stress at the dam heel was significantly affected by the interior temperature recovery, and the arch direction stress in the middle of the upstream face was significantly affected by the reservoir water level. The measuring points of the focused locations with reliable observation data can be selected as a monitoring index to guide the initial operation.

Bayesian and likelihood estimation of multicomponent stress–strength reliability from power Lindley distribution based on progressively censored samples

In this article, the problem of estimation of reliability of a ℓ-component system when both the stress and strength components are assumed to have a power Lindley distribution is discussed. The multicomponent stress–strength reliability parameter is obtained using both the Bayesian and the classical approaches when component-wise each unit follows a power Lindley distribution. To estimate the multicomponent stress–strength reliability parameter under the classical approach, the method of maximum likelihood and the asymptotic confidence interval estimation method are used as point and interval estimation methods, respectively. Under the Bayesian paradigm, the reliability parameter is estimated under the linear exponential loss function using the Lindley approximation, the Tierney–Kadane approximation and the Markov chain Monte Carlo (MCMC) techniques and subsequently highest posterior density credible intervals are obtained. To validate the efficacy of the proposed estimation strategies, a simulation study is carried out. Finally, two real-life data sets are re-analysed for illustrative purposes.

Theoretical Analysis and Numerical Simulation of the Motion of RDX Deflagration-Driven Flyer Plate Based on Laser-Initiated Micro-Pyrotechnic Devices.

Miniaturized laser-initiated pyrotechnic devices have great application prospects in aerospace and modern weapon systems due to their excellent energy output performance and reliability. In order to develop a low-energy insensitive laser detonation technology based on a two-stage charge structure, it is important to deeply analyze the motion law of a titanium flyer plate driven by the deflagration of the first-stage charge (RDX). The effects of the charge mass of RDX, flyer plate mass, and barrel length on the motion law of flyer plates were studied through a numerical simulation method based on the Powder Burn deflagration model. The consistency between the numerical simulation and the experimental results was analyzed using the paired t confidence interval estimation method. The results show that the Powder Burn deflagration model can effectively describe the motion process of the RDX deflagration-driven flyer plate with a 90% confidence level, and its velocity error is ≤6.7%. The speed of the flyer plate is proportional to the mass of the RDX charge, inversely proportional to the mass of the flyer plate, and exponentially related to its moving distance. As the moving distance of the flyer plate increases, the RDX deflagration products and air in front of the flyer plate are compressed, which inhibits the motion of the flyer plate. In the optimum state (the mass of the RDX charge is 60 mg, the mass of the flyer is 85 mg, and the length of the barrel is 3 mm), the speed of the titanium flyer reaches 583 m/s, and the peak pressure of the RDX deflagration reaches 2182 MPa. This work will provide a theoretical basis for the refined design of a new generation of miniaturized high-performance laser-initiated pyrotechnic devices.

Scientific progress in information theory quantifiers

The Bandt and Pompe method (BPM) has been successfully applied to estimate the information theory quantifiers. The most significant limitation of the BPM is that this approach is based on point estimation. This research provides scientific progress into the several applications of the information theory quantifiers. In this way, we propose a new statistic confidence interval estimation method for the Permutation Entropy, Fisher Information Measure, and Macroeconophysics Indicator of Efficiency (MIEE). Therefore, we examine quarterly Gross Domestic Product (GDP) time series for 25 countries members of the Organization for Economic Co-operation and Development (OECD). The periods cover more than 59 years, from Q1-1960 to Q3-2019, with 238 data points. For each GDP time series, we employ the non-parametric method Local Block Bootstrap to provide a stylized fact about an empirical distribution for these data taking into account the information theory quantifiers. Based on the values of the empirical distribution of the information theory quantifiers, we construct the Shannon-Fisher causality plane (SFCP), which allows us to quantify the disorder and evaluate randomness present in the time series of quarterly GDP in each country. In addition, we use information theory quantifiers to rank the most efficient countries in allocating the resources arising from economic growth to generate a virtuous cycle of growth. Also, we apply the Principal Component Analysis (PCA) to check the results of the empirical distribution of the MIEE. We find the PCA promotes the same result as the MIEE. Our results suggest an alternative form of clustering using information theory quantifiers linked to the similarity of countries’ GDPs and the mutual influences of one country’s economic growth on the others.

Assessing standardized contrast effects in ANCOVA: Confidence intervals, precision evaluations, and sample size requirements.

Standardized effect sizes and confidence intervals are useful statistical assessments for comparing results across different studies when measurement units are not directly comparable. This paper aims to describe and compare confidence interval estimation methods for the standardized contrasts of treatment effects in ANCOVA designs. Sample size procedures are also presented to assure that the resulting confidence intervals yield informative estimation with adequate precision. Exact interval estimation approach has theoretical and empirical advantages in coverage probability and interval width over the approximate interval procedures. Numerical investigations of the existing method reveal that the omission of covariate variables has a negative impact on sample size calculations for precise interval estimation, especially when there is disparity in influential covariate variables. The proposed approaches and developed computer programs fully utilize covariate properties in interval estimation and provide accurate sample size determinations under the precision considerations of the expected interval width and the assurance probability of interval width.

Correction: Genetic Ancestry Inference from Cancer-Derived Molecular Data across Genomic and Transcriptomic Platforms

In the earlier version of this article (1), as it was published online on November 9, 2022, a special case occurred for the estimation of the 95% confidence intervals for the accuracy and AUROC measure of performance where all the inferred ancestry calls agree with the ground truth. This special case could not be handled by the confidence interval estimation methods originally employed, and the corresponding entries were previously indicated as missing in Table 1. The authors subsequently adapted the estimation methods as necessary for handling this special case and provided the revised confidence interval estimates, which are reflected in Table 1 and Supplementary Tables S7, S8, S11, and S15–S18. The HTML and PDF versions of this article were corrected on December 13, 2022, ahead of print.

Online confidence interval estimation for federated heterogeneous optimization

From a statistical viewpoint, it is essential to perform statistical inference in federated learning to understand the underlying data distribution. Due to the heterogeneity in the number of local iterations and in local datasets, traditional statistical inference methods are not competent in federated learning. This paper studies how to construct confidence intervals for federated heterogeneous optimization problems. We introduce the rescaled federated averaging estimate and prove the consistency of the estimate. Focusing on confidence interval estimation, we establish the asymptotic normality of the parameter estimate produced by our algorithm and show that the asymptotic covariance is inversely proportional to the client participation rate. We propose an online confidence interval estimation method called separated plug-in via rescaled federated averaging. This method can construct valid confidence intervals online when the number of local iterations is different across clients. Since there are variations in clients and local datasets, the heterogeneity in the number of local iterations is common. Consequently, confidence interval estimation for federated heterogeneous optimization problems is important.

Prediction and forewarning of axial force of steel bracing in foundation pit based on verhulst model.

The axial force of steel bracing is one of the essential indexes to measure the stability of the bracing system of a foundation pit. The steel bracing system of a foundation pit in Ningbo City, China was taken as the research object to guarantee the stability of the steel bracing system of the foundation pit. Besides, the change of axial force between the two steel bracing structures was analyzed to predict the axial force data of the steel bracing and perform the safety forewarning of the steel bracing system. Firstly, GM (1,1) and Verhulst models in the gray model were selected for prediction based on the characteristics of poor information and the small sample size of original monitoring data of the steel bracing. Secondly, the precision of the GM (1,1) model and Verhulst model was compared to determine a more accurate prediction method. Finally, the safety forewarning model of the confidence interval estimation method was established based on the data obtained from the prediction model and the deformation characteristics and indexes of the steel bracing. With the significance levels α = 5% and α = 2% as the demarcating points, the forewarning grades of the steel bracing system of the deep foundation pit were divided, and then the operating state of the current steel bracing system was determined. The results demonstrated that the Verhulst model had better prediction precision compared with the ordinary GM (1, 1) model. Besides, the steel bracing system was in the safe operation range, and the judgment results of the model were consistent with the actual situation of the foundation pit of the steel bracing system. Thus, the Verhulst prediction model and the confidence interval security early forewarning model could be used to judge the stability of the steel bracing system.

A sampling-based online Co-Location-Resistant Virtual Machine placement strategy

In this paper, we discuss the co-location attack problem in the cloud IaaS from the Virtual Machine (VM) placement strategy perspective. We formulate the online secure optimization VM placement problem in a way that guarantees—apriori—a specified level of security while minimizing the number of used physical servers. To solve such a problem, we propose an approximate online secure VM placement algorithm based on sampling. The polynomial-time algorithm is based on a sound security inference procedure based on the confidence interval estimation method. Our empirical results demonstrate the correctness and the effectiveness of our approach in guaranteeing a Co-Location-Resistant (CLR) VM placement with a specific level of confidence and a threshold error as new incoming VM requests are being assigned to servers online. We compared our algorithm to a CLR alternative presented in Azar et al. (2014).

Calculating Confidence Interval Estimation Using Maximum Likelihood Estimator For Dataset

Confidence interval estimation is a fundamental technique in statistical inference. Methods for confidence interval estimation used in the literature and implemented in system dynamics software packages typically assume that the data are normally distributed, autocorrelated and homoscedasticity. The objective of this paper is to demonstrate the calculation of confidence interval using maximum likelihood method for fatigue test data for the AISI 8630 M steel for surface roughnes. The advantages of maximum likelihood method are convenience to use and computational efficient. The computational results show that the confidence interval by 90 %, 95% and 99% have significance differences. The width of confidence interval showed that 99% is the highest width compare to 90% and 95%.

The use of the bootstrap method for the assessment of investment effectiveness and risk – the case of confidence intervals estimation for the Sharpe ratio and TailVaR

This paper is aimed at presenting application of bootstrap interval estimation methods to the assessment of financial investment’s effectiveness and risk. At first, we give an overview of various methods of bootstrap confidence interval estimation, i.e. bootstrap-t interval, percentile interval and BCa interval. Then, bootstrap confidence interval estimation methods are used to estimate confidence intervals for the Sharpe ratio and TailVaR of the Warsaw Stock Exchange sectoral indices. The results show that the bootstrap confidence intervals of different types are quite similarly positioned for each of the analysed index and measure. Taking into the account the locations of confidence intervals for both the Sharpe ratio and TailVaR, the real estate sector tends to be the most advantageous from the investor’s viewpoint.

Common Medical and Statistical Problems: The Dilemma of the Sample Size Calculation for Sensitivity and Specificity Estimation

Sample size calculation in biomedical practice is typically based on the problematic Wald method for a binomial proportion, with potentially dangerous consequences. This work highlights the need of incorporating the concept of conditional probability in sample size determination to avoid reduced sample sizes that lead to inadequate confidence intervals. Therefore, new definitions are proposed for coverage probability and expected length of confidence intervals for conditional probabilities, like sensitivity and specificity. The new definitions were used to assess seven confidence interval estimation methods. In order to determine the sample size, two procedures—an optimal one, based on the new definitions, and an approximation—were developed for each estimation method. Our findings confirm the similarity of the approximated sample sizes to the optimal ones. R code is provided to disseminate these methodological advances and translate them into biomedical practice.

Confidence interval estimation for the changepoint of treatment stratification in the presence of a qualitative covariate-treatment interaction.

The goal in stratified medicine is to administer the "best" treatment to a patient. Not all patients might benefit from the same treatment; the choice of best treatment can depend on certain patient characteristics. In this article, it is assumed that a time-to-event outcome is considered as a patient-relevant outcome and a qualitative interaction between a continuous covariate and treatment exists, ie,that patients with different values of one specific covariate should be treated differently. We suggest and investigate different methods for confidence interval estimation for the covariate value, where the treatment recommendation should be changed based on data collected in a randomized clinical trial. An adaptation of Fieller's theorem, the delta method, and different bootstrap approaches (normal, percentile-based, wild bootstrap) are investigated and compared in a simulation study. Extensions to multivariable problems are presented and evaluated. We observed appropriate confidence interval coverage following Fieller's theorem irrespective of sample size but at the cost of very wide or even infinite confidence intervals. The delta method and the wild bootstrap approach provided the smallest intervals but inadequate coverage for small to moderate event numbers, also depending on the location of the true changepoint. For the percentile-based bootstrap, wide intervals were observed, and it was slightly conservative regarding coverage, whereas the normal bootstrap did not provide acceptable results for many scenarios. The described methods were also applied to data from a randomized clinical trial comparing two treatments for patients with symptomatic, severe carotid artery stenosis, considering patient's age as predictive marker.

Measurement error in continuous endpoints in randomised trials: Problems and solutions.

In randomised trials, continuous endpoints are often measured with some degree of error. This study explores the impact of ignoring measurement error and proposes methods to improve statistical inference in the presence of measurement error. Three main types of measurement error in continuous endpoints are considered: classical, systematic, and differential. For each measurement error type, a corrected effect estimator is proposed. The corrected estimators and several methods for confidence interval estimation are tested in a simulation study. These methods combine information about error‐prone and error‐free measurements of the endpoint in individuals not included in the trial (external calibration sample). We show that, if measurement error in continuous endpoints is ignored, the treatment effect estimator is unbiased when measurement error is classical, while Type‐II error is increased at a given sample size. Conversely, the estimator can be substantially biased when measurement error is systematic or differential. In those cases, bias can largely be prevented and inferences improved upon using information from an external calibration sample, of which the required sample size increases as the strength of the association between the error‐prone and error‐free endpoint decreases. Measurement error correction using already a small (external) calibration sample is shown to improve inferences and should be considered in trials with error‐prone endpoints. Implementation of the proposed correction methods is accommodated by a new software package for R.

Research on Short-term Forecasting and Uncertainty of Wind Turbine Power Based on Relevance Vector Machine

Abstract With the increasingly serious environmental pollution, the development of clean energy has received widespread attention. This paper proposes a short-term wind power forecasting method for a single unit based on a correlation vector machine. This method uses a small amount of historical numerical weather forecasts and historic wind farm power data as training samples. Combining with future numerical weather forecasts, predict the power generated by wind turbines. This paper analyses the influencing factors of wind power forecast uncertainty, and describes the uncertainty of power forecasting through the confidence interval estimation method. The RVM, wavelet and RBF were used to predict and compare the power of three wind farms in a northern wind farm. The simulation results verified the accuracy and efficiency of the RVM method.

On confidence interval estimation of normal percentiles

Chakraborti and Li (Am Stat 61:331–336, 2007) considered several methods for confidence interval estimation of a normal distribution percentile. In this paper, we comment on two of their methods based on maximum likelihood and Bayesian inference. We show that the use of some approximations and simulations in the two methods is not necessary and some improvements and modifications can be made. Also, we compare the modified methods with methods in Chakraborti and Li (2007).

The Bland-Altman range of agreement: Exact interval procedure and sample size determination

The Bland-Altman analysis has been widely used to assess the agreement between two quantitative methods of measurement. The range of agreement is thus represented by the designated central proportion of the distribution of the paired differences. This article aims to provide concrete guidance on the use of accurate confidence intervals of the range of agreement. Theoretical examination and numerical comparison are conducted to support the exact approach and to demonstrate the disadvantages of the currently suggested methods for confidence interval estimation of the range of agreement. For the purpose of design planning, the associated sample size calculations for precise interval estimation of the range of agreement are delineated under the expected width and assurance probability considerations. To enhance the utility of the recommended confidence interval and sample size procedures in practical applications, both SAS and R computer algorithms are also developed.

Variable selection - A review and recommendations for the practicing statistician.

Statistical models support medical research by facilitating individualized outcome prognostication conditional on independent variables or by estimating effects of risk factors adjusted for covariates. Theory of statistical models is well‐established if the set of independent variables to consider is fixed and small. Hence, we can assume that effect estimates are unbiased and the usual methods for confidence interval estimation are valid. In routine work, however, it is not known a priori which covariates should be included in a model, and often we are confronted with the number of candidate variables in the range 10–30. This number is often too large to be considered in a statistical model. We provide an overview of various available variable selection methods that are based on significance or information criteria, penalized likelihood, the change‐in‐estimate criterion, background knowledge, or combinations thereof. These methods were usually developed in the context of a linear regression model and then transferred to more generalized linear models or models for censored survival data. Variable selection, in particular if used in explanatory modeling where effect estimates are of central interest, can compromise stability of a final model, unbiasedness of regression coefficients, and validity of p‐values or confidence intervals. Therefore, we give pragmatic recommendations for the practicing statistician on application of variable selection methods in general (low‐dimensional) modeling problems and on performing stability investigations and inference. We also propose some quantities based on resampling the entire variable selection process to be routinely reported by software packages offering automated variable selection algorithms.

Confidence interval estimation for electromechanical mode parameters obtained from stochastic subspace identification

Electromechanical modes estimated from ambient measurement signals are always subjected to statistical uncertainties. For evaluating the quality of the obtained results, it is necessary to know the respective confidence intervals of the mode estimates. A perturbation method for computing the variances of mode parameters (frequencies, damping ratios) obtained from covariance‐driven stochastic subspace identification of multiple synchrophasors is presented in this paper. The variance estimates are achieved by using the first‐order sensitivity of the mode parameter estimates to perturbations of the system matrixes, whose covariances are derived from the measured signals. The confidence interval estimation method is validated by Monte Carlo simulations with the two‐area system and the New England system. The comparison results between the mean values of the estimated variances and empirical sample variances of the estimated mode parameters show that it is feasible to estimate the confidence intervals of the mode parameters using a single set of multiple signals. The proposed method is further validated with field‐measured signals from the Western Electricity Coordinating Council system. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.