Estimation Of Mean Research Articles

The Impact of the Approach to Accounting for Age and Sex in Economic Models on Predicted Quality-Adjusted Life-Years.

The method used to model general population mortality estimates in cohort models can make a meaningful difference in appraisals; particularly in scenarios involving potentially curative treatments where a prior National Institute for Health and Care Excellence (NICE) appraisal demonstrated that this assumption alone could make a difference of ~£10,000 to the incremental cost-effectiveness ratio. Our objective was to evaluate the impact of different methods for calculating general population mortality estimates on the predicted total quality-adjusted life expectancy (QALE) as well as absolute and proportional quality-adjusted life year (QALY) shortfall calculations. We employed three distinct methods for deriving general population mortality estimates: firstly, utilizing the population mean age at baseline; secondly, modelling the distribution of mean age at baseline by fitting a parametric distribution to patient-level data sourced from the Health Survey for England (HSE); and thirdly, modelling the empirical age distribution. Subsequently, we simulated patient age distributions to explore the effects of mean starting age and variance levels on the predicted QALE and applicable severity modifiers. Provided sample code in R and Visual Basic for Applications (VBA) facilitates the utilization of individual patient age and sex data to generate weighted average survival and health-related quality of life (utility) outputs. We observed differences of up to 10.4% (equivalent to a difference of 1.01 QALYs in quality-adjusted life-expectancy) between methods using the HSE dataset. In our simulation study, increasing variance in baseline age diminished the accuracy of predictions relying solely on mean age estimation. Differences of -0.30 to 2.24 QALYs were found at a standard deviation of 20%; commonly observed in trials. For potentially curative treatments this would represent a difference in economically justifiable price of -£4,500-+£33,600 at a cost-effectiveness threshold of £30,000 per QALY for a treatment with a 50% cure rate. For lower baseline ages, the population mean method tended to overestimate QALE, whereas for higher baseline ages, it tended to underestimate QALE compared with individual patient age-based approaches. The severity modifier assigned did not vary, however, apart from simulations with means at the extremes of the age distribution or with very high variance. Our analysis underscores the necessity of accounting for the distribution of mean age at baseline, as failure to do so can lead to inaccurate QALE estimates, thereby affecting calculations of incremental costs and QALYs in models, which base survival and quality of life predictions on general population expectations. We would recommend that patient age and sex distribution should be accounted for when incorporating general population mortality in economic models. Provided sufficient sample size, utilizing the observed empirical distribution for the expected population in clinical practice is likely to yield the most accurate results. However, in the absence of patient-level data, selecting a suitable parametric distribution is recommended.

An Improved Divide-and-Conquer Approach to Estimating Mean Functional, with Application to Average Treatment Effect Estimation

Mean estimation is an important issue in statistical inference and machine learning. We are concerned with estimating mean functional that is a function of several nonparametric functions when there is a large amount of observations. Directly estimating such mean functional through nonparametric smoothing has the complexity of at least a quadratic order of the sample size, which is computationally prohibitive for massive data. The divide-and-conquer approach are thus readily used to alleviate the computational complexity issue, which however imposes a stringent condition on the sample size in each local machine if a locally optimal bandwidth is used. To address this issue, we suggest to use a globally optimal bandwidth in each local machine, which alleviates the restriction on the local sample sizes substantially. We show that the divide-and-conquer approach with a globally optimal bandwidth achieves the estimation efficiency bound as if all observations were pooled together. In terms of computational efficiency, our proposal outperforms the pooled algorithm dramatically. We demonstrate these properties through average treatment effect estimation from both the asymptotic and the non-asymptotic perspectives.

Pretest Estimation for the Common Mean of Several Normal Distributions: In Meta-Analysis Context

The estimation of unknown quantities from multiple independent yet non-homogeneous samples has garnered increasing attention in various fields over the past decade. This interest is evidenced by the wide range of applications discussed in recent literature. In this study, we propose a preliminary test estimator for the common mean (μ) with unknown and unequal variances. When there exists prior information regarding the population mean with consideration that μ might be equal to the reference value for the population mean, a hypothesis test can be conducted: H0:μ=μ0 versus H1:μ≠μ0. The initial sample is used to test H0, and if H0 is not rejected, we become more confident in using our prior information (after the test) to estimate μ. However, if H0 is rejected, the prior information is discarded. Our simulations indicate that the proposed preliminary test estimator significantly decreases the mean squared error (MSE) values compared to unbiased estimators such as the Garybill-Deal (GD) estimator, particularly when μ closely aligns with the hypothesized mean (μ0). Furthermore, our analysis indicates that the proposed test estimator outperforms the existing method, particularly in cases with minimal sample sizes. We advocate for its adoption to improve the accuracy of common mean estimation. Our findings suggest that through careful application to real meta-analyses, the proposed test estimator shows promising potential.

Enhancing subset simulation through Bayesian inference

Analyzing and reducing uncertainty in estimating failure probability has always been a crucial part of reliability analysis using Monte Carlo simulation. This paper employs Bayesian inference to capture uncertainty within Subset Simulation (SuS), with a specific emphasis on constructing the posterior distribution of failure probability. Two types of Bayesian models are discussed. The first type is based on the distribution form of the failure probability estimator from the SuS, where the Log-normal and Beta distributions are compared and analyzed. The second type is based on the distribution of statistics in Bernoulli trials in SuS, involving models such as the Beta-Binomial and Uniform-Bernoulli trials with Sequential Dependence. After evaluating all models among two types, the Log-normal distribution-based model was selected as the optimal solution due to its consideration of sample correlation and closed form of Maximum A Posteriori (MAP). Further exploration of this model reveals that its MAP estimation can provide less bias and deviation compared to mean estimation when SuS is run multiple times. Additionally, when compared to the point estimation of failure probability in conventional SuS, the posterior distribution of failure probability provides a more comprehensive overview, capturing the effects of sample size and MCMC algorithms.

Experimental and theoretical modeling of droplet break-up of W/O emulsion flow in ESPs

The behavior of water-in-oil emulsions flow within Electrical Submersible Pumps (ESPs) is of significant interest in the oil and gas industry due to its complex rheological characteristics, which are influenced by operational parameters and the chemical properties of both phases. Operational parameters such as dispersed phase fraction, temperature, flow rate, and pump design were investigated experimentally in this work. Improved semi-empirical models for mean and maximum droplet diameter estimation were also proposed. Through extensive experimentation and statistical analysis, this study reveals that smaller droplets form with increasing dispersed phase fraction and the flow geometry significantly affects droplet breakage intensity. The proposed models integrate the dispersed phase fraction, dimensionless flow rate, specific speed, and energy dissipation rate, exhibiting commendable alignment with experimental findings. This not only helps predict effective viscosity but offers valuable insights for further analyses, particularly regarding catastrophic phase inversion (CPI) prediction. These aspects have significant importance in the oil and gas industry and can enable the optimization of production systems and processing facilities.

A roadmap for generating annual bycatch estimates from sparse at-sea observer data

Abstract To support ecosystem-based fisheries management, monitoring data from at-sea observer (ASO) programs should be leveraged to understand the impact of fisheries on discarded species (bycatch). Available techniques to estimate fishery-scale quantities from observations range from simple mean estimators to more complex spatiotemporal models, each making assumptions with differing degrees of support. However, the resulting implementation and analytical trade-offs are rarely discussed when applying these techniques in practice. Using blue shark (Prionace glauca) bycatch in the Canadian pelagic longline fishery as a case study, we evaluated the performance of seven contrasting approaches to estimating total annual discard amounts and assessed their trade-offs in application. Results demonstrated that simple approaches such as mean estimator and nearest neighbors are feasible to implement and can be as efficient for prediction as complex models such as random forest and mixed-effects models. The traditionally used catch-ratio estimator consistently underperformed among all tested models, likely due to misspecified correlative relationships between target and bycatch species. Overall, efforts in model-based approaches were rewarded with very small gains in predictive ability, suggesting that such models relying on environmental, biological, spatial, and/or temporal patterns to improve prediction of bycatch may lack sufficient foundation in data-limited contexts.

The adaptive mean estimation of heavy tailed distribution under random censoring

We propose an alternative estimator of the heavy tailed mean under censored data relies with the threshold t which divides it into two parts for x ≤ t and x > t respectively. In the first parts we present an empirical distribution function under random censoring (rc). Then, we check the convergence of Lyapunov condition to ensuring the asymptotic normality of this parts. For the second parts we use the Peaks-Over-Threshold (POT) method of the tail distribution and fitting to the generalized Pareto distribution (GPD). Intentionally to give an alternative estimator of the tail expected value for the heavy tailed distribution when x > t under random censoring relies the KIB estimators of the GPD parameters. Ditto, we ensuring the asymptotic normality property of the KIB estimators with bias reduced and we present the asymptotic normality of the second parts when x > t. An asymptotically normally distributed estimate for the heavy tailed mean estimation with infinite variance under censored data is introduced by combining the two parts. Finally, numerical examples are presented at the end of the paper to demonstrate the reliability of this estimation procedure and to better illustrate the results of this paper.

Efficient ARL estimation for general control charts using censored run lengths

The average run length (ARL), the average number of in-control signals before an out-of-control signal occurs, is a critical measure of the performance of a control chart. Various methods have been explored for estimating the ARL, including Markov chain-based approximation, integration method, and the Monte Carlo method, especially for time-dependent charting statistics. Although computationally expensive, the Monte Carlo method is generic and applicable to all control charts. Typically, it involves choosing the maximum run length in advance and discarding iterations that fail to produce out-of-control signals to accommodate some unusually lengthy runs. However, these discarded runs provide information for estimating the run length. This paper introduces a new Monte Carlo approximation that retains failed iterations as Type I censored observations for ARL estimation. Our approach relies on the memoryless expectation of the run length distribution to have a simple and efficient ARL estimator. This assumption is necessary for mean estimation in Type I censored data and aligns with existing ARL approximations used in popular control charts like Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) charts. Numerical simulations demonstrate our method’s computational and statistical efficiency across the mean, median, EWMA, and CUSUM charts.

An optimal estimation approach in stratified random sampling utilizing two auxiliary attributes with application in agricultural, demography, finance, and education sectors

In the contemporary era of information technology, copious amounts of data are ubiquitous, generated across various sectors on a daily basis. Analyzing every unit of data is impractical due to constraints such as limited resources in terms of time, labor, and cost. In such scenarios, survey sampling becomes a recommended approach for extracting information about population parameters. The primary goal of this study is to devise an estimation method for acquiring information about population parameters. We propose an optimal estimator for an improved estimation of the population mean in stratified random sampling by leveraging the information from two auxiliary attributes. The proposed estimator's bias, mean squared error (MSE), and minimum mean squared error are determined up to the first-order approximation. It is demonstrated that, under the derived conditions, the proposed estimator theoretically outperforms existing estimators. Four population are utilized to evaluate both the performance and applicability of the proposed estimator. The percentage relative efficiency (PRE) of proposed estimator for all the populations is 178.389, 142.881, 181.383, and 152.679 respectively. The suggested estimator superior to existing estimators, as demonstrated by the numerical examples.

Preliminary estimators of population mean using ranked set sampling in the presence of measurement error and non-response error with applications and simulation study

In order to estimate the population mean in the presence of both non-response and measurement errors that are uncorrelated, the paper presents some novel estimators employing ranked set sampling by utilizing auxiliary information. Up to the first order of approximation, the equations for the bias and mean squared error of the suggested estimators are produced, and it is found that the proposed estimators outperform the other existing estimators analysed in this study. Investigations using simulation studies and numerical examples show how well the suggested estimators perform in the presence of measurement and non-response errors. The relative efficiency of the suggested estimators compared to the existing estimators has been expressed as a percentage, and the impact of measurement errors has been expressed as a percentage computation of measurement errors.

Efficient population mean estimation via stratified sampling with dual auxiliary information: A real estate perspective

Auxiliary information is an essential component in the field of survey sampling since it enables precise estimation of population parameters like mean, variance, distribution function, and so on, which in turn guarantees the best possible outcomes. In order to estimate the population mean of a study variable, this study makes use of auxiliary information in a two-fold approach. Through a stratified random sampling scheme, we introduce a novel class of estimators that utilize auxiliary information and their corresponding ranks. By conducting a thorough evaluation based on metrics such as mean square error and percentage relative efficiency, these proposed estimators have been shown to be effective in the estimation process. Empirical validation is conducted using a real dataset sourced from the domain of real estate. Exploring the relationship between Assessed Value (X) and Sale Amount (Y) during a five-year period extending from 2017 to 2021 is the primary emphasis of the empirical validation process, which is carried out with the assistance of a real dataset of real estate data. Furthermore, in order to demonstrate that our suggested estimator is superior to conventional unbiased estimators, as well as traditional regression estimators and other estimators that have been considered in the literature, a full simulation analysis is carried out. Our proposed estimator appears to be the most effective choice after being subjected to a comparison study against a variety of preexisting approaches. The findings of this study not only make a significant contribution to the development of the methodology of survey sampling but also offer vital insights for predictive modeling within the real estate sector.

Automated estimation of thoracic rotation in chest X-ray radiographs: a deep learning approach for enhanced technical assessment.

This study aims to develop an automated approach for estimating the vertical rotation of the thorax, which can be used to assess the technical adequacy of chest X-ray radiographs (CXRs). Total 800 chest radiographs were used to train and establish segmentation networks for outlining the lungs and spine regions in chest X-ray images. By measuring the widths of the left and right lungs between the central line of segmented spine and the lateral sides of the segmented lungs, the quantification of thoracic vertical rotation was achieved. Additionally, a life-size, full body anthropomorphic phantom was employed to collect chest radiographic images under various specified rotation angles for assessing the accuracy of the proposed approach. The deep learning networks effectively segmented the anatomical structures of the lungs and spine. The proposed approach demonstrated a mean estimation error of less than 2° for thoracic rotation, surpassing existing techniques and indicating its superiority. The proposed approach offers a robust assessment of thoracic rotation and presents new possibilities for automated image quality control in chest X-ray examinations. This study presents a novel deep-learning-based approach for the automated estimation of vertical thoracic rotation in chest X-ray radiographs. The proposed method enables a quantitative assessment of the technical adequacy of CXR examinations and opens up new possibilities for automated screening and quality control of radiographs.

New Modification of Ranked Set Sampling for Estimating Population Mean: Neutrosophic Median Ranked Set Sampling with an Application to Demographic Data

The study addressed the limitations of classical statistical methods when dealing with ambiguous data, emphasizing the importance of adopting neutrosophic statistics as a more effective alternative. Classical methods falter in managing uncertainty inherent in such data, necessitating a shift towards methodologies like neutrosophic statistics. To address this gap, the research introduced a novel sampling approach called “neutrosophic median ranked set sampling” and incorporated neutrosophic estimators tailored for estimating the population mean in the presence of ambiguity. This modification aims to address the inherent challenges associated with estimating the population mean when dealing with neutrosophic data. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Additionally, neutrosophic estimators were developed to leverage auxiliary information within the framework of median-ranked set sampling, enhancing the accuracy of population mean estimation under uncertain conditions. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Bias and mean squared error equations for the suggested estimators were provided, offering insights into their theoretical underpinnings. To illustrate the effectiveness and practical applications of the proposed methodology and estimators, a numerical demonstration and simulation study have been conducted using the R programming language. The key results highlighted the superior performance of the proposed estimators compared to existing alternatives, as demonstrated through comprehensive evaluations based on mean squared error and percentage relative efficiency criteria. The conclusions drawn underscored the effectiveness of the neutrosophic median ranked set sampling approach and suggested estimators in estimating the population mean under conditions of uncertainty, particularly when utilizing neutrosophic auxiliary information and validated real-life applicability. The methodology and estimators presented in the study were shown to yield interval-based results, providing a more realistic representation of uncertainty associated with population parameters. This interval estimation, coupled with minimum mean squared error considerations, enhanced the efficacy of the estimators in determining population mean values. The novelty of the work lies in its introduction of a tailored sampling approach and estimators designed specifically for neutrosophic data, filling a significant gap in the literature. By extending classical statistics to accommodate ambiguity, the study offers a substantial advancement in statistical methodology, particularly in domains where precise data is scarce and uncertainty is prevalent. Furthermore, the empirical validation through numerical demonstrations and simulation studies using the R programming language adds robustness to the proposed methodology and contributes to its practical applicability.

Accounting for regression to the mean under the bivariate -distribution.

Regression to the mean occurs when an unusual observation is followed by a more typical outcome closer to the population mean. In pre- and post-intervention studies, treatment is administered to subjects with initial measurements located in the tail of a distribution, and a paired sample -test can be utilized to assess the effectiveness of the intervention. The observed change in the pre-post means is the sum of regression to the mean and treatment effects, and ignoring regression to the mean could lead to erroneous conclusions about the effectiveness of the treatment effect. In this study, formulae for regression to the mean are derived, and maximum likelihood estimation is employed to numerically estimate the regression to the mean effect when the test statistic follows the bivariate -distribution based on a baseline criterion or a cut-off point. The pre-post degrees of freedom could be equal but also unequal such as when there is missing data. Additionally, we illustrate how regression to the mean is influenced by cut-off points, mixing angles which are related to correlation, and degrees of freedom. A simulation study is conducted to assess the statistical properties of unbiasedness, consistency, and asymptotic normality of the regression to the mean estimator. Moreover, the proposed methods are compared with an existing one assuming bivariate normality. The -values are compared when regression to the mean is either ignored or accounted for to gauge the statistical significance of the paired -test. The proposed method is applied to real data concerning schizophrenia patients, and the observed conditional mean difference called the total effect is decomposed into the regression to the mean and treatment effects.

Mean and covariance estimation for discretely observed high-dimensional functional data: Rates of convergence and division of observational regimes

Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which p, the number of curves per subject, is often much larger than the sample size n. In this setting of high-dimensional functional data, much of developed methodology relies on preliminary estimates of the unknown mean functions and the auto- and cross-covariance functions. This paper investigates the convergence rates of local linear estimators in terms of the maximal error across components and pairs of components for mean and covariance functions, respectively, in both L2 and uniform metrics. The local linear estimators utilize a generic weighting scheme that can adjust for differing numbers of discrete observations Nij across curves j and subjects i, where the Nij vary with n. Particular attention is given to the equal weight per observation (OBS) and equal weight per subject (SUBJ) weighting schemes. The theoretical results utilize novel applications of concentration inequalities for functional data and demonstrate that, similar to univariate functional data, the order of the Nij relative to p and n divides high-dimensional functional data into three regimes (sparse, dense, and ultra-dense), with the high-dimensional parametric convergence rate of log(p)/n1/2 being attainable in the latter two.

Novel logarithmic imputation procedures using multi auxiliary information under ranked set sampling

Ranked set sampling (RSS) is known to increase the efficiency of the estimators while comparing it with simple random sampling. The problem of missingness creates a gap in the information that needs to be addressed before proceeding for estimation. Negligible amount of work has been carried out to deal with missingness utilizing RSS. This paper proposes some logarithmic type methods of imputation for the estimation of population mean under RSS using auxiliary information. The properties of the suggested imputation procedures are examined. A simulation study is accomplished to show that the proposed imputation procedures exhibit better results in comparison to some of the existing imputation procedures. Few real applications of the proposed imputation procedures is also provided to generalize the simulation study.

Utilization of genetic algorithm in tuning the hyper-parameters of hybrid NN-based side-slip angle estimators

This paper proposes a solution to enhance and compare different neural network (NN)-based side-slip angle estimators. The feed-forward neural networks (FFNNs), recurrent neural networks, long short-term memory units (LSTMs), and gated recurrent units are investigated. However, there is a lack in the selection criteria of the architectures’ hyper-parameters. Therefore, the genetic algorithm is integrated with the NN-based estimators to find the optimal hyper-parameters for the studied architectures. The tuned hyper-parameters in this work include the number of neurons, number of layers, activation function, optimizer type, and learning rate. The objective function of the optimization problem is minimizing the root-mean-square error (RMSE) on multiple testing data. The optimal models are further included in the design of a hybrid NN estimator with Kalman filter. In the hybrid estimators, the optimal NN estimators are used as virtual sensors to correct the prediction of the side-slip angle resulting from the mathematical lateral vehicle model. Eventually, the performance of the best selected model is evaluated in terms of different metrics; mean RMSE, mean error variance, mean training time, and mean estimation time. LSTMs are found to achieve the lowest mean RMSE while being tested on highly generalized data yielding the highest training and estimation time. However, FFNNs achieve the lowest RMSE while being tested on low generalized data and the lowest training and estimation time. Meanwhile, it is observed that the hybrid estimators achieved lower RMSE with great enhancement compared to the non-hybridized ones proving the effectiveness of the proposed approach and increasing the side-slip estimation generalization ability in unknown environments with high uncertainties, which are not covered by the training dataset for the NNs estimators.

Using Satellite Data Assimilation Techniques to Combine Infrasound Observations and a Full Ray-Tracing Model to Constrain Stratospheric Variables

Abstract Infrasound waves generated at Earth’s surface can reach high altitudes before returning to the surface to be recorded by microbarometer array stations. These waves carry information about the propagation medium, in particular temperature and winds in the atmosphere. It is only recently that studies on the assimilation of such data into atmospheric models have been published. Intending to advance this line of research, we here use the modulated ensemble transform Kalman filter (METKF)—commonly used in satellite data assimilation—to assimilate infrasound-related observations in order to update a column of three vertically varying variables: temperature and horizontal wind speeds. This includes stratospheric and mesospheric heights, which are otherwise poorly observed. The numerical experiments on synthetic data but with realistic reanalysis product atmospheric specifications (following the observing system simulation experiment paradigm) reveal that a large ensemble is capable of reducing errors, especially for wind speeds in stratospheric heights close to 30–60 km. While using a small ensemble leads to incorrect analysis increments and large estimation errors, the METKF ameliorates this problem and even achieves error reduction from the prior to the posterior mean estimator. Significance Statement The stratosphere and mesosphere have significantly less observational coverage compared to the troposphere, especially for the winds. This lack of information can reduce the accuracy of medium-range weather forecasts. By mimicking a realistic setup, this study paves the way for including novel observations in the estimation of the atmospheric state in these heights using an ensemble data assimilation method. These observations come from a dataset of opportunity containing infrasound-related measurements that are routinely carried out at several stations around the world.

Exponential Ratio Class of Estimators of Finite Population Mean Using Deciles of an Auxiliary Variable

Practitioners of survey sampling have been working to reduce bias and increase efficiency in the estimation of finite population parameters. The present work aims at developing an exponential ratio class of finite population mean estimators with deciles of an auxiliary variable. Using the Taylor's series technique, the mean square error (MSE) of the developed estimators was obtained up to the first order of approximation. The study's suggested estimators outperform competing estimators, according to the findings of a numerical analysis that was done on them in comparison to the existing estimators that were taken into consideration.

Impact of government expenditure on unemployment in Asian countries: does institutional quality matter?

Purpose Asian countries have had persistent unemployment levels. The purpose of this paper is to investigate the impact of government spending on unemployment. Furthermore, this paper investigates the moderating role of institutional quality on the government spending–unemployment nexus. Design/methodology/approach Using data from 35 Asian countries from 2000 to 2022, the dynamic ordinary least squares and fully modified ordinary least squares technique is used to tackle with aforementioned issue. In addition, pooled mean group estimation is applied to verify the robustness of the findings. Findings The results show that an increase in government expenditure and better institutions reduce the unemployment rate. Interestingly, the negative impact of government expenditure on unemployment will enhance and intensify with better institutional quality. Furthermore, trade openness and foreign direct investment decrease unemployment in Asian countries. The results are robust to various specifications. Practical implications Findings from this study provide important implications for governments. Governments should use public expenditure efficiently and enhance and improve institutional quality to reduce unemployment. Originality/value To the best of the author’s knowledge, this study pioneers the investigation of the moderating role of institutional quality in the relationship between government expenditure and unemployment in Asian countries.