Estimation Of Mean Research Articles

Gaussian differentially private robust mean estimation and inference

Gaussian differentially private robust mean estimation and inference

Calibration Estimators with Different Types of Distance Measures Under Stratified Sampling in the Presence of Measurement Error

The calibration method is used in stratified random sampling in the presence of measurement error to achieve optimum strata weights for better precision. In this study we attempt to analyze the behaviour of calibration estimators with different types of distance measures in the presence of measurement error for the estimation of population mean under stratified random sampling. The proposed estimators are compared with the estimators in the absence of measurement error. A simulation study has been carried out to evaluate the proposed estimators.

On the efficiency of paired ranked set sampling for estimating the population mean in the presence of non-response

Non-response is a common problem faced by surveyors while conducting surveys; this introduces a potential bias in the estimates of population parameters. One method of dealing with non-response is subsampling of the non-respondents, which increases precision in estimates by increasing the sample size. This study proposes an unbiased mean estimator in the presence of non-response using the Paired Ranked Set Sampling (PRSS) technique. The proposed estimator is based on a suggested strategy for adapting the subsampled units into the initial sample. Variance of the proposed estimator is derived, and conditions are provided for which the proposed estimator performs better than existing estimators. We conduct a simulation study to evaluate the precision of the proposed estimator in comparison with other existing estimators for estimating the population mean. In simulation, we assume populations based on normal distribution, exponential distribution, and real-life data on abalone. Simulation results show that the proposed mean estimator exhibits a higher probability of precisely estimating the finite population mean.

Impact of Malnutrition on the Length of Stay for Hospitalized Chimeric Antigen Receptor T-cell (CAR-T) Therapy Patients in the United States (2020).

Background Chimeric antigen receptor T-cell (CAR-T) therapy offers a promising treatment for certain malignancies but can be associated with complications. Malnutrition and cachexia are common in cancer patients and may worsen outcomes. This study investigated the impact of malnutrition on the length of hospital stay (LOS) in patients with hematologic malignancies undergoing CAR-T therapy. The analysis focused on different subpopulations, including those with acute lymphoblastic leukemia (ALL), multiple myeloma (MM), diffuse large B-cell lymphoma (DLBCL), and non-Hodgkin lymphoma (NHL) excluding DLBCL. Methods Utilizing the 2020 National Inpatient Sample (NIS) data, we performed survey-based mean estimation analyses for LOS across various subpopulations of CAR-T therapy patients. These subpopulations were defined by specific diagnoses: ALL, myeloma, DLBCL, and NHL excluding DLBCL. We compared the LOS between patients with and without malnutrition using STATA accounting for the complex survey design. Cachexia was included as disease-induced malnutrition. Results The total CAR-T population used for analyses included 439 patients, and malnutrition was present in 50 (11.39%). The overall CAR-T population demonstrated a significantly longer LOS for patients with malnutrition (30.92 days, 95% CI: 24.30 to 37.54) compared to those without malnutrition (17.97 days, 95% CI: 15.48 to 20.46, p = 0.0002). This trend held true across subgroups. Specifically, the ALL population had a significantly longer LOS with malnutrition (45.25 days, 95% CI: 35.46 to 55.04) compared to non-malnourished patients (27.58 days, 95% CI: 16.74 to 38.42, p = 0.0279). For the DLBCL population, the mean LOS was 24.47 days (95% CI: 19.22 to 29.71) with malnutrition and 17.17 days (95% CI: 13.29 to 21.04, p = 0.0161) without malnutrition. The NHL population excluding DLBCL exhibited a mean LOS of 33.86 days (95% CI: 22.66 to 45.07) for malnourished patients and 17.44 days (95% CI: 14.76 to 20.11, p = 0.0055) for non-malnourished patients. The myeloma population showed a similar trend although not statistically significant, with a mean LOS of 39.00 days (95% CI: -3.54 to 81.54) for malnourished patients and 18.03 days (95% CI: 15.02 to 21.03, p = 0.3337) for non-malnourished patients. These findings highlight significant variations in LOS across different CAR-T-treated cancer subtypes, emphasizing the impact of malnutrition on healthcare resource utilization in oncology. Conclusion Malnutrition is associated with a significantly longer hospital stay among patients undergoing CAR-T therapy. This trend is consistent across various subpopulations, including those with ALL, DLBCL, and NHL (excluding DLBCL). While the impact of malnutrition on LOS was not statistically significant in the myeloma population, this could potentially be attributed to the smaller sample size in this group. Overall, these findings underscore the critical role of nutritional status in managing patients undergoing CAR-T therapy. Future studies should investigate the most effective methods for identifying and treating malnutrition in this patient population to reduce hospital stays and optimize overall patient care.

An improved variant of quantitative randomized response techniques using forced responses

The randomized response technique has gained a wide popularity among survey researchers over the past few decades. Randomized response procedure is applicable in a variety of fields including sociology, psychology, business, and education, etc. It is a useful method which helps the researcher in dealing with the high non-response rates in sample surveys on sensitive issues such as monthly income, traffic rules violations, income tax amount, and expenditure on luxury items, etc. We introduce an optimal scrambling technique which uses forced responses. The algebraic properties of the estimator of population mean using the suggested technique have been derived. For the purpose of comparison with existing models, the different measures of model-evaluation have been obtained. Our analysis suggests that the new quantitative technique using forced responses is better than the available scrambling techniques not only in efficiency, but also in the combined metric of model’s efficiency and level of privacy, which make it more useful than the available models for practical problems. Using real-world example, we illustrate its practical implementation to sensitive sample surveys.

Moment-Based Estimation of Linear Panel Data Models with Factor-Augmented Errors

Abstract I compare two popular methods of estimation for linear panel data models with unobserved factors: the first eliminates the factors with a parameterized quasi-long-differencing (QLD) transformation. The other, referred to as common correlated effects (CCE), uses cross-sectional averages of the data to proxy for the factor space. I show that the CCE assumptions imply unused moment conditions that can be exploited by the QLD transformation. I also derive new linear estimators that weaken identifying assumptions and have desirable theoretical properties. Unlike CCE, these estimators do not require the number of covariates to be less than the number of time periods. I provide the first proof of a fixed-T consistent mean group estimator for heterogeneous linear models with interactive fixed effects. I investigate the effects of per-student expenditure on standardized test performance using data from the state of Michigan.

Memory-type Mean Estimators for Surveys with Non-response: A Regression-imputation and Ewma Approach

Sampling survey mostly faces the challenge of missing information or non-response, Missing data naturally occurs in sample surveys when a few sampling units refuse to respond or are unable to participate in the survey. In time based survey, this could happen due to relocation or system malfunctioning after some period. This missing information can bring about a substantial amount of bias, make the handling and analysis of the data more arduous and create reductions in efficiency of the estimator. Surmounting this challenge bring about the development of various imputation-based mean estimation methods. Some of these, ratio-type regression estimators have been devised to compute population parameters using only current sample data. However, recent researches has changed this approach by integrating both past and current sample information through the application of exponentially weighted moving averages (EWMA). This new invented methodology has given rise to the creation of memory-type estimators tailored for surveys conducted over time. In this paper, we present regression- imputation and EWMA based memory-type mean estimators in the presence of non- response. For the performance assessment between existing and proposed estimators, two real-life time-scaled data sets are considered. In the first data set proposed estimators (Tp1 and Tp2) have the minimum MSE and higher PRE and also in the second data set, results show that the proposed estimators (estimators (Tp1 and Tp2) have the minimum MSE and higher PRE when compared with the existing estimators at all levels of smoothing parameter. Therefore the proposed estimator will perform better in estimating the EWMA-based mean in the presence non response for time based survey and longitudinal survey. Most especially in quality control data that are collected over time. The current work is limited to simple random sampling which assumes homogeneity of the population units. Further work can be done on stratify random sampling which assumes heterogeneity of the population units.

Robust and Efficient Estimation of Potential Outcome Means Under Random Assignment

We study efficiency improvements in randomized experiments for estimating a vector of potential outcome means using regression adjustment (RA) when there are more than two treatment levels. We show that linear RA which estimates separate slopes for each assignment level is never worse, asymptotically, than using the subsample averages. We also show that separate RA improves over pooled RA except in the obvious case where slope parameters in the linear projections are identical across the different assignment levels. We further characterize the class of nonlinear RA methods that preserve consistency of the potential outcome means despite arbitrary misspecification of the conditional mean functions. Finally, we apply these regression adjustment techniques to efficiently estimate the lower bound mean willingness to pay for an oil spill prevention program in California.

Optimizing population mean estimation under ranked set sampling with applications to Engineering

This article aims to develop two novel mean estimators of finite populations under ranked set sampling. The suggested estimators result in a high-efficiency gain due to their efficient formulation by taking the linear combination of classical estimators using optimization constants. We also discuss the theoretical properties and derive bias and mean squared error up to the first order of approximation. To theoretically validate our proposed estimators, we derive the conditions under which our estimators prevail over the competing estimators. The findings suggest that when ranked set sampling is implemented effectively, it saves cost and improves precision, serving as a potent instrument for improved decision-making, specifically in engineering applications, such as environmental monitoring, resource management, and quality control. An empirical and simulation study has been conducted using real and synthetic data to validate our methodology empirically. The suggested estimators offer a significant contribution to survey sampling in estimating mean under ranked set sampling. Further, the proposed estimator can be seamlessly adapted in other sampling designs such as simple random sampling, stratified random sampling, cluster sampling, etc, as well as in estimating other parameters such as variance, skewness, coefficient of correlation, etc. in various domains.

Efficient private SCO for heavy-tailed data via averaged clipping

AbstractWe consider stochastic convex optimization for heavy-tailed data with the guarantee of being differentially private (DP). Most prior works on differentially private stochastic convex optimization for heavy-tailed data are either restricted to gradient descent (GD) or performed multi-times clipping on stochastic gradient descent (SGD), which is inefficient for large-scale problems. In this paper, we consider a one-time clipping strategy and provide principled analyses of its bias and private mean estimation. We establish new convergence results and improved complexity bounds for the proposed algorithm called AClipped-dpSGD for constrained and unconstrained convex problems. We also extend our convergent analysis to the strongly convex case and non-smooth case (which works for generalized smooth objectives with H$$\ddot{\text {o}}$$ o ¨ lder-continuous gradients). All the above results are guaranteed with a high probability for heavy-tailed data. Numerical experiments are conducted to justify the theoretical improvement.

Artificial Intelligence Analysis of Periorbital Rejuvenation.

Periorbital rejuvenation surgery aims to restore a youthful appearance to the face. Despite the popularity of these procedures, few objective measurements exist to evaluate their impact on perceived facial aging. This study aims to quantify the impact of brow lift and blepharoplasty on age as perceived by convolutional neural network (CNN) algorithms. A retrospective review was performed on patients who underwent upper blepharoplasty, lower blepharoplasty, and/or brow lift at a single cosmetic practice between 2018 and 2023. Collected data included patient demographics, procedure performed, fat pad resection, and pre- and postoperative frontal images. Each photo was analyzed by four artificial intelligence (AI) platforms to estimate the change in perceived age following surgery. The estimated age reduction was compared between procedures. Of the 153 included patients, 118 underwent blepharoplasty, 12 underwent brow lift, and 23 had both blepharoplasty and brow lift. Across all AI platforms, the mean age estimation percent error was 10.6%, with a tendency for AI to underestimate compared to true age. Univariate analysis revealed an age reduction following any surgery of 1.03 years (p<0.001). When controlling for other variables, brow lift patients saw a mean age reduction of 1.432 years (p=0.031). Upper and lower blepharoplasty, patient characteristics, and ancillary procedures were not found to be independently associated with significant age reduction. Brow lifts provide significant reduction in perceived age. When planning for periorbital rejuvenation, a thorough preoperative evaluation should be performed, and additional consideration should be given to brow lifting procedures.

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 &gt; 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 &gt; 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 &gt; 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.