Estimation Of Mean Research Articles

An Effective Method for Estimating the Population Mean That Utilizes Dual Auxiliary Information

To improve the effectiveness of population estimators, researchers have recently implemented dual supplementary information. They employed traditional rankings, the empirical cumulative distribution function, and indicator functions as supplementary sources of information in their analysis. An improved family of population mean estimators is introduced in this article, which utilizes the relative ranks of the auxiliary information’s configurations to incorporate the relevant information. A first-order approximation is employed to derive the mathematical expressions for the bias and the mean-squared error (MSE) of the proposed family of estimators. The empirical analysis is investigated to demonstrate the practicality of the proposed estimators in real-world scenarios. Additionally, the theoretical conclusions are effectively validated by the Monte Carlo simulation integration. Our results unequivocally indicate that the proposed family of estimators surpasses their current counterparts.

A New Modified Confidence Interval Estimator of Location Parameter for Skewed Distribution

A new modified confidence interval has been proposed which incorporates a new point estimator of the location parameter mean for skewed data distribution. Traditionally, the trimmed mean confidence interval estimator (Trm-ci) is a robust method for dealing with the skewness of the underlying data distribution. However, the Trm-ci method trims a certain fraction of endpoint observations to address skewness, which may result in a loss data information. The Students’t confidence interval (t-ci) estimator, while the most efficient estimator at normal models, becomes impractical in a situation where observed data is subject to non-normality due to robustness. In between the two, the median confidence interval estimator (Med-ci) is expected to retain the robustness of Trm-ci and the efficiency of t-ci. The idea behind the proposed new modified confidence interval estimator (Mod-ci) is to consider both the sample mean and sample median simultaneously, while also using end-point information without trimming any observations. As such, the proposed Mod-ci is expected to be as good as or better than other underlying methods regarding robustness and efficiency when dealing with skewed data distributions. In this study, we examine the performance of the new method compared to most commonly used methods through examples and simulating data from skewed distribution with varying degree of skewness. The results of examples and simulations suggest that the proposed method is as good as, or better than other estimators relevant to this study, as measured by estimated coverage probability and the width of associated confidence interval. Therefore, this method is recommended for practical application while dealing with real-life data exhibiting skewness.

Kawí Tamiruyé: a permanent research forest plot in the Sierra Tarahumara

This study characterizes the dasometric and structural parameters of a permanent research plot in northern Mexico. From a total census, 2165 trees (n) were recorded in an area of 1.4 ha-1 and, through the application of various sampling schemes, dasometric variables, and diversity indices were estimated for comparison with the census of a reference plot. We calculated the following dasometric measurements, Quadratic Mean Diameter (QMD)= 12.16 cm, Crown Area (CA)= 61.6%, Reineke's Stand Density Index (SDI)= 668 individuals, Basal Area (BA)= 25.16 m2, Total Volume (Vol)= 158.83 m3 ha-1, aboveground biomass (AGB= 142.78 Mg ha-1) and Carbon (C= 71.39 Mg ha-1). Ecologically, the species with the highest importance value index (IVI) were P. engelmannii and J. deppeana (50.8% and 35%, respectively). The Simpson's dominance index (δ)= 0.39 and diversity (λ)= 0.61 were low, as was the Shannon-Weaver index of diversity (H'= 1.3), which is in agreement with the Margalef index (DMg= 1.04). The value of Pielou's evenness (J'= 0.53) confirmed low abundance. Equidistant systematic sampling at 40 m was closer to the reference census, presenting lower values in the mean and variance estimators compared to the other sampling methods. The results can be included in management portfolios to improve decision-making. Although further studies on site size, inclusion of additive indices, and operational costs are required.

Secondary school students’ strategies when interpreting histograms and case-value plots: an eye-tracking study

AbstractMany students persistently misinterpret histograms. This calls for closer inspection of students’ strategies when interpreting histograms and case-value plots (which look similar but are different). Using students’ gaze data, we ask: How and how well do upper secondary pre-university school students estimate and compare arithmetic means of histograms and case-value plots? We designed four item types: two requiring mean estimation and two requiring means comparison. Analysis of gaze data of 50 students (15–19 years old) solving these items was triangulated with data from cued recall. We found five strategies. Two hypothesized most common strategies for estimating means were confirmed: a strategy associated with horizontal gazes and a strategy associated with vertical gazes. A third, new, count-and-compute strategy was found. Two more strategies emerged for comparing means that take specific features of the distribution into account. In about half of the histogram tasks, students used correct strategies. Surprisingly, when comparing two case-value plots, some students used distribution features that are only relevant for histograms, such as symmetry. As several incorrect strategies related to how and where the data and the distribution of these data are depicted in histograms, future interventions should aim at supporting students in understanding these concepts in histograms. A methodological advantage of eye-tracking data collection is that it reveals more details about students’ problem-solving processes than thinking-aloud protocols. We speculate that spatial gaze data can be re-used to substantiate ideas about the sensorimotor origin of learning mathematics.

A GIS-RS Approach for RUSLE-Based Method of Mean Estimation of Mean Annual Soil Loss of the Tagoloan River Basin, Philippines

Abstract. Soil erosion is a serious environmental concern in Tagoloan River Basin (TRB), a major watershed in Northern Mindanao, Philippines. It leads to soil loss causing detrimental impacts such as decreased soil productivity, nutrient loss, siltation, and water quality degradation among others. These impacts are better understood by estimating the degree of soil loss in the watershed and visualized in a GIS-based and factor-based approach using the Revised Universal Soil Loss Equation (RUSLE) model. Thematic maps of soil loss were generated with factors for rainfall erosivity (R), soil erodibility (K), topographic (LS) consisting of slope length (L) and slope steepness (S), cover management (C), and support practice (P). Factors were calculated separately and multiplied together to develop combined soil loss maps. Results show that TRB has an actual mean annual soil loss of 153.20 tons/hectare/year with 47.15% of the study area having very high to very severe susceptibility to soil loss. Further, a comparison of the potential (RKLS) and actual (RKLSCP) soil loss maps indicates the significance of cover management and support practices to the resulting mean annual soil loss. The present characterized soil loss level maps and its understanding driving forces of soil erosion for the planning of management practices and mitigating environmental hazards in the watershed.

Extending Cochran’s Sample Size Rule to Stratified Simple Random Sampling with Applications to Audit Sampling

Audit samples are selected by businesses, institutions, government agencies, and other organizations to check the accuracy of financial reports and assess the quality of services provided among other reasons. A standard design used in auditing is stratified simple random sampling. Point estimates and confidence intervals for population values are usual products of an audit. Cochran’s sample size rule and its extension by Sugden, Smith, and Jones provided minimum sample size formulas for a simple random sample to ensure effective normal approximation and adequate coverage for nominal 95% confidence intervals of a standardized or Studentized sample mean. The purpose of this paper is to extend Cochran’s rule and establish a formula for the minimum sample size for the normal approximation and the use of traditional one-sided or two-sided confidence intervals to be acceptable for mean estimation in stratified simple random samples. We concentrate on variables that are at least partially continuous. Simulations are used to examine the performance of our sample size formula with a variety of skewed populations based on ones encountered in auditing.

EFFICIENCY OF LOGARITHMIC RATIO CUM LOGARITHMIC PRODUCT ESTIMATORS IN DOUBLE SAMPLING USING IMPUTATION TECHNIQUES

In literature, there are many estimators of finite population mean, some of which are superior to the others. In practical situations, all the information on sample units may not be available due to non-response in sample surveys. Thus, our objective in this study is to get more precise estimators of the finite population mean of the study variable under two-phase sampling in case of missing data. Three new logarithmic ratio cum logarithmic product type imputation methods and corresponding point estimators have been introduced and observed to be better under two-phase sampling, which adds contribution to the field of imputation techniques. The bias and mean square errors of the proposed estimators are calculated in terms of population parameters. The performance of the proposed estimators is compared theoretically and empirically as well with existing traditional estimators.

Gaussian differentially private robust mean estimation and inference

Gaussian differentially private robust mean estimation and inference

Estimation of mean using under-reported and overdispersed count data

Count data arising in various fields of applications are often under-reported. Ignoring undercount naturally leads to biased estimators and inaccurate confidence intervals. Further, overdispersion in count data may arise due to inherent heterogeneity of the data. Negative Binomial distribution is a viable candidate for modeling overdispersed count data. However, in presence of undercount the negative binomial model needs to be adjusted. In this paper, we shall develop likelihood-based methodologies for estimation of mean using validation data after accounting for underreporting and overdispersion. The impact of ignoring undercount on the coverage and length of the confidence intervals is investigated using extensive numerical studies. The study is supplemented with a real-life data analysis.

Measuring How AI Innovations and Financial Accessibility Influence Environmental Sustainability in the G-7: The Role of Globalization with Panel ARDL and Quantile Regression Analysis

This study investigates the impact of AI innovation on environmental sustainability in the G-7 region from 2010 to 2022. Additionally, it tests the Load Capacity Curve (LCC) hypothesis in relation to financial accessibility, globalization, and urbanization. Cross-sectional dependence and slope homogeneity tests reveal the presence of cross-sectional dependence and heterogeneity issues. Panel unit root and panel cointegration tests confirm that the variables are free from unit root problems and are cointegrated in the long run. To identify significant factors influencing environmental sustainability, this study employs Panel ARDL and Quantile Regression methods. Both methods confirm the LCC hypothesis in the G-7 region, demonstrating a U-shaped relationship between income and the load capacity factor. The results indicate that AI innovation and financial accessibility are significantly positively correlated with the load capacity factor, while globalization and urbanization are negatively correlated, leading to lower environmental sustainability. To validate the robustness of the Panel ARDL and Quantile Regression results, Driscoll-Kraay standard errors, Augmented Mean Group, and Common Correlated Effects Mean Group estimation approaches are applied, all of which support the initial findings. Furthermore, the D-H causality test reveals unidirectional causality from economic growth, financial accessibility, globalization, and urbanization to the load capacity factor, and bidirectional causality between AI innovation and the load capacity factor.

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.