Estimation Of Mean Research Articles

Improvement on Calibration Weightings in Stratified Random Sampling

Calibration weightings is the process of formulating calibration constraints using a given distance measure to obtain expression of the calibration weights. One of the major limitations of the simple calibration technique by Deville and Sarndal (1992); is that the calibration weights obtained by this process may be negative and or extremely large. To overcome this challenge, this study develops a new framework for obtaining optimum calibration weightings using inverse exponentiation. A new calibration regression estimator of population mean is proposed in stratified random sampling. Properties of the new estimator are derived and its efficacy established through empirical comparisons with existing estimators. Results of analysis showed that the new estimator obtained by the new calibration weightings is more precise and highly efficient than calibration estimators obtained by the simple calibration technique by Deville and Sarndal (1992), under the same optimum conditions. International Journal of Statistical Sciences, Vol. 24(2), November, 2024, pp 125-136

On a Corrective Decile-based Confidence Interval Estimator of Mean for Normal and Skewed Distributions

This study addresses an issue with the decile t-confidence interval (dt-CI), which fails to achieve the desired coverage probabilities for large samples or skewed distributions (Mokhtar, Yusof & Sapiri, 2024). The article proposes a new corrective decile t-confidence interval (cdt-CI) that resolves these issues by modifying the decile standard deviation. Simulations using normal, chi-squared, log-normal, and gamma distributions show that the cdt-CI outperforms existing methods, particularly for skewed data, in terms of coverage probability and robustness. The real-life data sets analyzed in this study also support the conclusions of the simulation study.

An Enhanced Exponential Dual to Ratio-cum-Product Type Estimator of Population mean under Stratified Random Sampling

This article investigates an exponential estimator in dual form for the population mean in stratified random sampling using two auxiliary variates that are modified from the ratio-cum-product type estimators. The formulae for bias and mean squared error (MSE) have been determined for the suggested stratified random sample estimator. Additionally, in a stratified sample scheme, the propounded estimator has been practically and conceptually compared to current ones. It is proven that the improved estimator that has been presented is more effective than all other competing population mean estimators. . KEYWORDS :Ratio-cum-Product estimator, Stratified sample scheme, Population mean, Mean squared error, Bias.

Estimation of Population Mean using Multi-auxiliary Information in the Presence of Non-response

In this article, we have proposed almost unbiased estimators of population mean using multi-auxiliary information in the presence of non-response. It is seen that the suggested estimators are more efficient than existing estimators. Theoretical results are supported by numerically illustrations.. KEYWORDS :Non-response, Multi-auxiliary variables, Bias, Mean squared error (MSE).

A New Modified Estimator for Population Mean using Auxiliary Character and Attribute in Double Sampling

In sample surveys, when information on two auxiliary characters is available, several authors prefer chain-type estimators to improve the performance of estimators of the population mean. These authors have assumed that the information (population mean, total, etc.) on the first auxiliary or auxiliary character is not available but on the second or additional auxiliary character. However, there are instances where the latter and former may also be unavailable. In such cases, we have suggested a novel modified regression-type estimator that uses the data from the auxiliary character and the auxiliary attribute in double sampling to estimate the population mean. We have derived the expressions for bias and mean square error of the suggested estimator using the large sample approximation. After mathematical comparisons, we have obtained mathematical conditions under which the suggested estimator has lower mean square error than the existing estimators. Further, we supported these theoretical comparisons using a numerical analysis with a real-life dataset.. KEYWORDS :Bias, Double sampling, Mean square error, Auxiliary attribute, Auxiliary character.

Parameter Estimation in case of Incomplete Frames using Double Sampling

Sampling frames play an important role in survey research as they lay the foundation on the basis of which representative sample drawn from a target population. However, in practice, sampling frames are often incomplete, meaning that they do not fully capture the complete population of interest. In such cases, as a consequence of the incompleteness in sampling frame, the sample drawn does not provide a good representation of the population and hence, the results infer to vague and misleading conclusions. The present study is an attempt to somehow uplift the efficacy of the estimator of population mean by taking into consideration, the additional information gathered from the units currently excluded in the existing sampling frame along with mean square error of the proposed estimator. Optimum sample sizes are also obtained using suitable cost function under Neyman scheme. To compare the proposed estimator with the traditional ones, a simulation study has been done.. KEYWORDS :Incomplete sampling frame, Double sampling, Stratified sampling, Predecessor-successor method, Mean square error.

Artificial intelligence for herbicide recommendation: case study for the use of clomazone in Brazilian soils

The use of herbicides has been carried out without considering the physical and chemical properties of the soil and its variation in the different producing regions. Its interaction is dependent on the properties of the soil and the herbicide itself and, therefore, is considered complex. An alternative to optimize the use of herbicides is the application of mathematical models to estimate the sorption in the soil, contributing to a more efficient control of weeds and bringing more environmental safety. In this study, the efficiency of Artificial Neural Networks (ANNs) was evaluated as a tool to predict clomazone sorption in different Brazilian soils. The herbicide sorption coefficients were determined in the laboratory with 45 soils from different soil environments. Multilayer perceptron (MLP) ANN models were used to predict clomazone sorption. The variables were selected using the feature selection tool using the physical and chemical properties of the soils. Multivariate statistics were performed to determine the correlations between the physical and chemical properties of the soil with the sorption coefficient. Potassium (K), phosphorus (P), magnesium (Mg), organic matter (OM), silt, clay, and cation exchange capacity (CEC) were the ANN inputs and the sorption coefficient (Kfs) the output. The general performance of the model was evaluated by its precision and error values, namely: coefficient of determination (R2), mean absolute relative error (RMSE), mean absolute error (MAE), mean estimation error (MBE), and the coefficient Pearson correlation test (r). The ANN models were able to predict the Kfs of clomazone in the studied soils. The input variables that determined the best performing network for Kfs prediction were: CTC, Silt, Mg, and K. The variables that showed greater relative importance in the sensitivity analysis in the construction of the model for the Kfs of clomazone were: K (37%) and Silt (29%). The best RNA model was able to recommend reducing the dose of clomazone compared to the commercial package insert method.

Confirmatory Factor Analysis of the Hyperacusis Impact Questionnaire, Sound Sensitivity Symptoms Questionnaire, and Screening for Anxiety and Depression in Tinnitus, Including Preliminary Analyses of the Parent Versions for Use with Children.

We previously reported the results of exploratory factor analysis (EFA) of the Hyperacusis Impact Questionnaire (HIQ), the Sound Sensitivity Symptoms Questionnaire (SSSD), and the Screening for Anxiety and Depression in Tinnitus (SAD-T). Confirmatory factor analysis (CFA) is necessary to confirm the latent constructs determined using EFA. CFA should use different samples but with similar characteristics to those used for EFA. The aim was to use CFA to confirm latent constructs derived using EFA of the HIQ, SSSQ, and SAD-T. We further evaluated the psychometric properties of parent versions of these questionnaires (indicated by -P), which are intended for use with children. This was a retrospective cross-sectional study. Data for 323 consecutive adults and 49 children who attended a Tinnitus and Hyperacusis Therapy Clinic in the United Kingdom within a 6-month period were included. Data were collected retrospectively from the records of patients held at the Audiology Department. CFA with the weighted least-squares mean and variance-adjusted estimator was applied to assess the previously proposed factor structures of the HIQ, SSSQ, and SAD-T. The internal consistency of the scales was assessed via Cronbach's α (α). The items of the HIQ, SSSQ, and SAD-T were tested for measurement invariance regarding age and gender using the multiple indicator multiple cause (MIMIC) model. All questionnaires showed good to excellent internal consistency, with α = 0.93 for the HIQ, 0.87 for the SSSQ, and 0.91 for the SAD-T. The parent versions showed acceptable to good internal consistency, with α = 0.88 for the HIQ-P, 0.71 for the SSSQ-P, and 0.86 for the SAD-T-P. CFA showed that the HIQ, SSSQ, and SAD-T were all one-factor questionnaires and the factors generally were similar to those obtained for the EFA. The MIMIC model showed that all three questionnaires can be considered as measurement invariant, with scores similar across genders and ages. The HIQ, SSSQ, and SAD-T are internally consistent one-factor questionnaires that can be used in clinical and research settings to assess the impact of hyperacusis, the severity of sound sensitivity symptoms, and to screen for anxiety and depression symptoms. Future studies should further explore the psychometric properties of the parent versions of the HIQ, SSSQ, and SAD-T.

Level of job burnout among employees of King Khalid University

This study aimed at measuring the level of job burnout among King Khalid University staff. The descriptive-analytical approach was employed to describe job burnout, determine its prevalence, identify its causes, and propose ways to address it. This method was used for comparison, interpretation, and generating information to assist in understanding the phenomena of job burnout and to devise recommendations for mitigating its prevalence. The results showed that the overall mean estimation of the dimensions of the level of occupational burnout from the perspective of university staff was (2.28), with a standard deviation of (0.81), indicating a low degree. The arithmetic means of the study sample responses to the dimensions ranged from (1.98–2.66). This provides a good indicator of the prevalence of occupational burnout. The findings showed that individuals in higher ranks experience higher levels of job burnout compared to the rest of the ranks classified in the study.

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.

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.

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.

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.

Isotonic Regression for Variance Estimation and Its Role in Mean Estimation and Model Validation

We study isotonic regression which is a nonparametric rank-preserving regression technique. Under the assumption that the variance function of a response is monotone in its mean functional, we investigate a novel application of isotonic regression as an estimator of this variance function. Our proposal of variance estimation with isotonic regression is used in multiple classical regression problems focused on mean estimation and model validation. In a series of numerical examples, we (1) explore the power variance parameter of the variance function within Tweedie’s family of distributions, (2) derive a semi-parametric bootstrap under heteroscedasticity, (3) provide a test for auto calibration, (4) explore a quasi-likelihood approach to benefit from best-asymptotic estimation, and (5) deal with several difficulties under Lognormal assumptions. In all of these problems we verify that the variance estimation with isotonic regression is essential for proper mean estimation and beneficial compared to traditional statistical techniques based on local polynomial smoothers.

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.

CUAHN-VIO: Content-and-uncertainty-aware homography network for visual-inertial odometry

Learning-based visual ego-motion estimation is promising yet not ready for navigating agile mobile robots in the real world. In this article, we propose CUAHN-VIO, a robust and efficient monocular visual-inertial odometry (VIO) designed for micro aerial vehicles (MAVs) equipped with a downward-facing camera. The vision frontend is a content-and-uncertainty-aware homography network (CUAHN). Content awareness measures the robustness of the network toward non-homography image content, e.g. 3-dimensional objects lying on a planar surface. Uncertainty awareness refers that the network not only predicts the homography transformation but also estimates the prediction uncertainty. The training requires no ground truth that is often difficult to obtain. The network has good generalization that enables “plug-and-play” deployment in new environments without fine-tuning. A lightweight extended Kalman filter (EKF) serves as the VIO backend and utilizes the mean prediction and variance estimation from the network for visual measurement updates. CUAHN-VIO is evaluated on a high-speed public dataset and shows rivaling accuracy to state-of-the-art (SOTA) VIO approaches. Thanks to the robustness to motion blur, low network inference time (∼23 ms), and stable processing latency (∼26 ms), CUAHN-VIO successfully runs onboard an Nvidia Jetson TX2 embedded processor to navigate a fast autonomous MAV.

Performance Evaluation of QT-RR Adaptation Time Lag Estimation in Exercise Stress Testing.

Slower adaptation of the QT interval to sudden changes in heart rate has been identified as a risk marker of ventricular arrhythmia. The gradual changes observed in exercise stress testing facilitates the estimation of the QT-RR adaptation time lag. The time lag estimation is based on the delay between the observed QT intervals and the QT intervals derived from the observed RR intervals using a memoryless transformation. Assuming that the two types of QT interval are corrupted with either Gaussian or Laplacian noise, the respective maximum likelihood time lag estimators are derived. Estimation performance is evaluated using an ECG simulator which models change in RR and QT intervals with a known time lag, muscle noise level, respiratory rate, and more. The accuracy of T-wave end delineation and the influence of the learning window positioning for model parameter estimation are also investigated. Using simulated datasets, the results show that the proposed approach to estimation can be applied to any changes in heart rate trend as long as the frequency content of the trend is below a certain frequency. Moreover, using a proper position of the learning window for exercise so that data compensation reduces the effect of nonstationarity, a lower mean estimation error results for a wide range of time lags. Using a clinical dataset, the Laplacian-based estimator shows a better discrimination between patients grouped according to the risk of suffering from coronary artery disease. Using simulated ECGs, the performance evaluation of the proposed method shows that the estimated time lag agrees well with the true time lag.

Gaussian differentially private robust mean estimation and inference

Gaussian differentially private robust mean estimation and inference