Logistic regression is widely used for binary outcomes, yet generalized maximum entropy (GME) estimators are often recommended when data are limited or ill-conditioned. Applied guidance on when GME and logistic regression provide practically similar predictive performance—particularly probability calibration—remains limited. We conducted a Monte Carlo study comparing SAS PROC LOGISTIC (maximum likelihood) with SAS PROC ENTROPY (GME-D; GMED) across four baseline scenarios: (S1) large well-specified samples (n = 5000), (S2) small samples with high collinearity (n = 100; corr(x1,x2) ≈ 0.95), (S3) rare events with a quasi-separation tendency (n = 1000; β0 = −3.50; 1% of observations with x1 shifted by +12), and (S4) heavy-tailed contamination/outliers (n = 1000; 5% contaminated with t(1) noise). Each condition was replicated R = 200 times with a 70/30 train–test split. Performance was evaluated on test data using discrimination (AUC), proper scoring rules (Brier score, log loss), and calibration via logistic recalibration (intercept and slope). Across S1–S2, AUC and scoring rules were nearly identical between methods, but PROC ENTROPY produced modestly larger calibration slopes. In S3, AUC remained similar (ΔAUC ≈ 0.0014), while calibration diverged substantially (Δ intercept ≈ 0.456; Δ slope ≈ 0.278). In S4, PROC LOGISTIC showed better discrimination (ΔAUC ≈ −0.0055) and slightly better scoring rules, while PROC ENTROPY again produced larger calibration slopes. Sensitivity analyses varying event prevalence, ESUPPORTS width, and sample size confirmed that calibration differences are most pronounced under rare events and depend on entropy support specifications. Routine calibration reporting is essential when comparing binary classifiers and PROC ENTROPY users should assess sensitivity to ESUPPORTS choices when probability estimation is the goal.
We study persistent instructor effects in university grading when grades are discrete, ordinal, and pile up at institutional thresholds (18 = legal passing grade; 30~e~lode = honors above 30). In such data, the canonical hierarchical specification---a mixed-effects proportional-odds (cumulative logit) model with professor-level random intercepts---is not estimable in practice: quasi-complete separation at the professor level drives the random intercepts toward ±∞ and prevents the likelihood from attaining a finite maximum. We propose a separation-robust alternative. First, we fit a pooled proportional-odds model for the grade as a function of observed student characteristics (gender, off schedule status, age), exam year, and disciplinary area, explicitly excluding professor identifiers. This model yields, for each exam, the full predicted grade distribution and its expected value on the transcript scale. Second, for each professor we define a grading severity index as the average deviation between realized grades and these predicted benchmarks. This index is always finite, directly interpretable in transcript points, and can be analyzed using standard sampling, shrinkage, and persistence tools. Using over 1.2 million exam records from a large Italian university (2007--2019), we find that grading standards differ sharply across professors: the gap between the severe and generous tails approaches five grade points even after conditioning on observables. These differences are highly persistent over time (year-to-year persistence around 0.8), are not explained by professor gender or by broad disciplinary area, and do not generate systematic subgroup undercoverage in predictive calibration.
Stratification is a foundational technique in survey sampling, designed to enhance the precision of estimates by reducing within-group variability and maximizing differences between subgroups. Choosing the right level of stratification is essential for obtaining accurate and policy-relevant data in a vast and diverse nation like India, where socioeconomic and health status vary significantly even within relatively small administrative units called districts. National surveys use the typical urban-rural division to solve this, although finer segmentation can yield even more precise results, particularly in the more diverse rural settings. This study assesses the relative efficiency of two- versus four-segment stratification frameworks in estimating key health indicators at the district-level in India. Using data from a large-scale health survey, four indicators child stunting, immunization coverage, four plus antenatal care, and sanitation access were analyzed. Results showed that while the two-segment design produced better precision in most districts, particularly in the populous states, the four-segment approach delivered substantial improvements in specific states and for indicators prone to higher sampling variability. These findings emphasize the importance of context-specific stratification strategies, balancing operational feasibility with statistical precision. The study advocates for adaptive survey designs that align stratification choices with local population heterogeneity and indicator-specific characteristics to optimize data quality and policy utility.
Standard survival models assume that time is greater than zero. However, there are several practical examples where a proportion of the data presents times equal to zero. Based on this issue, survival models including this proportion have been proposed and are called zero-inflated survival models. It is important to consider flexible distributions in this context in order to model more complex patterns. In this paper, we propose a Generalized Gamma zero-inflated cure-rate survival model, motivated by the pattern observed in the labor progression times. Based on simulation study, we show that estimation methods (maximum likelihood estimates and asymptotic confidence intervals) present a good performance even for small sample sizes. Concerning the model selection, we verified that Likelihood Ratio Test showed the best results. The proposed model was considered to analyze the labor time of pregnant women from sub-Saharan Africa. For diagnostic analysis, we used Cox-Snell residuals and Local Influence methods. In general, the model showed as an adequate tool to describe the labor and we conclude that this model can be a tool in the study of childbirth times supporting management in obstetrical healthcare. We acknowledge the World Health Organization for granting us permission to use the data set.
An alternative method for obtaining a Bayesian estimate for coefficient alpha by way of a posterior normal distribution was recently proposed. The performance of this method was initially assessed using Bayesian credible intervals (CrIs) via simulation under mundane conditions to establish baseline performance. It was found to generally have good performance under that set conditions. However, the performance of the alternative method using non-normal data was not assessed. Here, the alternative method is assessed using CrIs via simulation with a focus on non-normal data. Again, it was found that the alternative method generally had good performance. However, there were instances of poor performance when data came from simulation conditions that resulted in items being binary, non-normal, or not varying enough.
We propose a new analytical improvement to the multivariate Ljung-Box test that addresses the inherent pronounced deviations of the original test from nominal type I error rates under almost all scenarios. Prior attempts to mitigate this issue have been directed at modification of the test statistics or correction of the test distribution to achieve precise results in finite samples. In previous studies, focused on designing corrections to the univariate Ljung-Box, a method that specifically adjusts the test rejection region has been the most successful of attaining the best type I error rates. We adopt the same approach for the more complex, multidimensional time series scenarios. We use large sample simulation data (multivariate normal) for a range of sample sizes (n = 40 to 300), lags (m = 2 to n − 1), and multivariate time series dimension (k = 2 to 10) to obtain an empirical estimation of the correct rejection regions for the particular combination of these variables. Furthermore, we use regression modeling with interactions and covariate power combinations to parametrically extend these precise rejection regions to all combinations of sample sizes, lags, and number of time series. Thus, we design and implement the correction based on regression models fit to empirically estimate rejection thresholds. Our results are validated to independent validation simulations and show that we attain almost perfect type I error rates with mean absolute deviation of 0.0011 across all scenarios compare to 0.0276 for the classical Ljung-Box test, which represents a 96% improvement. These findings will enhance the goodness-of-fit diagnostics for multivariate time series.
This study aims to analyze the effect of the drill method on the mathematics learning outcomes of seventh-grade students at SMP Negeri 5 Jombang. The pre-test results were tested for normality using the Shapiro-Wilk test and for homogeneity using the Bartlett test. The pre-test results showed the data were normally distributed and homogeneous. The t-test indicated that the pre-test mean scores between the control and experimental classes were the same. However, the post-test data for the experimental class were not normally distributed, so homogeneity was tested using the Levene test. The Mann-Whitney test showed a significant difference, proving that the drill method affects students' learning outcomes.
The purpose of this paper is to present an analytically easy-to-use procedure for estimating extreme quantiles of continuous random variables using the Peak Over Threshold approach and a statistically sound approach to the problem of threshold selection that needs to be resolved in this context. A web link included in the text points to a ready-to-use implementation of the proposed method in the popular programming language Python.
Among recommendation systems, collaborative filtering is a widely used method that leverages user preferences and collective actions to provide accurate book recommendations. With so many books available today, it can be harder and harder for readers to find books that suit their interests. As a result, recommender systems have become a vital tool for addressing this problem head-on, attempting to provide users with personalized book recommendations based on their unique interests and preferences. The studies have employed diverse datasets and machine learning technique KNN with Sparse Matrix, and Deep learning algorithm collaborative filtering Neural Network . Preprocessing carried out by Exploratory Data Analysis. These algorithms have demonstrated a significant improvement in recommendation accuracy. The KNN achieved accuracy levels of 81%, 85%, and 93% for different neighbour values 4, 5, 6 while CFNN achieved the accuracy of 95%. The studies have also delved into understanding the impact of various factors on book recommendations, including user preferences and collaborative patterns among readers and it recommends CFNN is suitable method for recommendation system.
China's economic trajectory has garnered significant attention globally, driven by its impressive growth and increased integration into the international trade arena. In response to this, China has strategically implemented a series of trade liberalization policies aimed at fostering economic development, attracting foreign investment, and enhancing global competitiveness. Despite the importance of these policies and their potential impact on the nation's export performance, there is a discernible gap in the literature that necessitates a more sophisticated and forward-looking approach. Traditional forecasting methods applied in economic analyses, while valuable, face challenges in capturing the inherent complexity of economic variables influenced by rapidly changing policies and the dynamic nature of global market forces. Acknowledging this gap, our research is inherently motivated by the urgent need for an accurate and efficient forecasting model capable of navigating the intricate and ever-evolving economic landscape of China. In this study, we introduce an optimal machine learning-based forecasting model to analyze the impact of trade liberalization on China's economy and its export performance. Initially, we extract meaningful features from the provided China's economic dataset, optimizing these features through the modified chicken swarm optimization (MCSO) algorithm. Furthermore, we design the convolutional neural network–bagged decision tree (CNN-BDT) for China's economic forecasting, specifically designed to reduce the false positive rate. Finally, we validate the performance of the proposed CNN-BDT model using sample data of China's exports to the US from 2015 to 2021. The results demonstrate the effectiveness of the proposed CNN-BDT model in terms of performance metrics, including accuracy, precision, recall, and F-measure.
In the present paper, the analysis of growth and instability in production, area and yield of wheat for some wheat growing states of India is carried out by computing compound growth rate (CGR) and Cuddy-Della Valle (CDV) instability index on utilizing secondary time series data of wheat pertaining to the period 2011-2020 in the concerned states. The percentage change in production, area and yield of wheat is examined by considering the base year as 2011. Moreover, the percentage share of production, area and yield of wheat are demonstrated graphically for the year 2020.
Purpose: The purpose of the study is to investigate blue zone lifestyle on Indian diet management system through optimized diet plans. The study explores menu planning with plant-based, animal-, and dairy-based recipes promoting longevity and reduction of chronic diseases in India. Design/Methodology/Approach: The macro- and micronutrient data is collected for the regionally available food items in India. The study proposed linear programming problems to maximize the calories with 66 food items, satisfying the Required Nutrient Intake (RNI) for normal individuals living in rural and urban areas of India. Findings: Three optimization models, such as Linear Programming Problem (LPP), Integer Linear Programming (ILP), and Stigler’s Diet Programming (SDP), were proposed for selecting menus with varying calorie ranges (1900 kcal-3100 kcal). The percentage of nutrients contained in the diet plans was close to Blue Zone food guidelines adoptable to the Indian population. Originality/Value: The revised Stigler Diet Problem (SDP) has well-optimized objective function with the highest accommodation of recipes in optimal menus. This approach is helpful to nutritionists and dieticians for preparing affordable diet plans for distinct income groups. Also, the study provides insights to policymakers working on improving the health conditions of people by adopting the blue zone diet.
This study aims to determine the effect of resampling RACOG and RACOG-RUS data on Gradient Boosting and Naïve Bayes classification in predicting water quality with unbalanced data. The data used in this study were 720 data from January 2022 to December 2023. It was found that Gradient Boosting performed best when using RACOG-RUS resampling data and feature selection with a number of numIntances of 200. While Naïve Bayes has the best performance when using RACOG-RUS resampling data without feature selection with a number of numIntances of 300. It can be seen that resampling RACOG data does not outperform RACOG-RUS in both classification models because it is known that the data generated in RACOG does not make the dataset more balanced than RACOG-RUS. Hybrid sampling is necessary if RACOG samples are used as the training dataset.
Principal component analysis is a multivariate statistical method used for reducing data dimension which can be applied in various fields. One of them is in computer science application, i.e. dimension reduction of image data for face recognition. This research focuses on obtaining average faces matrix, eigenfaces, and data projection results based on principal component scores. The results were then used for further step in face recognition namely classification. Here two classification methods are used, namely Euclidean distance and artificial neural networks (ANN) with single and multi-layers. The data used are from AT&T Laboratories Cambridge collections in April 1992 - April 1994, each line of the data contains pixel from a single image that has 256 levels of black and white color between 0 and 1. Based on the analysis results, the accuracy rate of face recognition using the Euclidean distance method is 89%. At the same time, single-layer ANN produce the accuracy of 90.5% for two hidden layers, 89% for 3 and 4 hidden neurons, while multi-layer ANN produce the accuracy of 89.5% for hidden neurons (3.2), and 91% for hidden neurons (3,3) and (4,2). However, the smallest error was obtained by multi-layer ANN with hidden neurons (4,2) which resulted the error value of 7.5303. Thus we conclude that the multilayer ANN (4.2) outperformed the others and then is chosen as the best classification for the face recognition analysis of the data.
The main key objective of this paper is to address the nonresponse problems by adapting Hansen and Hurwitz’s technique (1964) and Saini et al.’s estimator (2022) to propose a novel estimator of population mean under sub-sampling technique using multiple auxiliary variables. A comparative analysis of the proposed novel estimator's efficacy has been performed through theoretical and numerical studies. The results of this paper confirm that our estimator is more effective than others under the same situation.
Autonomous vehicles (AVs) are revolutionizing Intelligent Transportation Systems by seamlessly exchanging real-time data with other AVs and the network. For humans, controlled transportation has numerous advantages. But safety and security are the main concerns because malicious autonomous vehicles can make consequences. To avoid these consequences nanosensors are integrated with Vision Transformer (ViT) in AV which play a pivotal role in enhancing anomaly detection. To evaluate performance of the proposed framework, various evaluation metrics were employed. The experimental findings are compared with existing models, such as Convolution Neural Networks (CNN), Recurrent Neural Networks (RNN), Deep Reinforcement Learning (DRL), and Deep Belief Networks (DBN). The result shows that ViT method achieves accuracy, precision, recall of about 92%, 93% and 93%, respectively. Experimental results demonstrate the superiority of ViT and nano sensor integration over traditional methods, showcasing its ability to detect a wide range of attacks with high accuracy and robustness.
This research aims to compare the performance of Ordinary Least Square (OLS), Least Absolute Shrinkage and Selection Operator (LASSO), Ridge Regression (RR) and Elastic-Net in controlling multicollinearity problems between independent variables in multiple regression analysis using simulation data and case data. Data simulation uses a multiple regression model with p = 6 with a high level of multicollinearity (ρ = 0.99) at several sample sizes (n = 25, 50, 75). The best method is measured based on the smallest Average Mean Square Error (AMSE) and AIC values. The research results show that Elastic-Net is the best method for simulated data compared to LASSO and Ridge because it has the smallest AMSE and AIC values for each sample size studied. Similar things were also obtained when applying these three methods to data on stunting toddler cases in Indonesia which had high multicollinearity. By using the best method, namely the Elastic Net method, real data shows that cases of stunted toddlers in Indonesia are influenced by the percentage of toddlers who are malnourished (????????), the percentage of toddlers who receive exclusive breast milk (????????), the percentage of toddlers whose growth is monitored (????????), coverage of health services for pregnant women (????????), number of nutrition workers (????????), percentage of households with adequate drinking water (????????), percentage of households with adequate sanitation (????????????), human development index (????????????), and population density (????????????).
We propose and develop the four-parameter Harris Extended Fréchet distribution. It is obtained by inserting the two-parameter Frechet distribution as the baseline in the Harris family and may be a useful alternative method to model income distribution and could be applied to other areas. We demonstrate that the new distribution can have decreasing, increasing and upside-down-bathtub hazard functions and that its probability density function is an infinite linear combination of Frechet densities. Some standard mathematical properties of the proposed distribution are derived, such as the quantile function, ordinary and incomplete moments, incomplete moments, Lorenz and Bonferroni curves, Gini index, Renyi and ????-entropies, mean residual life and mean inactivity time, probability weighted moments, stress-strength reliability, and order statistics. We also obtain the maximum likelihood estimators of the model. The potentiality/flexibility of the new distribution is illustrated by means two applications to failure and waiting time data sets
Transportation facilities and means have developed very rapidly and become the basic needs of the community from time to time. This development ultimately requires the availability of capable and adequate transportation facilities and infrastructure in the form of the availability of good facilities. In general, the movement of the number of flight passengers at Sultan Hasanudin Airport tends not to be stationary on average because in certain times the movement forms an uptrend pattern. In addition, the number of flight passengers at Sultan Hasanudin Airport has an irregular pattern with varying increases and decreases. To forecast fluctuations in the number of flight passengers at Sultan Hasanudin Airport in the coming period, it can be done by time series analysis. The Triple Exponential Smoothing method or commonly referred to as Winter Exponential Smoothing is one of the Time Series methods that is suitable for handling seasonal data such as the number of domestic passengers at Sultan Hasanuddin Airport Makassar. The analysis step of the Triple Exponential Smoothing method is model identification, parameter estimation by trial and error, then is the calculation of the initial value of data smoothing, trends, and seasonality with a length of one season L = 12 and the last is to calculate the error value using MAPE and RMSE. The best model is obtained from a combination of parameters α = 0.9; β = 0,1; and γ=0.1 which results in the smallest forecasting error using RMSE with a value of 56,674.56 and MAPE with a value of 56,674.56. Using a forecasting model: So the forecasting results are obtained that look close and not too far from the previous year's data so that it can be used as a reference for the management of the aircraft company to make the right decisions and anticipate a surge in the number of passengers.
The single-parameter “Bell distribution” for discrete data allows for over-dispersion in the data. The maximum likelihood estimator for its parameter is downward-biased in finite samples. We consider various methods for reducing this bias. A simulation study shows that these are effective and also lead to a small improvement in the mean squared error of the estimator. The Cox-Snell correction is the recommended. choice among the options that are considered.
