Sample Variance Research Articles

Validation of semi-analytical, semi-empirical covariance matrices for two-point correlation function for early DESI data

ABSTRACT We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of luminous red galaxies (LRGs) data collected during the initial 2 months of operations of the Stage-IV ground-based Dark Energy Spectroscopic Instrument (DESI). We run the pipeline on multiple effective Zel’dovich (EZ) mock galaxy catalogs with the corresponding cuts applied and compare the results with the mock sample covariance to assess the accuracy and its fluctuations. We propose an extension of the previously developed formalism for catalogs processed with standard reconstruction algorithms. We consider methods for comparing covariance matrices in detail, highlighting their interpretation and statistical properties caused by sample variance, in particular, non-trivial expectation values of certain metrics even when the external covariance estimate is perfect. With improved mocks and validation techniques, we confirm a good agreement between our predictions and sample covariance. This allows one to generate covariance matrices for comparable data sets without the need to create numerous mock galaxy catalogs with matching clustering, only requiring 2PCF measurements from the data itself. The code used in this paper is publicly available at https://github.com/oliverphilcox/RascalC.

Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling

This paper presents improved population mean estimators using auxiliary variables in Stratified Ranked Set Sampling. We have derived the expressions for bias and mean square errors up to the first order of approximation and shown that the proposed estimators under optimum conditions are more efficient than other estimators taken in this paper. In an attempt to verify the efficiencies of proposed estimators, theoretical results are supported by numerical illustrations and simulation study for which we have considered two populations.

A Facies Proportional Determination Method Based on the Theory of Confidence Intervals: A Case Study in the M Gas Field in the East China Sea

A reservoir is the space and gathering place of underground oil and gas reservoirs. Lithofacies proportion is the key parameter of a reservoir. Due to the heterogeneity of geological bodies, the multi-solution of seismic data and the limited and uneven distribution of logging data, it is unclear how to determine the lithofacies proportion in the study area directly from the available data. The mean is a way to make a quick estimate, but the mean cannot quantify the uncertainty of the lithofacies proportion using the available data. In this paper, a new method for quantifying uncertainty and determining the value of the three levels of the facies proportion is proposed. Taking sandstone proportion as an example, a normality test was carried out to verify the applicability of the sandstone proportion data to this method, and then the mean and variance of samples were calculated. Based on the confidence interval theory, the uncertainty of the mean value and the range of sandstone proportion were determined, that is, the optimistic value and the pessimistic value of the sandstone proportion. The results show that this method provides a new reference for quantifying values for the three levels of the uncertainty, and it uses the petrographic proportion as an example to provide the data basis for subsequent modeling and reservoir research.

Sampling Theory for Mineral Process Flows

Current literature dealing with the theory of sampling process flows is limited in scope, a situation addressed by papers presented at conferences by the author. This paper provides a summary of methods to quantify process sampling variance in a sound statistical manner. Two methods of calculation of the process sampling variance are presented here with models for robust estimation of the process covariance/variogram. The strategies for process sampling to acquire the data for process characterisation are described. The method for process characterisation can be based on special sampling campaigns, on the analysis of on-line measurement data, or on the analysis of historical data, which may be based on composite samples, such as shift samples. These scenarios are all dealt with as well as methods based on analysis of process dynamics. The latter analysis demonstrates that use of covariance functions drawn from geostatistical practice can be inappropriate for process analysis. The work is supported with plant data examples and quantitative analyses of process conditions.

Meta-analyzing partial correlation coefficients using Fisher's z transformation.

The partial correlation coefficient (PCC) is used to quantify the linear relationship between two variables while taking into account/controlling for other variables. Researchers frequently synthesize PCCs in a meta-analysis, but two of the assumptions of the common equal-effect and random-effects meta-analysis model are by definition violated. First, the sampling variance of the PCC cannot assumed to be known, because the sampling variance is a function of the PCC. Second, the sampling distribution of each primary study's PCC is not normal since PCCs are bounded between -1 and 1. I advocate applying the Fisher's z transformation analogous to applying Fisher's z transformation for Pearson correlation coefficients, because the Fisher's z transformed PCC is independent of the sampling variance and its sampling distribution more closely follows a normal distribution. Reproducing a simulation study by Stanley and Doucouliagos and adding meta-analyses based on Fisher's z transformed PCCs shows that the meta-analysis based on Fisher's z transformed PCCs had lower bias and root mean square error than meta-analyzing PCCs. Hence, meta-analyzing Fisher's z transformed PCCs is a viable alternative to meta-analyzing PCCs, and I recommend to accompany any meta-analysis based on PCCs with one using Fisher's z transformed PCCs to assess the robustness of the results.

A Statistical Theory for Sampling of Particulate Materials

The concepts currently applied to the sampling of broken minerals and particulate materials were recognised over 100 years ago. The first integrated theory of sampling for the mineral industries was proposed by Gy, who brought together means of estimation of the variance of sampling due to both the particulate nature of a broken ore and the time variation of composition of process streams. However, his theory deals only with sampling variance and cannot determine the full sampling distribution. The full distribution of the composition of potential samples arising from their particulate nature is developed in this paper based solely on the assumption that particle numbers in correct samples follow independent Poisson distributions. The enabling mathematical method is the use of the characteristic function of the sampling distribution. The practical means of calculating the full distribution completes the theory of sampling of particulate materials. The method is applied to a sample of gold ore to calculate the full sampling distribution and effectively clarifies several difficulties when sampling this material. The method has general applicability to all particulate materials, including foodstuffs.

Avoiding Optimal Mean Robust and Sparse BPCA with L1-norm Maximization

<p>Recently, the robust PCA/2DPCA methods have achieved great success in subspace learning. Nevertheless, most of them have a basic premise that the average of samples is zero and the optimal mean is the center of the data. Actually, this premise only applies to PCA/2DPCA methods based on L2-norm. The robust PCA/2DPCA method with L1-norm has an optimal mean deviate from zero, and the estimation of the optimal mean leads to an expensive calculation. Another shortcoming of PCA/2DPCA is that it does not pay enough attention to the instinct correlation within the part of data. To tackle these issues, we introduce the maximum variance of samples’ difference into Block principal component analysis (BPCA) and propose a robust method for avoiding the optimal mean to extract orthonormal features. BPCA, which is generalized from PCA and 2DPCA, is a general PCA/2DPCA framework specialized in part learning, can makes better use of the partial correlation. However, projection features without sparsity not only have higher computational complexity, but also lack semantic properties. We integrate the elastic network into avoiding optimal mean robust BPCA to perform sparse constraints on projection features. These two BPCA methods (non-sparse and sparse) make the presumption of zero-mean data unnecessary and avoid optimal mean calculation. Experiments on reference benchmark databases indicate the usefulness of the proposed two methods in image classification and image reconstruction.</p> <p> </p>

Effective sample pairs based contrastive learning for clustering

As an indispensable branch of unsupervised learning, deep clustering is rapidly emerging along with the growth of deep neural networks. Recently, contrastive learning paradigm has been combined with deep clustering to achieve more competitive performance. However, previous works mostly employ random augmentations to construct sample pairs for contrastive clustering. Different augmentations of a sample are treated as positive sample pairs, which may result in false positives and ignore the semantic variations of different samples. To address these limitations, we present a novel end-to-end contrastive clustering framework termed Contrastive Clustering with Effective Sample pairs construction (CCES), which obtains more semantic information by jointly leveraging an effective data augmentation method ContrastiveCrop and constructing positive sample pairs based on nearest-neighbor mining. Specifically, we augment original samples by adopting ContrastiveCrop, which explicitly reduces false positives and enlarges the variance of samples. Further, with the extracted feature representations, we provide a strategy to construct positive sample pairs via a sample and its nearest neighbor for instance-wise and cluster-wise contrastive learning. Experimental results on four challenging datasets demonstrate the effectiveness of CCES for clustering, which surpasses the state-of-the-art deep clustering methods.

DropMessage: Unifying Random Dropping for Graph Neural Networks

Graph Neural Networks (GNNs) are powerful tools for graph representation learning. Despite their rapid development, GNNs also face some challenges, such as over-fitting, over-smoothing, and non-robustness. Previous works indicate that these problems can be alleviated by random dropping methods, which integrate augmented data into models by randomly masking parts of the input. However, some open problems of random dropping on GNNs remain to be solved. First, it is challenging to find a universal method that are suitable for all cases considering the divergence of different datasets and models. Second, augmented data introduced to GNNs causes the incomplete coverage of parameters and unstable training process. Third, there is no theoretical analysis on the effectiveness of random dropping methods on GNNs. In this paper, we propose a novel random dropping method called DropMessage, which performs dropping operations directly on the propagated messages during the message-passing process. More importantly, we find that DropMessage provides a unified framework for most existing random dropping methods, based on which we give theoretical analysis of their effectiveness. Furthermore, we elaborate the superiority of DropMessage: it stabilizes the training process by reducing sample variance; it keeps information diversity from the perspective of information theory, enabling it become a theoretical upper bound of other methods. To evaluate our proposed method, we conduct experiments that aims for multiple tasks on five public datasets and two industrial datasets with various backbone models. The experimental results show that DropMessage has the advantages of both effectiveness and generalization, and can significantly alleviate the problems mentioned above. A detailed version with full appendix can be found on arXiv: https://arxiv.org/abs/2204.10037.

Variance reduced Shapley value estimation for trustworthy data valuation

Data valuation, especially quantifying data value in algorithmic prediction and decision-making, is a fundamental problem in data trading scenarios. The most widely used method is to define the data Shapley and approximate it by means of the permutation sampling algorithm. To make up for the large estimation variance of the permutation sampling that hinders the development of the data marketplace, we propose a more robust data valuation method using stratified sampling, named variance reduced data Shapley (VRDS for short). We theoretically show how to stratify, how many samples are taken at each stratum, and the sample complexity analysis of VRDS. Finally, the effectiveness of VRDS is illustrated in different types of datasets and data removal applications.

Data weighting: An iterative process linking surveys, data synthesis, and population models to evaluate mis-specification

Integrated stock assessments specify a distribution for multiple data types, and these distributions control the relative leverage assigned to each datum. A decade of research has demonstrated that (1) proper data weighting is necessary to avoid bias resulting from overweighting noisy age- and length-composition data; (2) sampling data can be pre-processed to estimate the likely sampling variance for composition data; and (3) using random effects to estimate time-varying parameters can improve the fit to data while also changing statistical leverage, and thereby serve a similar role to reweighting data. However, there are also unresolved questions including: (A) Is it more appropriate to model age and length data as proportions-at-age and as an index for the total, or as a series of indices-at-age? (B) Are correlated residuals appropriately addressed via data weighting or do they require additional model changes (i.e., time-varying parameters)? (C) How to efficiently communicate information about sampling imprecision and model errors between sampling and stock-assessment teams? (D) How does model-based expansion of sampling data affect data weighting? and (E) How to address alternative hypotheses about factors driving poor fit to data? Here, we argue that stock assessment errors can be classified using four categories: sampling bias (e.g., changes in survey coverage), sampling imprecision (e.g., finite sample sizes), assessment model bias (e.g., incorrect demographic assumptions) and assessment model imprecision (e.g., random effects). This categorization has several implications with resulting practical recommendations. For example, we define Percent Excess Variance (PEV) from the ratio of input sample size (the measured variance of sampling imprecision) and effective sample sizes (the variance of assessment-model residuals). We propose calculating PEV as standardized diagnostic measuring the net effect of survey bias and assessment model bias and imprecision. We demonstrate PEV in a simulation experiment fitted using the Woods Hole Assessment Model (WHAM) conditioned upon Gulf of Alaska walleye pollock, where unacknowledged variation in fishery selectivity results in a PEV of 77 % and this is eliminated when correctly specifying a time-varying estimation model. We also argue that model-based expansion of data inputs using auxiliary information can mitigate sampling bias, while also measuring sampling imprecision for spatially unrepresentative surveys. Similarly, including random effects can mitigate model bias while increasing model imprecision when the demographic model has little explanatory power. Finally, we observe that down-weighting compositional data for a given fleet fails to propagate information about model residuals when interpreting abundance indices or reference points for that same fleet. When PEV is large for important fleets, we therefore encourage focused research to explain the sources of these errors rather than simply downweighting without propagating information about residuals. However, we acknowledge a continuing role for automated data weighting for less important fleets, although we recommend explicit hypotheses about potential sources of errors in those cases.

How the sampling variances affect the linear predictor of the Fay-Herriot model

How the sampling variances affect the linear predictor of the Fay-Herriot model

Skin Lesion Intelligent Diagnosis in Edge Computing Networks: An FCL Approach

In recent years, automatic skin lesion diagnosis methods based on artificial intelligence have achieved great success. However, the lack of labeled data, visual similarity between skin diseases, and restriction on private data sharing remain the major challenges in skin lesion diagnosis. In this article, first, we propose a federated contrastive learning framework to break down data silos and enhance the generalizability of diagnostic model to unseen data. Subsequently, by combining data features from different participated nodes, the proposed framework can improve the performance of contrastive training. To extract discriminative features during on-device training, we propose a contrastive learning based intelligent skin lesion diagnosis scheme in edge computing networks. Specifically, a contrastive learning based dual encoder network is designed to overcome training sample scarcity by fully leveraging unlabeled samples for performance improvement. Meanwhile, we devise a maximum mean discrepancy based supervised contrastive loss function, which can efficiently explore complex intra-class and inter-class variances of samples. Finally, the diagnosis simulations demonstrate that compared with existing methods, our proposed scheme can achieve superior accuracy in both on-device training and distributed training scenarios.

#3406 CARDIOPROTECTIVE EFFECT OF SOY PROTEIN ON LONG-TERM HIGH-SALT DIET IN CYNOMOLGUS MONKEYS

Abstract Background and Aims A high salt content in the diet is one of the reasons for the increase in blood pressure (BP) and the development of cardiovascular disorders. However, high intake of sodium chloride does not always lead to an increase in blood pressure, but causes endothelial dysfunction and cardiac remodeling. It has been established that the introduction of soy products into the diet can have a nephro- and cardioprotective effect in chronic kidney disease. At the same time, it is not clear whether the damaging effect of a high-salt diet on the cardiovascular system can be offset by other dietary interventions, in particular, soy proteins. In this regard, the aim of the study was to study the effect of long-term use of diets with different content of sodium chloride and soy protein on myocardial remodeling in cynomolgus monkeys. Method A total of 18 cynomolgus male monkeys with age 6–8 years were studied. The animals were divided into three groups (six in each group). The first (control) group received the standard diet. The second group received the diet rich in common salt (8 g of NaCl/kg), and the third, the high salt diet in combination with soy protein SUPRO 760 (200 g/kg; Protеin Tеchnology Intеrnational, USA). Systolic (BP) and diastolic (BPd) blood pressure (BP) in monkeys was recorded by oscillometric method on a veterinary tonometer ML-410 VET (Microlux, Russia) under anesthesia. After registration of blood pressure, an echocardiographic study (EchoCG) was performed with a sector sensor with a frequency of 3-5 MHz on an ultrasound system Chison SonoTouch 60 (China). Echocardiography was performed in B-mode (two-dimensional scanning), M-mode (one-dimensional scanning), as well as in pulsed and tissue Doppler modes. Echocardiography and blood pressure measurements were performed at baseline, after 4 and 12 months of follow-up. Results BP values (group 1 - BPs: 109±10.09, BPd: 60±7.42; group 2 - BPs: 109±25.14, BPd: 57±11.86; group 3 - BPs: 101±8, 59, BPd: 57±6.92 mm Hg, all p>0.05) and heart rate (group 1 - 77±12.61, group 2 - 81±18.07, group 3-80±19.9 beats/min, all p>0.05) in macaques did not undergo significant changes over 12 months of the experiment in any of the groups. In group 1, there were also no significant changes in echocardiographic parameters. Group 2 monkeys showed no early changes in LV shortening fraction (FU) and ejection fraction (EF). However, after 12 months, FU decreased by an average of 26.6%, and EF by 12.8% compared with the indicator for a period of 4 months. In addition, the speed of the transmitral flow in early diastole (E) decreased by 19.1% compared with the baseline. Long-term intake of soy proteins prevented a decrease in LV FU in macaques on a high-salt diet. Its value was 25.1% greater than in group 2. In group 3 monkeys, after 12 months, the magnitude of systolic excursion of the mitral annulus plane and the maximum rate of excursion of the fibrous annulus of the mitral valve in early diastole (e') increased, the thickness of the interventricular septum in diastole decreased, and E/e' ratio. In group 3, the thickness of the posterior wall of the left ventricle decreased in systole (0.57±0.056 mm), the mass of the LV myocardium (14.9±2.94 g/m2), the average diameter of the base of the right ventricle (1.20±0.115 mm) compared with group 2 (0.69±0.040 mm, 19.6±2.83 g/m2, 1.40±0.111 mm, respectively; all p<0.01). Conclusion The obtained results can be considered as confirmation of the hypothesis that high consumption of sodium chloride leads to adverse structural and functional changes in the heart and blood vessels, not associated with an increase in blood pressure. The inclusion of isolated soy proteins in the diet is likely to reduce the effects of this negative impact. The specific mechanisms of this cardioprotective effect remain to be explored. Statistical analysis used One-way analysis of variance for unrelated samples when comparing the data of 3 studied groups and one-way analysis of variance for related samples when studying the dynamics of the indicator in each of the groups during 12 months of observation. Results are presented as mean ± standard deviation (M ± SD). Differences were considered significant at p<0.05.

A New Estimator: Median of the Distribution of the Mean in Robustness

In some statistical methods, the statistical information is provided in terms of the values used by classical estimators, such as the sample mean and sample variance. These estimations are used in a second stage, usually in a classical manner, to be combined into a single value, as a weighted mean. Moreover, in many applied studies, the results are given in these terms, i.e., as summary data. In all of these cases, the individual observations are unknown; therefore, computing the usual robustness estimators with them to replace classical non-robust estimations by robust ones is not possible. In this paper, the use of the median of the distribution Fx¯ of the sample mean is proposed, assuming a location-scale contaminated normal model, where the parameters of Fx¯ are estimated with the classical estimations provided in the first stage. The estimator so defined is called median of the distribution of the mean, MdM. This new estimator is applied in Mendelian randomization, defining the new robust inverse weighted estimator, RIVW.

William George Hill. 7 August 1940—17 December 2021

William (Bill) Hill was an internationally acclaimed statistical, population and quantitative geneticist. His work was inspired by practical problems in animal breeding, but is widely applicable to evolutionary biology and human genetics. Bill's work focused on the joint effects of linkage, mutation and genetic architecture in finite populations. He showed that linked loci under selection can interfere with each other, reducing the rate of response to selection. He derived a widely used metric for linkage disequilibrium and showed that there is likely to be substantial linkage disequilibrium between closely linked variants in finite populations. He also showed that the sampling variance of linkage disequilibrium is very large, hampering its use in estimating effective population size or recombination rates. Bill derived sampling variances for inbreeding and realized relatedness between individuals with the same expected degree of relatedness. He raised awareness about the importance of new mutations for quantitative genetic variation and the response to artificial selection, and developed models for the maintenance of quantitative genetic variation by a balance between mutation and stabilizing selection. His experimental designs for estimating heritability and conducting artificial selection experiments have been widely adopted, and were utilized in his own long-term mouse selection experiments. Bill influenced animal breeding directly through consultancies with breeding companies, and his influence on quantitative genetics continues today via his numerous mentees.

Impact of study partner type on primary endpoint volatility in a phase 3 registration trial of mild‐to‐moderate Alzheimer’s disease

AbstractBackgroundIn Alzheimer’s disease (AD) clinical trials, participants are required to enroll with a study partner (SP) who ensures compliance and completes outcomes assessing participant cognitive and functional ability. The SP role is commonly filled by spouses and other family members. Spouse and non‐spouse SPs differ in numerous ways, including average time in contact with the participant. These differences may impact volatility of SP‐reported assessments, which may in turn impact trial integrity. We quantified the impact of SP type on the variance of SP‐reported Disability Assessment for Dementia (DAD) scores.MethodWe analyzed data from the Bapineuzumab 301 (ApoE e4 non‐carriers) and 302 (ApoE e4 carriers) phase 3 trials in mild‐to‐moderate AD, provided by the trial sponsor, Janssen Research & Development, LLC for use in these analyses. We compared the sample variances of end‐of‐study DAD scores for spousal and non‐spousal SPs in each trial. 95% confidence intervals (CIs) for the corresponding parameters were computed via bootstrapping. We used similar methods to compare the variances in the difference between baseline and end‐of‐study DAD scores for SP types.ResultAmong the 1,232 and 1,121 participants analyzed from trials 301 and 302, 818 (66.4%) and 837 (74.7%) had spousal SPs at baseline, respectively (Table 1). On the other hand, 665 (665/973 = 68.3%) and 697 (697/924 = 75.4%) spousal SPs in each trial completed the end‐of‐study visit, respectively. In trial 301, the variance of end‐of‐study DAD scores for spousal SPs were observed to be 14% lower compared to non‐spousal SPs (spousal/non‐spousal = 630.41/746.55 = 0.84, 95% CI = [0.71, 1.03]). In trial 302 this relative decrease was observed to be 9%, though with less precision (spousal /non‐spousal = 610.85/673.86 = 0.91, 95%CI = [0.77, 1.12]). Neither trial had significant differences in spousal vs non‐spousal variances of the change‐from‐baseline DAD scores (Trial 301: spousal/non‐spousal = 378.10/425.17 = 0.91, 95%CI = [0.66, 1.22]; Trial 302: spousal/non‐spousal = 354.38/352.22 = 1.01, 95%CI = [0.77, 1.35]). DAD variance over time is depicted in Figure 1. Differences in the linear trend of DAD variance did not significantly differ between SP types in either trial (Trial 301 Est.: ‐1.74, 95%CI: [‐3.58, 0.23]; Trial 302 Est.: 0.94, 95%CI: [‐5.83, 4.31]).ConclusionSP type was not associated with variation in SP‐reported study endpoints in this study.

Competition and moral behavior: A meta-analysis of forty-five crowd-sourced experimental designs

Does competition affect moral behavior? This fundamental question has been debated among leading scholars for centuries, and more recently, it has been tested in experimental studies yielding a body of rather inconclusive empirical evidence. A potential source of ambivalent empirical results on the same hypothesis is design heterogeneity-variation in true effect sizes across various reasonable experimental research protocols. To provide further evidence on whether competition affects moral behavior and to examine whether the generalizability of a single experimental study is jeopardized by design heterogeneity, we invited independent research teams to contribute experimental designs to a crowd-sourced project. In a large-scale online data collection, 18,123 experimental participants were randomly allocated to 45 randomly selected experimental designs out of 95 submitted designs. We find a small adverse effect of competition on moral behavior in a meta-analysis of the pooled data. The crowd-sourced design of our study allows for a clean identification and estimation of the variation in effect sizes above and beyond what could be expected due to sampling variance. We find substantial design heterogeneity-estimated to be about 1.6 times as large as the average standard error of effect size estimates of the 45 research designs-indicating that the informativeness and generalizability of results based on a single experimental design are limited. Drawing strong conclusions about the underlying hypotheses in the presence of substantive design heterogeneity requires moving toward much larger data collections on various experimental designs testing the same hypothesis.

Development and Statistical Validation of E-Probe Diagnostic Nucleic Acid Analysis (EDNA) Assays for the Detection of Citrus Pathogens from Raw High-Throughput Sequencing Data

The cost for high-throughput sequencing (HTS) has decreased significantly and has made it possible for the application of this technology for routine plant diagnostics. There are constraints to the use of HTS as a diagnostic tool, including the need for dedicated personnel with a bioinformatic background for data analysis and the lack of a standardized analysis pipeline that makes evaluating and validating results generated at different HTS laboratories difficult. E-probe diagnostic nucleic acid analysis (EDNA) is an in-silico bioinformatic tool that utilizes short curated electronic probes (e-probes) designed from pathogen-specific sequences that allow users to detect and identify single or multiple pathogens of interest in raw HTS data sets. This platform streamlines the bioinformatic data analysis into a graphical user interface as a plant diagnostic tool used by diagnosticians. In this study, we describe the process for the development, validation, and use of e-probes for detection and identification of a wide range of taxonomically unique citrus pathogens that include citrus exocortis viroid, citrus tristeza virus, ‘ Candidatus Liberibacter asiaticus’, and Spiroplasma citri. We demonstrate the process for evaluating the analytical and diagnostic sensitivity and specificity metrics of the in-silico EDNA assays. In addition, we show the importance of including background noise (internal controls) to generate variance in noninfected samples for a valid statistical test using the quadratic discriminant analysis. The fully validated EDNA assays from this study can be readily integrated into existing citrus testing programs that utilize HTS. [Formula: see text] Copyright © 2023 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license .

Estimating fuzzy measures of deprivation at local level in Tuscany.

In this paper we estimate monetary and non-monetary poverty measures at two sub-regional levels in the region of Tuscany (Italy) using data from the ad-hoc Survey on Vulnerability and Poverty held by Regional Institute from Economic Planning of Tuscany (IRPET). We estimate the percentage of households living in poverty conditions and three supplementary fuzzy measures of poverty regarding deprivation in basic needs and lifestyle, children deprivation, and financial insecurity. The key feature of the survey is that it was carried out after the COVID-19 pandemic, therefore, some of the items collected focus on the subjective perception of poverty eighteen months after the beginning of the pandemic. We assess the quality of these estimates either with initial direct estimates along with their sampling variance, and with a secondary small area estimation when the formers are not sufficiently accurate.