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Sampling survey data can sometimes contain outlier observations. When the mean estimator becomes skewed due to the presence of extreme values in the sample, results can be biased. The tendency to remove outliers from sample data is common. However, performing such removal can reduce the accuracy of conventional estimating techniques, particularly with regard to the mean square error (MSE). In order to increase population mean estimation accuracy while taking extreme values into consideration, this study presents an enhanced class of estimators. The method uses extreme values from an auxiliary variable as a source of information rather than eliminating these outliers. Using a first-order approximation, the properties of the suggested class of estimators are investigated within the context of a stratified two-phase sampling framework. A simulation research is conducted to examine the practical performance of these estimators in order to validate the theoretical conclusions. To further demonstrate the superiority of the suggested class of estimators for dealing with extreme values, an analysis of three different datasets demonstrates that they consistently provide higher percent relative efficiency (PRE) when compared to existing estimators. [ABSTRACT FROM AUTHOR]

Two-phase sampling is a useful technique for sample surveys, particularly when prior auxiliary data is not accessible. The ranks of the auxiliary variable often coincide with those of the research variable when two variables are correlated. By considering this relationship, we can significantly increase estimator accuracy. In this paper, we use the ranks of the auxiliary variable along with extreme values to estimate the population mean of the study variable. Up to a first-order approximation, we analyze the characteristics of the suggested class of estimators with an emphasis on biases and mean squared errors in stratified two-phase sampling. The theoretical results are verified using different datasets and a simulation study, which demonstrates that the proposed estimators outperform the existing ones in terms of percent relative efficiency. [ABSTRACT FROM AUTHOR]

In this article, we explore how to efficiently estimate the population mean utilizing past and current sample information through exponentially weighted moving average (EWMA) statistics in temporal surveys. We propose some optimal classes of memory-type estimators of population mean for temporal surveys within the framework of simple random sampling (SRS). We derive the expressions for the bias and mean square error (MSE) of the suggested estimators up to first-order approximation. We compare the traditional and newly introduced memory-type estimators and establish the efficiency conditions. Moreover, we conduct a thorough simulation study using real and artificial populations to refine our theoretical outcomes. The simulation results show that studying past and current sample data increase the efficiency of the proposed estimators.

Auxiliary information is an essential component in the field of survey sampling since it enables precise estimation of population parameters like mean, variance, distribution function, and so on, which in turn guarantees the best possible outcomes. In order to estimate the population mean of a study variable, this study makes use of auxiliary information in a two-fold approach. Through a stratified random sampling scheme, we introduce a novel class of estimators that utilize auxiliary information and their corresponding ranks. By conducting a thorough evaluation based on metrics such as mean square error and percentage relative efficiency, these proposed estimators have been shown to be effective in the estimation process. Empirical validation is conducted using a real dataset sourced from the domain of real estate. Exploring the relationship between Assessed Value (X) and Sale Amount (Y) during a five-year period extending from 2017 to 2021 is the primary emphasis of the empirical validation process, which is carried out with the assistance of a real dataset of real estate data. Furthermore, in order to demonstrate that our suggested estimator is superior to conventional unbiased estimators, as well as traditional regression estimators and other estimators that have been considered in the literature, a full simulation analysis is carried out. Our proposed estimator appears to be the most effective choice after being subjected to a comparison study against a variety of preexisting approaches. The findings of this study not only make a significant contribution to the development of the methodology of survey sampling but also offer vital insights for predictive modeling within the real estate sector.

AbstractDifferential privacy (DP) is a rigorous notion of data privacy, used for private statistics. The canonical algorithm for differentially private mean estimation is to first clip the samples to a bounded range and then add noise to their empirical mean. Clipping controls the sensitivity and, hence, the variance of the noise that we add for privacy. But clipping also introduces statistical bias. This tradeoff is inherent: we prove that no algorithm can simultaneously have low bias, low error, and low privacy loss for arbitrary distributions. Additionally, we show that under strong notions of DP (i.e., pure or concentrated DP), unbiased mean estimation is impossible, even if we assume that the data is sampled from a Gaussian. On the positive side, we show that unbiased mean estimation is possible under a more permissive notion of differential privacy (approximate DP) if we assume that the distribution is symmetric. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

Auxiliary information is an essential component in the field of survey sampling since it enables precise estimation of population parameters like mean, variance, distribution function, and so on, which in turn guarantees the best possible outcomes. In order to estimate the population mean of a study variable, this study makes use of auxiliary information in a two-fold approach. Through a stratified random sampling scheme, we introduce a novel class of estimators that utilize auxiliary information and their corresponding ranks. By conducting a thorough evaluation based on metrics such as mean square error and percentage relative efficiency, these proposed estimators have been shown to be effective in the estimation process. Empirical validation is conducted using a real dataset sourced from the domain of real estate. Exploring the relationship between Assessed Value (X) and Sale Amount (Y) during a five-year period extending from 2017 to 2021 is the primary emphasis of the empirical validation process, which is carried out with the assistance of a real dataset of real estate data. Furthermore, in order to demonstrate that our suggested estimator is superior to conventional unbiased estimators, as well as traditional regression estimators and other estimators that have been considered in the literature, a full simulation analysis is carried out. Our proposed estimator appears to be the most effective choice after being subjected to a comparison study against a variety of preexisting approaches. The findings of this study not only make a significant contribution to the development of the methodology of survey sampling but also offer vital insights for predictive modeling within the real estate sector. [ABSTRACT FROM AUTHOR]

This paper proposes a new family of estimators for population mean with a non-response using a simple random sampling. It specifically applies this method to estimate the mean in Turkey’s Education sector data sets, accounting for non-response. The study integrates additional information in the form of mean and cdf of the auxiliary variable which is highly positively correlated with the study variable to develop a general class of estimators tailored for the non-response using a simple random sampling scheme. Through numerical research, the characteristics of these estimators – namely, their biases and mean square errors – have been carefully investigated and deeply evaluated. The basic estimator of a population mean is under-performed by the suggested estimators. The empirical investigation validates the results, demonstrating the improved relative efficiency of the proposed estimator over the existing estimators, as demonstrated by theoretical and numerical comparisons.

Federated Computation is an emerging area that seeks to provide stronger privacy for user data, by performing large scale, distributed computations where the data remains in the hands of users. Only the necessary summary information is shared, and additional security and privacy tools can be employed to provide strong guarantees of secrecy. The most prominent application of federated computation is in training machine learning models (federated learning), but many additional applications are emerging, more broadly relevant to data management and querying data. This survey gives an overview of federated computation models and algorithms. It includes an introduction to security and privacy techniques and guarantees, and shows how they can be applied to solve a variety of distributed computations providing statistics and insights to distributed data. It also discusses the issues that arise when implementing systems to support federated computation, and open problems for future research. [ABSTRACT FROM AUTHOR]

This paper proposes a new family of estimators for population mean with a non-response using a simple random sampling. It specifically applies this method to estimate the mean in Turkey's Education sector data sets, accounting for non-response. The study integrates additional information in the form of mean and cdf of the auxiliary variable which is highly positively correlated with the study variable to develop a general class of estimators tailored for the non-response using a simple random sampling scheme. Through numerical research, the characteristics of these estimators – namely, their biases and mean square errors – have been carefully investigated and deeply evaluated. The basic estimator of a population mean is under-performed by the suggested estimators. The empirical investigation validates the results, demonstrating the improved relative efficiency of the proposed estimator over the existing estimators, as demonstrated by theoretical and numerical comparisons. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating the mean of a random vector based on N independent, identically distributed observations. We prove the existence of an estimator that has a nearoptimal error in all directions in which the variance of the one-dimensional marginal of the random vector is not too small: with probability 1-δ, the procedure returns μ N ​ which satisfies, for every direction u∈Sd-1, ... where σ²(u)=Var(X,u) and C is a constant. To achieve this, we require only slightly more than the existence of the covariance matrix, in the form of a certain moment-equivalence assumption. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the mean estimation problem in differential privacy query.After introducing the current mainstream local differential privacy design scheme of numerical data mean estimation,it first introduces the random censoring mechanism in random response technology to reveal the basic principle of mean calculation under local differential privacy,proposes a utility optimization theorem about the variance of mean estimation,and gives a boundary optimization formula,which improves the interpretability and operability of utility optimization theory in this field.Based on this theory,this paper proposes a practical,concise and efficient mean estimation algorithm protocol RCP for the first time,which can be used to collect and analyze the data of intelligent device users connected to the Internet,while meeting the requirements of local differential privacy.RCP is simple in structure,supports data analysis tasks on any number of numerical attributes,and has efficient communication and calculation,effectively alleviating the practical problems of complex algorithm design,difficult optimization,and low efficiency.Finally,empirical research demonstrates that the proposed method outperforms other existing schemes in terms of utility,efficiency and asymptotic error bounds.

Survey sampling has a wide range of applications in biomedical, meteorological, stock exchange, marketing, and agricultural research based on data collected through sample surveys or experimentation. The collected set of information may have a fuzzy nature, be indeterminate, and be summarized by a fuzzy number rather than a crisp value. The neutrosophic statistics, a generalization of fuzzy statistics and classical statistics, deals with the data that have some degree of indeterminacy, imprecision, and fuzziness. In this article, we introduce a fuzzy decision-making approach for deciding a sample size under a fuzzy measurement cost modeled by an intuitionistic fuzzy cost function. Our research introduces neutrosophic ratio-type estimators for estimating the population mean of the neutrosophic study variable Y N ∈ [ Y L , Y U ] utilizing all the indeterminate values of the neutrosophic auxiliary variable X N ∈ [ X L , X U ] rather than only the extreme values X L and X U . Three simulation studies are carried out to explain the proposed methods of parameter estimation, sample size determination, and efficiency comparison. The results reveal that the proposed neutrosophic class of estimators produces more accurate and precise estimates of the neutrosophic population mean than the existing neutrosophic estimators in simple random sampling, which is the ultimate goal of inferential statistics. [ABSTRACT FROM AUTHOR]

Under classical statistics, research typically relies on precise data to estimate the population mean when auxiliary information is available. Outliers can pose a significant challenge in this process. The ultimate goal is to determine the most accurate estimates of the population mean while minimizing variance. Neutrosophic statistics is a generalization of classical statistics that deals with imprecise, uncertain data. Our research introduces the neutrosophic Hartley–Ross-type ratio estimators for estimating the population mean of neutrosophic data, even in the presence of outliers. We also incorporate neutrosophic versions of several robust regression methods, including LAD, Huber-M, Hampel-M, and Tukey-M. Our approach assumes that the study variable is both non-sensitive and sensitive, meaning that it can cause discomfort to participants during personal interviews, and measurement errors can occur due to dishonest responses. To address potential measurement errors, we propose the use of neutrosophic scrambling response models. Our proposed neutrosophic robust estimators are more effective than existing classical estimators, as confirmed by a computer-based numerical study using real data and simulation. [ABSTRACT FROM AUTHOR]

Crowdsourced data from distributed sources are routinely collected and analyzed to produce effective data-mining mo-dels in crowdsensing systems.Data usually contains personal information,which leads to possible privacy leakage in data collection and analysis.The local differential privacy (LDP) has been deemed as the de facto measure for trade-off between privacy guarantee and data utility.Currently,the key-value data is a kind of heterogeneous data types in which the key is categorical data and the value is numerical data.Achieving LDP for key-value data is challenging.This paper focuses on key-value data publishing and correlation analysis under the framework of LDP.Firstly,the frequency correlation and mean correlation in key-value data are defined.Then the indexing one-hot perturbation mechanism is proposed to provide LDP guarantees.At last,the correlation results can be estimated in the perturbed space.Theoretical analysis and experimental results on both real-word and synthetic dataset va-lidate the effectiveness of proposed mechanism.

In environmental and many other areas, the main focus of survey is to measure elements using an efficient and cost-effective sampling technique. One way to reach that is by using Ranked set sampling (RSS). RSS is an alternative sampling technique that can be advantageous when measuring the variable of interest is either costly or time-consuming but ranking small sets of units according to the character under investigation by eye or other methods not requiring actual quantifications. The purpose of this article is to introduce a new modification of RSS to estimate the mean of the target population. This proposed technique is a double-stage approach that combines median RSS (MRSS) and MiniMax RSS (MMRSS). The performance of the empirical mean and variance estimators based on the proposed technique are compared with their counterparts in Double RSS (DRSS), Extreme RSS (ERSS), Double Extreme RSS (DERSS), MMRSS, RSS, and simple random sampling (SRS) via Monte Carlo simulation. Simulation results revealed that this new modification is almost always more efficient than their counterparts using MMRSS and SRS, while it is more efficient than RSS in many cases especially when the distribution is asymmetric. [ABSTRACT FROM AUTHOR]

In sampling theory, the auxiliary information is widely used to increase precision of the estimators when the study variable is correlated with the auxiliary variable. In several practical situations, the auxiliary information is available in the form of the auxiliary attribute(s). In this paper, we proposed a generalized estimator for the estimation of finite population mean using the auxiliary attribute under stratified two-phase sampling. The mathematical expressions of approximate bias and mean square error (MSE) of the proposed estimator are obtained to the first-order. Many special cases of the proposed estimator are also obtained using the known parameters of the auxiliary attribute. The algebraic comparisons of the MSE of the proposed estimator have been made the MSE of the competing estimators. The performance of the proposed estimator is evaluated using real data-sets. The results illustrate the good performance of the proposed estimators and its sub-cases. [ABSTRACT FROM AUTHOR]

Traffic speed estimation plays a key role in various situations, ranging from individual's trip planning to urban traffic management. Despite many studies on short-term prediction, there is only a limited number of studies focusing on long-term prediction and only a couple of them does go beyond 24 h. On the contrary, this study presents a novel hybrid architecture using location-based traffic characteristic for traffic speed estimation up to 7 days. In this architecture, the introduced mean filtering estimation (MFE) model and long short-term memory (LSTM) neural network are jointly utilized for minimizing the error for traffic flow estimation. Both MFE and LSTM utilizes the speed data, collected from roadside sensors in İstanbul, of previous weeks that have the same weekday and the same time with target time to be predicted. Results in this study indicate that the use of MFE gives lower error rates for locations with low traffic complexity while LSTM outperforms MFE model for locations with high traffic complexity. Thanks to the introduced MFE and the proposed hybrid architecture, we are able to predict the speed data of a given location with an error of lower than +/- 10 km/h. [ABSTRACT FROM AUTHOR]

Based on the traditional ranked set sampling (RSS), Al-Nasser and Al-Omari [1] have recently presented a cost-effective sampling technique called MiniMax RSS (MMRSS). However, MMRSS has some drawbacks when the distribution is asymmetric. To overcome this situation, in this article, we consider developing a modified version of MMRSS (MMMRSS). Monte Carlo simulations from numerous symmetric and asymmetric distributions are employed to assess the performance of the suggested MMMRSS mean estimator. Simulation findings demonstrated that MMMRSS estimator is more efficient than their counterparts using simple random sample (SRS) and MMRSS for all distributions considered in this article. Moreover, we have constructed Quality control charts to monitor the process mean based on the suggested MMMRSS. The performance of the average run length (ARL) of these new charts was compared with the control charts based on several sampling techniques. The results, based on a simulation study, indicate that our suggested MMMRSS control charts performed the best in detecting changes in process mean in most simulated scenarios. A real-life application concerning the global temperature is also provided as an illustration of the suggested charts. [ABSTRACT FROM AUTHOR]

Signal denoising--also known as non-parametric regression--is often performed through shrinkage estimation in a transformed (e.g., wavelet) domain; shrinkage in the transformed domain corresponds to smoothing in the original domain. A key question in such applications is how much to shrink, or, equivalently, how much to smooth. Empirical Bayes shrinkage methods provide an attractive solution to this problem; they use the data to estimate a distribution of underlying "effects," hence automatically select an appropriate amount of shrinkage. However, most existing implementations of empirical Bayes shrinkage are less flexible than they could be--both in their assumptions on the underlying distribution of effects, and in their ability to handle heteroskedasticity--which limits their signal denoising applications. Here we address this by adopting a particularly flexible, stable and computationally convenient empirical Bayes shrinkage method and applying it to several signal denoising problems. These applications include smoothing of Poisson data and heteroskedastic Gaussian data. We show through empirical comparisons that the results are competitive with other methods, including both simple thresholding rules and purpose-built empirical Bayes procedures. Our methods are implemented in the R package smashr, "SMoothing by Adaptive SHrinkage in R," available at https://www.github.com/stephenslab/smashr. [ABSTRACT FROM AUTHOR]

We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data in both the univariate and multivariate settings. We focus on estimators based on median-of-means techniques, but other methods such as the trimmed-mean and Catoni's estimators are also reviewed. We give detailed proofs for the cornerstone results. We dedicate a section to statistical learning problems—in particular, regression function estimation—in the presence of possibly heavy-tailed data. [ABSTRACT FROM AUTHOR]

Rank-based sampling designs are powerful alternatives to simple random sampling (SRS) and often provide large improvements in the precision of estimators. In many environmental, ecological, agricultural, industrial and/or medical applications the interest lies in sampling designs that are cheaper than SRS and provide comparable estimates. In this paper, we propose a new variation of ranked set sampling (RSS) for estimating the population mean based on the random selection technique to measure a smaller number of observations than RSS design. We study the properties of the population mean estimator using the proposed design and provide conditions under which the mean estimator performs better than SRS and some existing rank-based sampling designs. Theoretical results are augmented with some numerical studies and a real-life example, where we also study the performance of our proposed design under perfect and imperfect ranking situations. [ABSTRACT FROM AUTHOR]

Some authors have recently warned about the risks of the sentence with enough data, the numbers speak for themselves. The problem of nonparametric statistical inference in big data under the presence of sampling bias is considered in this work. The mean estimation problem is studied in this setup, in a nonparametric framework, when the biasing weight function is unknown (realistic). The problem of ignoring the weight function is remedied by having a small SRS of the real population. This problem is related to nonparametric density estimation. The asymptotic expression for the MSE of the estimator proposed is considered. Some simulations illustrate the performance of the nonparametric method proposed in this work.