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In this paper, we propose various sampling strategies under random non response framework and proposed estimators to estimate population mean on current occasion. The formulation of the estimator is allied with Cochran (1977) and Searls (J. Am. Stat. Assoc.59, 1225–1226 1964) in the framework of random non response. The characteristics of each proposed estimator have been studied under optimum replacement policy. We have examined the performance of these estimators under the analytical study and validated it through numerical study. We have also gauged the loss with the available complete response case and reported in numerical illustration. Suitable recommendations have been put forward to the survey statisticians for its practical application. [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]

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.

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.

We propose an estimator for the population mean θ0=피(Y) under the semi‐supervised learning setting with the Missing at Random (MAR) assumption. This setting assumes that the probability of observing Y$$ Y $$, denoted by πM∗$$ {\pi}_M^{\ast } $$, depends on the total sample size M$$ M $$ and satisfies πM∗=o(1)$$ {\pi}_M^{\ast }=o(1) $$. To efficiently estimate θ0$$ {\theta}_0 $$, we introduce an adaptive estimator based on inverse probability weighting and cross‐fitting. Theoretical analysis reveals that our proposed estimator is consistent and efficient, with a convergence rate of MπM∗$$ \sqrt{M{\pi}_M^{\ast }} $$, slower than the typical M$$ \sqrt{M} $$ rate, due to the diminishing proportion of labelled data as the sample size M$$ M $$ increases in the semi‐supervised setting. We also prove the consistency of inverse probability weighting (IPW)–Nadaraya–Watson density function estimators. Extensive simulations and an application to the Los Angeles homeless data validate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

Estimating the mean of a population is a recurrent topic in statistics because of its multiple applications. If previous data is available, or the distribution of the deviation between the measurements and the mean is known, it is possible to perform such estimation by using L-statistics, whose optimal linear coefficients, typically referred to as weights, are derived from a minimization of the mean squared error. However, such optimal weights can only manage sample sizes equal to the one used to derive them, while in real-world scenarios this size might slightly change. Therefore, this paper proposes a method to overcome such a limitation and derive approximations of flexible-dimensional optimal weights. To do so, a parametric family of functions based on extreme value reductions and amplifications is proposed to be adjusted to the cumulative optimal weights of a given sample from a symmetric distribution. Then, the application of Yager's method to derive weights for ordered weighted average (OWA) operators allows computing the approximate optimal weights for sample sizes close to the original one. This method is justified from the theoretical point of view by proving a convergence result regarding the cumulative weights obtained for different sample sizes. Finally, the practical performance of the theoretical results is shown for several classical symmetric distributions. [ABSTRACT FROM AUTHOR]

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]

In recent years, the research field of data collection under local differential privacy (LDP) has expanded its focus fromelementary data types to includemore complex structural data, such as set-value and graph data. However, our comprehensive review of existing literature reveals that there needs to be more studies that engage with key-value data collection. Such studies would simultaneously collect the frequencies of keys and the mean of values associated with each key. Additionally, the allocation of the privacy budget between the frequencies of keys and the means of values for each key does not yield an optimal utility tradeoff. Recognizing the importance of obtaining accurate key frequencies and mean estimations for key-value data collection, this paper presents a novel framework: the Key-Strategy Framework forKey-ValueDataCollection under LDP. Initially, theKey-StrategyUnary Encoding (KS-UE) strategy is proposed within non-interactive frameworks for the purpose of privacy budget allocation to achieve precise key frequencies; subsequently, the Key-Strategy Generalized Randomized Response (KS-GRR) strategy is introduced for interactive frameworks to enhance the efficiency of collecting frequent keys through group-anditeration methods. Both strategies are adapted for scenarios in which users possess either a single or multiple key-value pairs. Theoretically, we demonstrate that the variance of KS-UE is lower than that of existing methods. These claims are substantiated through extensive experimental evaluation on real-world datasets, confirming the effectiveness and efficiency of the KS-UE and KS-GRR strategies. [ABSTRACT FROM AUTHOR]

When measuring the research variable is complicated, expensive, or problematic, median ranked set sampling (MRSS) is often utilized since it is straightforward to rank the components using a low-cost sorting criterion. Using this sampling scheme, many authors considered the problem of population mean estimation with a single auxiliary variable in order to obtain more precised estimators than the traditional ratio type regression estimators. In this article, we extend their ideas based on regression approach using two auxiliary variables and introduce a new regression-type estimator along with its theoretical expression of minimum mean square error (MSE). The suggested estimator's applicability is demonstrated using both simulated and real-world data sets.

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]

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.

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]

In real-world surveys, non-response and measurement errors are common, therefore studying them together seems rational. Some population mean estimators are modified and studied in the presence of non-response and measurement errors. Bias and mean squared error expressions are derived under different cases. For all estimators, a theoretical comparison is made with the sample mean per unit estimator. The Monte-Carlo simulation is used to present a detailed picture of all estimators' performance. [ABSTRACT FROM AUTHOR]

Maintaining privacy while dealing with the sensitive issue in the sample survey is one of the very important tasks. Randomize response technique is a useful tool to handle the sensitive issue in surveys with privacy. Availability of auxiliary information helps in estimating the population mean of a study variable efficiently. When the population parameters of an auxiliary variable are not available in advance then two-phase sampling is required for efficient estimation. Here, we present a class of estimators to estimate the population mean of a sensitive variable using randomize response technique under two-phase sampling. Theoretical and simulation approaches are used to illustrate the advantage of the proposed study over the existing one. The simulation result shows that the mean square error of the proposed class of estimators is smaller than that of the existing estimators and so, the proposed class of estimators is more efficient than the existing estimators. The proposed class of estimators can be used in surveys of various fields such as social, agricultural, health, education, etc., to estimate the population mean of a sensitive variable. [ABSTRACT FROM AUTHOR]

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 YN∈[YL,YU] utilizing all the indeterminate values of the neutrosophic auxiliary variable XN∈[XL,XU] rather than only the extreme values XL and XU. 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.

Inference with incomplete data, especially non-ignorable, is one of the challenging tasks in data analysis. Moreover, it is well known that results obtained from incomplete data are prone to bias. Parameter estimation with non-ignorable missing data is even more challenging to handle and extract useful information. This paper proposes a method based on the Influential tilting resampling approach (ITRA) to handle non-ignorable missing data for inference on the mean. One of the bases of the proposed approach is assuming that the model for the non-respondents corresponds to an exponential tilting of the respondents' model, and the specified function in the tilted model is the influential function of the functional (parameter) of interest. Extensive simulation studies were conducted to investigate the performance of the proposed methods. We provided the theoretical justification, as well as application to real data. [ABSTRACT FROM AUTHOR]

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]

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.

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.

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]

The fast development of the Internet and mobile devices results in a crowdsensing business model, where individuals (users) are willing to contribute their data to help the institution (data collector) analyze and release useful information. However, the reveal of personal data will bring huge privacy threats to users, which will impede the wide application of the crowdsensing model. To settle the problem, the definition of local differential privacy (LDP) is proposed. Afterwards, to respond to the varied privacy preference of users, researchers propose a new model, i.e., personalized local differential privacy (PLDP), which allow users to specify their own privacy parameters. In this paper, we focus on a basic task of calculating the mean value over a single numeric attribute with PLDP. Based on the previous schemes for mean estimation under LDP, we employ PLDP model to design novel schemes (LAP, DCP, PWP) to provide personalized privacy for each user. We then theoretically analysis the worst-case variance of three proposed schemes and conduct experiments on synthetic and real datasets to evaluate the performance of three methods. The theoretical and experimental results show the optimality of PWP in the low privacy regime and a slight advantage of DCP in the high privacy regime. [ABSTRACT FROM AUTHOR]

This article studies interval estimation of the population mean in ranked set sampling. Eight types of confidence intervals are considered which are based on asymptotic theory, resampling methods, or a combination of them. A comprehensive simulation study is conducted to investigate performance of these intervals, and to deal with some limitations of a relevant work in the literature. Lastly, a data example is presented to illustrate the procedures. [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]

The processing of sequentially presented numerical information is a prerequisite for decisions from experience, where people learn about potential outcomes and their associated probabilities and then make choices between gambles. Little is known, however, about how people's preference for choosing a gamble is affected by how they perceive and process numerical information. To address this, we conducted a series of experiments wherein participants repeatedly sampled numbers from continuous outcome distributions. They were incentivized either to estimate the means of the numbers or to state their minimum selling prices to forgo a consequential draw from the distributions (i.e., the certainty equivalents or valuations). We found that participants valued distributions below their means, valued high‐variance sequences lower than low‐variance sequences, and valued left‐skewed sequences lower than right‐skewed sequences. Though less pronounced, similar patterns occurred in the mean estimation task where preferences should not play a role. These results are not consistent with prior findings in decision from experience such as the overweighting of high numbers and the underweighting of rare events. Rather, the qualitative effects, as well as the similarity of effects in valuation and estimation, are consistent with the assumption that people process numbers on a compressed mental number line in valuations from experience. [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]

In sequential analysis, an experimenter gathers information regarding an unknown functional (parameter) by observing random samples in successive steps. We discuss a number of distribution-free scenarios under a variety of loss functions. The number of observations gathered upon termination is a positive integer-valued random variable, customarily denoted by N. Often, a standardized version of N would follow an approximate normal distribution in the asymptotic sense. We provide exploratory data analysis (EDA) with the help of a number of interesting illustrations. We do so via large-scale simulation studies to demonstrate broad applicability of the purely sequential methodologies along with the appropriateness of asymptotic normality of the standardized stopping variables as a practical and useful guideline. [ABSTRACT FROM AUTHOR]

We consider the classical statistical learning/regression problem, when the value of a real random variable Y is to be predicted based on the observation of another random variable X. Given a class of functions F and a sample of independent copies of (X, Y), one needs to choose a function bf from F such that bf (X) approximates Y as well as possible, in the mean-squared sense. We introduce a new procedure, the so-called median-of-means tournament, that achieves the optimal tradeoff between accuracy and confidence under minimal assumptions, and in particular outperforms classical methods based on empirical risk minimization. [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]

When measuring the research variable is complicated, expensive, or problematic, median ranked set sampling (MRSS) is often utilized since it is straightforward to rank the components using a low-cost sorting criterion. Using this sampling scheme, many authors considered the problem of population mean estimation with a single auxiliary variable in order to obtain more precised estimators than the traditional ratio type regression estimators. In this article, we extend their ideas based on regression approach using two auxiliary variables and introduce a new regression-type estimator along with its theoretical expression of minimum mean square error (MSE). The suggested estimator's applicability is demonstrated using both simulated and real-world data sets., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Author(s).)

Ranked set sampling (RSS) is an advanced sampling method which is very effective for estimating mean of the population when exact measurement of observation is difficult and/or expensive. Balanced Groups RSS (BGRSS) is one of the modification of RSS where only the lowest, the median and the largest ranked units are taken into account. Although BGRSS is advantageous and useful for some specific cases, it has strict restrictions regarding the set size which could be problematic for sampling plans. In this study, we make an improvement on BGRSS and propose a new design called Partial Groups RSS which offers a more flexible sampling plan providing the independence of the set size and sample size. Partial Groups RSS also has a cost advantage over BGRSS. We construct a Monte Carlo simulation study comparing the performance of the mean estimators of the proposed sampling design and BGRSS according to their sampling costs and mean squared errors for various type of distributions. In addition, we give a biometric data application for investigating the efficiency of Partial Groups RSS in real life applications. [ABSTRACT FROM AUTHOR]

As a well-known method for selecting representative samples of populations, ranked set sampling (RSS) has been considered increasingly in recent years. This (RSS) method has proved to be more efficient than the usual simple random sampling (SRS) for estimating most of the population parameters. In order to have a more efficient estimate of the population mean, a new sampling scheme called as robust extreme double ranked set sampling (REDRSS) is introduced and investigated in this paper. A simulation study shows that using REDRSS scheme gives more efficient estimates of population mean with smaller variance than the usual SRS, RSS and most other sampling schemes based on RSS estimators in non-uniform (symmetric or non-symmetric) distributions. [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]