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The performance of a population mean estimator can be improved by transformation techniques using a subset of the population data. An improved family of estimators for population mean has been proposed under double sampling using a transformed auxiliary variable. The biases and mean square errors of the proposed family of estimators up to the first order of approximation have been investigated. Simulation studies and an application to fine particulate matter in Chiang Rai, Thailand, are used to study the efficiency of the proposed estimators. The results from an application to air pollution in Chiang Rai showed that the proposed estimators gave smaller biases, by at least a half of the existing ones, and gave at least four times less mean square error than the existing ones.

Values that are too large or small enough can be found in many data sets. Therefore, the estimator can yield ambiguous findings if several of the incredible deals are picked for the sample. When such extreme values occur, we propose improved estimators to determine the finite population means using double sampling based on probability proportional to size sampling (PPS). The properties of estimators are obtained up to the first order of approximations. When the size of the units varies widely, the PPS sampling technique may be employed. To determine the values of Pi when using PPS, we must be acquainted with the aggregate of the auxiliary variable Xi. However the designs and estimation techniques we have looked at so far are unsuccessful and are less effective when this information is difficult to locate or when other information is missing. The two-phase approach is preferable and more feasible in these kinds of circumstances. To demonstrate how effectively the recommended estimators performed, we used three actual data sets. We show mathematically and theoretically that the suggested estimators outperform alternative estimators.

The concept of monitoring the coefficient of variation has gained significant interest in quality control, particularly in situations where the mean and standard deviation of a process are not constant. This study modified the procedure of the previous double sampling chart for monitoring the coefficient of variation, developed by Ng et al. in 2018. Instead of using only information from the second sample, here, information from both samples is used. The probability properties of the out-of-control signal and run length of this chart are presented. To evaluate the chart’s performance, the optimal design and a comparison with the previous double sampling control chart using average run-length criteria are described. It was found that the modified double sampling chart has better performance and is more efficient compared to the previous chart, especially when the total sample size is smaller. As a study case, the application of this chart is illustrated using real data from a molding process. This confirmed that the modified double sampling chart improved performance in detecting out-of-control signals. Thus, the modified chart is recommended to be applied in industry.

Abstract. The concept of monitoring the coefficient of variation has gained significant interest in quality control, particularly in situations where the mean and standard deviation of a process are not constant. This study modified the procedure of the previous double sampling chart for monitoring the coefficient of variation, developed by Ng et al. in 2018. Instead of using only information from the second sample, here, information from both samples is used. The probability properties of the out-of-control signal and run length of this chart are presented. To evaluate the chart's performance, the optimal design and a comparison with the previous double sampling control chart using average run-length criteria are described. It was found that the modified double sampling chart has better performance and is more efficient compared to the previous chart, especially when the total sample size is smaller. As a study case, the application of this chart is illustrated using real data from a molding process. This confirmed that the modified double sampling chart improved performance in detecting out-of-control signals. Thus, the modified chart is recommended to be applied in industry. [ABSTRACT FROM AUTHOR]

In this paper, an ultra-low-power second-order, single-bit discrete-time (DT) double sampling ΔΣ modulator was proposed for hearing aid applications. In portable biomedical devices that are permanently used such as hearing aids, short battery lifetime and power dissipation are considerable issues. In a typical delta–sigma modulator, the most power-consuming parts are the operational transconductance amplifiers (OTAs), and their elimination without loss of efficiency is now challenging. This proposed modulator includes an ultra-low-power self-biased inverter-based amplifier with swing enhancement instead of power-hungry OTAs. Low voltage amplifier design reduces output swing voltage, affecting delta–sigma modulator efficiency and decreasing the signal-to-noise and distortion ratio (SNDR) and dynamic range (DR) values. In this article, the proposed amplifier's source and tail transistors were biased in the sub-threshold region, increasing the output swing voltage significantly and leading to desired properties for a hearing aid modulator. The proposed amplifier peak-to-peak swing voltage was approximately 1.01 V at a 1 V power supply. In addition, the proposed modulator design used a standard 180 nm CMOS technology, which obtained 140 dB DR and 93.27 dB SNDR for a 10 kHz signal bandwidth with an oversampling ratio (OSR) of 128. Finally, the modulator's effective chip area was 0.02 mm2 and consumed only about 9.9 µW, while the figure of merit (FOMW) and FOMs achieved 1.31 fJ/step and 183.31, respectively. [ABSTRACT FROM AUTHOR]

The performance of a population mean estimator can be improved by transformation techniques using a subset of the population data. An improved family of estimators for population mean has been proposed under double sampling using a transformed auxiliary variable. The biases and mean square errors of the proposed family of estimators up to the first order of approximation have been investigated. Simulation studies and an application to fine particulate matter in Chiang Rai, Thailand, are used to study the efficiency of the proposed estimators. The results from an application to air pollution in Chiang Rai showed that the proposed estimators gave smaller biases, by at least a half of the existing ones, and gave at least four times less mean square error than the existing ones. [ABSTRACT FROM AUTHOR]

Several situations arise where decision-making is required for some characteristics of an asymmetrical population for example estimation of the weekly number of server breakdowns at a company. The estimation methods based upon classical sampling designs are not suitable in such situations and some specialized methods and/or estimators are required. The ranked set sampling is a procedure that is suitable in such situations. In this paper, a new estimator is proposed that can be used to estimate population characteristics in case of asymmetrical populations. The proposed estimator is useful for estimation of population mean in the presence of non-response in study variable by using ranked set sampling procedure. The estimator is based upon two auxiliary variables to reduce the effect of asymmetry. The use of two auxiliary variables is also helpful in minimizing the variation in the estimation of the population mean of the study variable. The ranked set sampling procedure is used to get better accuracy as the actual measurements may be time-consuming, expensive, or difficult to obtain in a small sample size. The use of ranked set sampling also reduces the effect of asymmetry in the characteristics under study. The expressions for the mean square error and bias for the proposed estimators have been derived. The performance of the proposed estimator is evaluated by using real-life data and a simulation study is carried out to get an overview of efficiency. The relative efficiency of the proposed estimator is compared with some existing estimators. It has been found that the proposed estimator is highly efficient as compared with Mohanty's regression cum ratio estimator in simple random sampling and is more reliable in the case of non-response with a small sample size.

This paper studies an attribute control chart for monitoring the number of nonconforming items using a triple sampling (TS-np) which has not yet been applied to attribute control charts. The chart design and procedure for the decision about the state of the process are given. Mathematical expressions for the average run length (ARL) for in-control and out-of-control processes and the average sample number (ASN) are given. A bi-objective genetic algorithm that seeks to minimize the ASN and the probability of type 2 error is implemented in order to optimize the design of the TS-np control chart. A comparison between TS-np, single sampling np (SS-np), double sampling np (DS-np), and multiple dependent state repetitive sampling (MDSRS) control charts is carried out in terms of the out-of-control average run length ( A R L 1 ). Tables of A R L 1 values for TS-np are presented in comparison with MDSRS and DS-np for various scenarios. The operation of the proposed control chart is shown through simulated data. Finally, it is concluded that the proposed TS-np chart has a better performance in terms of A R L 1 detecting small and moderate shifts in the process nonconforming rate in-control ( p 0 ) compared with MDSRS and DS-np. [ABSTRACT FROM AUTHOR]

Abstract Background A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. Methods The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula. Results Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas. Conclusions A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1 n $\frac {1}{n}$ where n is the number of sample points.

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]

Understanding the impact of management interventions on the environment over decadal and longer timeframes is urgently required. Longitudinal or large-scale studies with consistent methods are best practice, but more commonly, small datasets with differing methods are used to achieve larger coverage. Changes in methods and interpretation affect our ability to understand data trends through time or across space, so an ability to understand and adjust for such discrepancies between datasets is important for applied ecologists. Calibration or double sampling is the key to unlocking the value from disparate datasets, allowing us to account for the differences between datasets while acknowledging the uncertainties. We use a case study of livestock grazing impacts on riparian vegetation in southeastern Australia to develop a flexible and powerful approach to this problem. Using double sampling, we estimated changes in vegetation attributes over a 12-year period using a pseudo-quantitative visual method as the starting point, and the same technique plus point-intercept survey for the second round. The disparate nature of the datasets produced uncertain estimates of change over time, but accounting for this uncertainty explicitly is precisely the objective and highlights the need to look more closely at this very common problem in environmental management, as well as the potential benefits of the double sampling approach. [ABSTRACT FROM AUTHOR]

Abstract Background The double sampling method known as “big BAF sampling” has been advocated as a way to reduce sampling effort while still maintaining a reasonably precise estimate of volume. A well-known method for variance determination, Bruce’s method, is customarily used because the volume estimator takes the form of a product of random variables. However, the genesis of Bruce’s method is not known to most foresters who use the method in practice. Methods We establish that the Taylor series approximation known as the Delta method provides a plausible explanation for the origins of Bruce’s method. Simulations were conducted on two different tree populations to ascertain the similarities of the Delta method to the exact variance of a product. Additionally, two alternative estimators for the variance of individual tree volume-basal area ratios, which are part of the estimation process, were compared within the overall variance estimation procedure. Results The simulation results demonstrate that Bruce’s method provides a robust method for estimating the variance of inventories conducted with the big BAF method. The simulations also demonstrate that the variance of the mean volume-basal area ratios can be computed using either the usual sample variance of the mean or the ratio variance estimators with equal accuracy, which had not been shown previously for Big BAF sampling. Conclusions A plausible explanation for the origins of Bruce’s method has been set forth both historically and mathematically in the Delta Method. In most settings, there is evidently no practical difference between applying the exact variance of a product or the Delta method—either can be used. A caution is articulated concerning the aggregation of tree-wise attributes into point-wise summaries in order to test the correlation between the two as a possible indicator of the need for further covariance augmentation.

In sequential tests, typically a (pairwise) multiple comparison procedure (MCP) is performed after an omnibus test (an overall equality test). In general, when an omnibus test (e.g., overall equality of multiple proportions test) is rejected, then we further conduct a (pairwise) multiple comparisons or MCPs to determine which (e.g., proportions) pairs the significant differences came from. In this article, via likelihood-based approaches, we acquire three confidence intervals (CIs) for comparing each pairwise proportion difference in the presence of over-reported binomial data. Our closed-form algorithm is easy to implement. As a result, for multiple-sample proportions differences, we can easily apply MCP adjustment methods (e.g., Bonferroni, Šidák, and Dunn) to address the multiplicity issue, unlike previous literatures. We illustrate our procedures to a real data example.

Non-linear programming problems can be solved efficiently by geometric programming in which non-linear expressions can be expressed by an exponential or power functions. In this paper, Double Sampling Stratification (DSS) strategy is used in multivariate stratified population with unidentified strata weights, for optimum sampling design (OSD) in the presence of non-response to estimate the unidentified population means. The double sampling problem in the presence of non-response is formulated as Fuzzy Multiobjective Convex Programming Problem (FMOCPP). Then, we convert FMOCPP into Fuzzy Single Objective Convex Problem (FSOCP) by using membership function. Dual solution is obtained using LINGO Software by solving FSOCP. The optimum allocations of sample sizes of respondents and non- respondents for both the phases are obtained by applying dual solutions and primal-dual relationship theorem. The given technique is illustrated by projecting a numerical problem.

This paper studies an attribute control chart for monitoring the number of nonconforming items using a triple sampling (TS-np) which has not yet been applied to attribute control charts. The chart design and procedure for the decision about the state of the process are given. Mathematical expressions for the average run length (ARL) for in-control and out-of-control processes and the average sample number (ASN) are given. A bi-objective genetic algorithm that seeks to minimize the ASN and the probability of type 2 error is implemented in order to optimize the design of the TS-np control chart. A comparison between TS-np, single sampling np (SS-np), double sampling np (DS-np), and multiple dependent state repetitive sampling (MDSRS) control charts is carried out in terms of the out-of-control average run length (ARL1). Tables of ARL1 values for TS-np are presented in comparison with MDSRS and DS-np for various scenarios. The operation of the proposed control chart is shown through simulated data. Finally, it is concluded that the proposed TS-np chart has a better performance in terms of ARL1 detecting small and moderate shifts in the process nonconforming rate in-control (p0) compared with MDSRS and DS-np.

Ratio estimators have been used in survey sampling for estimating population mean when the population mean of an auxiliary variable is known. However, as the auxiliary information is not always available we cannot gain any benefit from using ratio estimators to increase the efficiency of the population mean estimator. New ratio estimators for population mean obtained using the quartile function of an auxiliary variable using double sampling have been proposed based upon the modified ratio estimators proposed by Subramani and Kumarapandiyan (2012). We propose the use of double sampling in order to estimate the unknown quartile function of an auxiliary variable. A simulation study has been conducted to compare these new ratio estimators with the classical ratio estimator using a percent relative efficiency using double sampling. The results show that the proposed estimators perform better than the classical ratio estimator using double sampling.

This paper proposes an exponential estimator of a population mean under double sampling using one auxiliary variable. The proposed estimator is modified from the estimator of Khatua and Misha (2013) and Ozgul and Cingi (2014). The bias and mean square error of the proposed estimator are derived under the second order of approximation. The efficiency of the proposed estimator is compared with the existing estimators based on mean square error. The results indicate that the proposed estimator is more efficient than others under empirical study with real datasets.

Background: A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. Methods: The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce's formula. Results: Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas. Conclusions: A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1 n where n is the number of sample points. [ABSTRACT FROM AUTHOR]

Milk production is an important aspect of the dairy animals. The present study was conducted to estimate the effect of different diseases on per day milk yield in the buffaloes. Data from a sample of 1,214 livestock owners in two divisions of Uttar Pradesh namely Agra and Aligarh were collected. The value of reduction in per day milk yield due to different diseases under two different situations, viz. when strata weights were known and when strata weights were not known was estimated. The estimated value of reduction in milk yield under the situation when strata weights were known was 4.28 kg with variance 0.014 kg2. Mastitis is a disease which has a large impact on milk yield in buffaloes. But under the situation when strata weights were unknown and were estimated by double sampling, post stratification and published sources, the estimated value of average reduction in per day milk yield due to different diseases were 4.33 kg, 4.33 kg and 4.35 kg with variance 0.015 kg2, 0.017 kg2 and 0.012 kg2 respectively. In buffaloes, the best estimated value of average reduction in milk was provided by double sampling estimator.

In this study, an economic-statistical design of the double sampling (DS) s chart is investigated. The optimal design parameters of the DS s chart are obtained by minimizing the cost subject to statistical constraints. The effectiveness of the DS s chart is evaluated by comparing its minimized cost against the cost of the Shewhart s chart. The comparison demonstrates the superiority of the DS s chart over the Shewhart s chart, where the DS s chart is economically superior to the Shewhart s chart. Sensitivity analyses are performed to investigate the effect of the cost parameters, process parameters and statistical properties on the design parameters, as well as the corresponding in-control average time to signal, out-of-control average time to signal and cost.

Background: The double sampling method known as "big BAF sampling" has been advocated as a way to reduce sampling effort while still maintaining a reasonably precise estimate of volume. A well-known method for variance determination, Bruce's method, is customarily used because the volume estimator takes the form of a product of random variables. However, the genesis of Bruce's method is not known to most foresters who use the method in practice. Methods: We establish that the Taylor series approximation known as the Delta method provides a plausible explanation for the origins of Bruce's method. Simulations were conducted on two different tree populations to ascertain the similarities of the Delta method to the exact variance of a product. Additionally, two alternative estimators for the variance of individual tree volume-basal area ratios, which are part of the estimation process, were compared within the overall variance estimation procedure. Results: The simulation results demonstrate that Bruce's method provides a robust method for estimating the variance of inventories conducted with the big BAF method. The simulations also demonstrate that the variance of the mean volume-basal area ratios can be computed using either the usual sample variance of the mean or the ratio variance estimators with equal accuracy, which had not been shown previously for Big BAF sampling. Conclusions: A plausible explanation for the origins of Bruce's method has been set forth both historically and mathematically in the Delta Method. In most settings, there is evidently no practical difference between applying the exact variance of a product or the Delta method—either can be used. A caution is articulated concerning the aggregation of tree-wise attributes into point-wise summaries in order to test the correlation between the two as a possible indicator of the need for further covariance augmentation. [ABSTRACT FROM AUTHOR]

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Publications in peer-reviewed journals are often looked upon as tenets on which future scientific thought is built. Published information is not always flawless and errors in published research should be expediently reported, preferably by a peer-review process. We review a recent publication by Gopalaswamy et al. (10.1111/2041-210X.12351) that challenges the use of “double sampling” in large-scale animal surveys. Double sampling is often resorted to as an established economical and practical approach for large-scale surveys since it calibrates abundance indices against absolute abundance, thereby potentially addressing the statistical shortfalls of indices. Empirical data used by Gopalaswamy et al. (10.1111/2041-210X.12351) to test their theoretical model, relate to tiger sign and tiger abundance referred to as an Index-Calibration experiment (IC-Karanth). These data on tiger abundance and signs should be paired in time and space to qualify as a calibration experiment for double sampling, but original data of IC-Karanth show lags of (up to) several years. Further, data points used in the paper do not match the original sources. We show that by use of inappropriate and incorrect data collected through a faulty experimental design, poor parameterization of their theoretical model, and selectively picked estimates from literature on detection probability, the inferences of this paper are highly questionable. We highlight how the results of Gopalaswamy et al. were further distorted in popular media. If left unaddressed, the paper of Gopalaswamy et al. could have serious implications on statistical design of large-scale animal surveys by propagating unreliable inferences.

Publications in peer-reviewed journals are often looked upon as tenets on which future scientific thought is built. Published information is not always flawless and errors in published research should be expediently reported, preferably by a peer-review process. We review a recent publication by Gopalaswamy et al. (10.1111/2041-210X.12351) that challenges the use of "double sampling" in largescale animal surveys. Double sampling is often resorted to as an established economical and practical approach for large-scale surveys since it calibrates abundance indices against absolute abundance, thereby potentially addressing the statistical shortfalls of indices. Empirical data used by Gopalaswamy et al. (10.1111/2041-210X.12351) to test their theoretical model, relate to tiger sign and tiger abundance referred to as an Index-Calibration experiment (IC-Karanth). These data on tiger abundance and signs should be paired in time and space to qualify as a calibration experiment for double sampling, but original data of IC-Karanth show lags of (up to) several years. Further, data points used in the paper do not match the original sources. We show that by use of inappropriate and incorrect data collected through a faulty experimental design, poor parameterization of their theoretical model, and selectively picked estimates from literature on detection probability, the inferences of this paper are highly questionable. We highlight how the results of Gopalaswamy et al. were further distorted in popular media. If left unaddressed, the paper of Gopalaswamy et al. could have serious implications on statistical design of large-scale animal surveys by propagating unreliable inferences. [ABSTRACT FROM AUTHOR]

Ratio estimators have been used in survey sampling for estimating population mean when the population mean of an auxiliary variable is known. However, as the auxiliary information is not always available we cannot gain any benefit from using ratio estimators to increase the efficiency of the population mean estimator. New ratio estimators for population mean obtained using the quartile function of auxiliary variable( s) using double sampling have been proposed based upon the modified ratio estimators proposed by Subramani and Kumarapandiyan (2012). We propose the use of double sampling in order to estimate an unknown quartile function of an auxiliary variable( s) . A simulation study has been conducted to compare these new ratio estimators with the classical ratio estimator using a percent relative efficiency using double sampling. The results show that the proposed estimators perform better than the classical ratio estimator using double sampling. [ABSTRACT FROM AUTHOR]

This paper proposes an exponential estimator of a population mean under double sampling using one auxiliary variable. The proposed estimator is modified from the estimator of Khatua and Misha (2013) and Ozgul and Cingi (2014). The bias and mean square error of the proposed estimator are derived under the second order of approximation. The efficiency of the proposed estimator is compared with the existing estimators based on mean square error. The results indicate that the proposed estimator is more efficient than others under empirical study with real datasets. [ABSTRACT FROM AUTHOR]

Since the run length distribution is generally highly skewed, a significant concern about focusing too much on the average run length (ARL) criterion is that we may miss some crucial information about a control chart’s performance. Thus it is important to investigate the entire run length distribution of a control chart for an in-depth understanding before implementing the chart in process monitoring. In this paper, the percentiles of the run length distribution for the double sampling (DS) X chart with estimated process parameters are computed. Knowledge of the percentiles of the run length distribution provides a more comprehensive understanding of the expected behaviour of the run length. This additional information includes the early false alarm, the skewness of the run length distribution, and the median run length (MRL). A comparison of the run length distribution between the optimal ARL-based and MRL-based DS X chart with estimated process parameters is presented in this paper. Examples of applications are given to aid practitioners to select the best design scheme of the DS X chart with estimated process parameters, based on their specific purpose.

A CMOS (Complementary metal-oxide-semiconductor) Hall sensor with low power consumption and simple structure is introduced. The tiny magnetic signal from Hall device could be detected by a high-resolution delta-sigma ADC in presence of offset and flickering noise. Also, the offset as well as the flickering noise are effectively suppressed by the current spinning technique combined with double sampling switches of the ADC. The double sampling scheme of the ADC reduces the operating frequency and helps to reduce the power consumption. The prototype Hall sensor is fabricated in a 0.18-µm CMOS process, and the measurement shows detection range of ±150 mT and sensitivity of 110 µV/mT. The size of active area is 0.7 mm2, and the total power consumption is 4.9 mW. The proposed system is advantageous not only for low power consumption, but also for small sensor size due to its simplicity.

Dash and Mishra [1] suggested an improved class of estimators without defining the optimum estimator. However, they gave the wrong Taylor’s series expression of their class of estimator and their minimum mean squared error expressions are also incorrect. Here we show that Ahmed et al.’s [2] class of chain estimators is more efficient than Dash and Mishra’s [1], with minimum mean squared error.

Values that are too large or small enough can be found in many data sets. Therefore, the estimator can yield ambiguous findings if several of the incredible deals are picked for the sample. When such extreme values occur, we propose improved estimators to determine the finite population means using double sampling based on probability proportional to size sampling (PPS). The properties of estimators are obtained up to the first order of approximations. When the size of the units varies widely, the PPS sampling technique may be employed. To determine the values of Pi when using PPS, we must be acquainted with the aggregate of the auxiliary variable X i . However the designs and estimation techniques we have looked at so far are unsuccessful and are less effective when this information is difficult to locate or when other information is missing. The two-phase approach is preferable and more feasible in these kinds of circumstances. To demonstrate how effectively the recommended estimators performed, we used three actual data sets. We show mathematically and theoretically that the suggested estimators outperform alternative estimators., Competing Interests: The authors declare that they have no known cometing finincial intersts or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Author(s).)

The implementation of an adaptive cluster sampling design often becomes logistically challenging because variation in the final sampling effort introduces uncertainty in survey planning. To overcome this drawback, an inexpensive and easy to measure auxiliary variable could be used in a two-phase survey strategy, called adaptive cluster double sampling (Félix-Medina and Thompson in Biometrika 91:877-891, 2004). In this paper, a two-phase sampling strategy is proposed which combines the idea of adaptive cluster double sampling with the principle of post-stratification. In the first-phase an adaptive cluster sample is selected by means of an inexpensive auxiliary variable. Networks from the first phase sampling are then post-stratified according to their size. In the second-phase, the network structure is used to select a subsample of units by means of stratified random sampling. The proposed sampling strategy employs stratificationwithout requiring an a priori delineation of the strata. Indeed, the strata sizes are estimated in the course of the two-phase sampling process. Therefore, it is suitable for situations where stratification is suspected to be efficient but strata cannot be easily delineated in advance. In this framework, a new type of estimator for the population mean which mimics the stratified sampling mean estimator and an estimator of the sampling variance are proposed. The results of a simulation study confirm, as expected, that the use of post-stratification leads to gain in precision for the estimator. The proposed sampling strategy is applied for targeting an epiphytic lichen community Lobarion pulmonariae in a forest area of the Northern Apennines (N-Italy), characterized by several species of conservation concern. [ABSTRACT FROM AUTHOR]

This article deals with the problems of efficient estimation of population variance in two-phase (double) sampling. Using information on two auxiliary variables, a class of chain exponential to regression type estimators has been proposed and its properties are studied under two different structures of two-phase sampling. Superiority of suggested class of estimators over some existing ones is established through numerical illustrations. Suitable recommendations to the survey statistician are also made.

The double sampling (DS) X bar chart, one of the most widely-used charting methods, is superior for detecting small and moderate shifts in the process mean. In a right skewed run length distribution, the median run length (MRL) provides a more credible representation of the central tendency than the average run length (ARL), as the mean is greater than the median. In this paper, therefore, MRL is used as the performance criterion instead of the traditional ARL. Generally, the performance of the DS X bar chart is investigated under the assumption of known process parameters. In practice, these parameters are usually estimated from an in-control reference Phase-I dataset. Since the performance of the DS X bar chart is significantly affected by estimation errors, we study the effects of parameter estimation on the MRL-based DS X bar chart when the in-control average sample size is minimised. This study reveals that more than 80 samples are required for the MRL-based DS X bar chart with estimated parameters to perform more favourably than the corresponding chart with known parameters.

Standard Shewhart process control chart has been widely used, but it is not sensitive in detecting small shift. A number of alternatives have been proposed to improve the capability of control chart. The double sampling (DS) control chart is aimed at improving the capability to detect any small shift out-of control condition by observing the second sample without interruption. The capabilities of DS control chart were measured as the expected sample size (as a measure of inspection cost) or the control chart power (as a measure for customer risk). Optimization of these criteria is used to determine the control limits. In this paper, we optimize both producer and customer risks under a certain expected number of sample sizes as the constraint. Comparing the result to the previous procedure that only optimize customer risk, the proposed optimization procedure gives the same first control limit but smaller second control limits with higher value of control chart power.

A class of estimator based on dual to ratio and dual to product-type estimator in double sampling for estimating finite population mean is proposed. The bias and mean square error of the proposed estimator are obtained in two different cases. A comparative study has been made with usual estimators, dual to ratio estimator, dual to product type estimator in double sampling in two different cases. The proposed estimator is found to be an improvement over the other estimators as special cases.

BACKGROUND: Meta-research can involve manual retrieval and evaluation of research, which is resource intensive. Creation of high throughput methods (e.g., search heuristics, crowdsourcing) has improved feasibility of large meta-research questions, but possibly at the cost of accuracy. OBJECTIVE: To evaluate the use of double sampling combined with multiple imputation (DS+MI) to address meta-research questions, using as an example adherence of PubMed entries to two simple Consolidated Standards of Reporting Trials (CONSORT) guidelines for titles and abstracts. METHODS: For the DS large sample, we retrieved all PubMed entries satisfying the filters: RCT; human; abstract available; and English language (n=322,107). For the DS subsample, we randomly sampled 500 entries from the large sample. The large sample was evaluated with a lower rigor, higher throughput (RLOTHI) method using search heuristics, while the subsample was evaluated using a higher rigor, lower throughput (RHITLO) human rating method. Multiple imputation of the missing-completely-at-random RHITLO data for the large sample was informed by: RHITLO data from the subsample; RLOTHI data from the large sample; whether a study was an RCT; and country and year of publication. RESULTS: The RHITLO and RLOTHI methods in the subsample largely agreed (phi coefficients: title=1.00, abstract=0.92). Compliance with abstract and title criteria has increased over time, with non-US countries improving more rapidly. DS+MI logistic regression estimates were more precise than subsample estimates (e.g., 95% CI for change in title and abstract compliance by Year: subsample RHITLO 1.050-1.174 vs. DS+MI 1.082-1.151). As evidence of improved accuracy, DS+MI coefficient estimates were closer to RHITLO than the large sample RLOTHI. CONCLUSIONS: Our results support our hypothesis that DS+MI would result in improved precision and accuracy. This method is flexible and may provide a practical way to examine large corpora of literature.