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A Difference-Cum-Exponential Type Efficient Estimator of Population Mean
Published in Rakhee Kulshrestha, Chandra Shekhar, Madhu Jain, Srinivas R. Chakravarthy, Mathematical Modeling and Computation of Real-Time Problems, 2021
Kuldeep Kumar Tiwari, Sandeep Bhougal, Sunil Kumar
Precision is the reason for most of the research work in statistical theory and computation. Auxiliary information usually enhances the precision in survey sampling. It can be used at the selection stage or in estimation or on both. In the literature, auxiliary information is used by authors to construct various efficient estimators of different population parameters. The ratio estimator works better when there is a positive correlation between study and auxiliary variables, while the product estimator performs well in case of the negative correlation. Generally, a linear regression estimator is better than both ratio and product estimators. The equality in the efficiencies is obtained if the intercept of the regression line of y on x is zero. Since the regression estimator either performs better or equal to ratio and product estimators, it is convenient to use linear regression estimator than classical ratio and product estimator to gain in the efficiency. Many authors, such as [1–16], etc., worked on ratio and product type estimator to get the better results of such type estimator. Further, to get a better result, researchers worked on difference and exponential type estimators and showed its usefulness. Some of them are [17–20], etc.
Innovations in Computer-Based Ability Testing
Published in Milton D. Hakel, Beyond Multiple Choice, 2013
The other alternative is to draw a representative sample, test the sample members, and estimate the population norms using the techniques of survey sampling statistics. This approach is taken in the 1997 Profile: A multistage area probability sample of households will be drawn; the households will be canvassed to enumerate and list military-eligible youths living in them; and these youths will be enticed to take the ASVAB tests. To accomplish this, the Department of Defense is working with the U.S. Bureau of Labor Statistics (BLS). BLS periodically conducts national longitudinal surveys to study various aspects of the U.S. labor market. BLS planned a national longitudinal survey of youth to begin in 1997; the Department of Defense will underwrite some of the costs of the survey in exchange for an opportunity to administer its ASVAB tests to many military-eligible members of the survey sample households. BLS is happy to cooperate, because it wanted to measure intellectual abilities in its sample; the ASVAB will serve this purpose well.
Conditioned Latin hypercube sampling
Published in Mark Stamp, Introduction to Machine Learning with Applications in Information Security, 2023
In a full factorial design, all combinations of factor levels are observed. With k factors and l levels per factor, the total number of observations is lk. With numerous factors and/or numerous levels per factor, observing lk experimental units becomes unfeasible in practice. Alternative experimental designs have been developed that need fewer observations but still provide detailed information about how the study variable responds to changes in the factor levels. This chapter will describe and illustrate the survey sampling analogue of Latin hypercube sampling. Response surface sampling follows in the next chapter.
A re-evaluation of repetitive sampling techniques in statistical process monitoring
Published in Quality Technology & Quantitative Management, 2023
Nesma A. Saleh, Mahmoud A. Mahmoud, William H. Woodall
Lee et al. (2015) assessed the use of repetitive sampling with an auxiliary information-based (AIB) Shewhart chart for monitoring the process mean. Saghir et al. (2019) extended the Lee et al. (2015) study with an AIB-EWMA chart. Auxiliary variables are defined as variables that are correlated with the variable of interest. In the survey sampling literature, auxiliary information is known to increase the efficiency in estimating the unknown population parameters. An AIB chart involves the use of an AIB estimator in place of the conventional sample statistic when computing the chart statistic to monitor the process parameter(s). Saleh et al. (2022) provided an extensive review and a critique of the integration of AIB estimators in control charting techniques and highlighted the fact that these methods are highly non-robust to violations of the unrealistic assumption that the distribution of the auxiliary variable must remain stable (unchangeable) during the monitoring process.
A review and critique of auxiliary information-based process monitoring methods
Published in Quality Technology & Quantitative Management, 2023
Nesma A. Saleh, Mahmoud A. Mahmoud, William H. Woodall, Sven Knoth
M. Riaz (2008a, 2008b) proposed the use of some auxiliary information to enhance the precision of the estimator used in monitoring the parameters of the QCs of interest. In the survey sampling literature, auxiliary information is useful when estimating unknown population parameters. It has been shown that auxiliary information increases the precision/efficiency of estimators when sampling from a fixed sampling frame (Cochran, 1977; Naik & Gupta, 1991; R. Singh & Mangat, 1996). Auxiliary variables are correlated to the variable of interest. The auxiliary variable is typically easy and inexpensive to measure compared to the variable of interest and its values are available for all members in the population. A rapidly growing number of researchers have proposed integrating the sampling theory auxiliary information-based (AIB) estimators into control charts. We review these studies in Section 3.
A critique of a variety of “memory-based” process monitoring methods
Published in Journal of Quality Technology, 2023
Sven Knoth, Nesma A. Saleh, Mahmoud A. Mahmoud, William H. Woodall, Víctor G. Tercero-Gómez
Perez Abreu and Schaffer (2017) used a DEWMA chart to monitor linear drifts/shifts in the quality characteristic of interest. Asif, Khan, and Noor-Ul Amin (2020) incorporated measurement error into the model used with the chart, while Noor et al. (2020) took a Bayesian “approach.” Noor-Ul Amin, Khan, and Sanaullah (2019), Raza et al. (2019), Tariq et al. (2020), and Haq, Ejaz, et al. (2021) incorporated auxiliary information into the DEWMA chart; with Raza et al. (2019) considering two auxiliary variables. Auxiliary variables are those that are highly correlated with the variable of interest. It is assumed that the parameters of the distribution of the auxiliary variables are both known and cannot change over time. In survey sampling literature, such variables are used to increase the efficiency of the estimators of the population parameters. The required assumptions are unlikely to hold in process monitoring applications, as discussed by Saleh et al. (2021).