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This article suggests an improved class of efficient estimators that use various transformations to estimate the finite population variance of the study variable. These estimators are particularly helpful in situations where we know about the minimum and maximum values of the auxiliary variable, and the ranks of the auxiliary variable are associated with the study variable. Consequently, these rankings can be applied as an effective tool to improve the accuracy of the estimator. A first-order approximation is used to investigate the properties of the proposed class of estimators, such as bias and mean squared error ( M S E ) under simple random sampling. A simulation study carried out in order to measure the performance and verify the theoretical results. The suggested class of estimators has a greater percent relative efficiency ( P R E ) than the other existing estimators in all of the simulated situations, according to the results. Three symmetric and asymmetric datasets are examined in the application section in order to show the superior performance of the proposed class of estimators over the existing estimators. [ABSTRACT FROM AUTHOR]

Saturated orthogonal array is an important type of fractional factorial designs in experimental design. On the basis of guaranteeing orthogonality, it maximizes the number of factors and saves the cost of experiments. Therefore, it is increasingly used in practical experiment. For quantitative factors, the minimum β-aberration criterion is suitable for selecting good designs under a polynomial model. However, construction methods of designs with less β-aberration have not been fully investigated. In this article, we apply the Rao-Hamming method to construct a class of three-level saturated orthogonal arrays, and perform a special level permutation on the designs of the Rao-Hamming construction, which makes the resultant designs mirror-symmetric ones. Furthermore, we analyze the distribution of elements in each row and among all possible pairs of rows of the mirror-symmetric designs, and discuss some properties of the β-wordlength pattern for three-level mirror-symmetric designs constructed by the Rao-Hamming method. In addition, we provide the explicit expressions of β3 and β4 for three-level mirror-symmetric designs, which can reduce the computational complexity of the β-wordlength pattern, and provide an effective idea for finding designs under the minimum β-aberration criterion. Finally, numerical examples are used to illustrate and verify the results. [ABSTRACT FROM AUTHOR]

This article presents an improved class of efficient estimators aimed at estimating the finite population variance of the study variable. These estimators are especially useful when we have information about the minimum/maximum values of the auxiliary variable within a framework of simple random sampling. The characteristics of the proposed class of estimators, including bias and mean squared error ( M S E ) under simple random sampling are derived through a first-order approximation. To assess the performance and validate the theoretical outcomes, we conduct a simulation study. Results indicate that the proposed class of estimators has lower M S E s as compared to other existing estimators across all simulation scenarios. Three datasets are used in the application section to emphasize the effectiveness of the proposed class of estimators over conventional unbiased variance estimators, ratio and regression estimators, and other existing estimators. [ABSTRACT FROM AUTHOR]

Supersaturated design is an important class of fractional factorial designs in which the number of experimental runs is not enough to estimate all the main effects. These designs are widely used in screening experiments, where the primary goal is to find important active factors at a low cost. The minimum β-aberration criterion is an appropriate criterion for measuring designs with quantitative factors. In this article, we first establish the explicit expression of β2 for three-level designs based on the relationship between the wordlength enumerator and the β-wordlength pattern. It can reduce the computational complexity of the β-wordlength pattern, and help provide an effective way for finding designs under the minimum β-aberration criterion. Moreover, a sharper lower bound of β2 is obtained, which can be considered as a benchmark for constructing optimal supersaturated designs. We further provide a simulated annealing algorithm to construct three-level supersaturated uniform designs with less β2. Finally, numerical results verify that our lower bound is sharper than the existing lower bound. [ABSTRACT FROM AUTHOR]