Search

Bootstrap is a widely applicable computational statistical method. The focus of this paper lies in developing a bootstrap method for linear mixed models under homoscedasticity violation (heteroscedasticity) in variance of errors. We assume that the form of heteroscedasticity is unknown. To generate bootstrap response data as close as possible to the actual response data, we transform the marginal residuals to ensure that the variance of the modified marginal residuals in bootstrap samples is an unbiased estimator for the variance of the response variable in the linear mixed models. The consistency is proved, implying that the parameter estimators by the proposed method are asymptotically unbiased. The simulations are conducted with varying error terms and sample sizes to show improvement of the proposed method in parameter estimation. The simulation results are compared to demonstrate that the proposed method outperforms the other considered approaches including the wild method in the heteroscedastic linear mixed models under small samples and performs competitively with the parametric method and both methods outperform the other considered methods in homoscedastic linear mixed models. The proposed bootstrap method is applied to squid data for illustration of its effectiveness. [ABSTRACT FROM AUTHOR]

Non-response situations are inevitable in sample survey work, and this is also true in dual sampling frame. In view of this, this study proposes alternative imputation techniques to solve the problem of missing data and further suggests an estimate of the population total in dual sampling frame. The properties of the suggested estimator are analyzed, and its empirical results are compared to the entire response situation. Based on the results obtained, appropriate suggestions have been proposed to survey practitioners and researchers for their practical applications. [ABSTRACT FROM AUTHOR]

In order to improve the efficiency of the mean square error control chart in detecting small to moderate shifts, an improved variable parameter mean square error (VPt MSE) control chart is proposed, which uses three different sampling intervals, two different sample sizes and two different control limits. Markov chain method is used to calculate the average time to signal and average number of observations to signal. The performance of the adaptive chart was compared with the variable sample size and sampling interval (VSSI), the improved variable sample size and sampling interval (VSSIt), the variable parameter (VP), the exponentially weighted moving average (EWMA), and the variable sampling interval exponentially weighted moving average (VSI EWMA) mean square error control chart. Numerical results show that the VPt MSE chart surpasses the other charts in detecting small to moderate shifts. At the same time, we also improve the VPt MSE chart, which greatly improves the statistical performance. An example is provided to illustrate the implementation of the VPt MSE chart. [ABSTRACT FROM AUTHOR]

In recent years, the impact of measurement errors on the performance of various control charts have been well evaluated. However, as far as we know, the multiple sampling control charts in the literature have been proposed based on the assumption that the measurements are precise. In this paper, we investigate the effect of measurement errors with both constant and linearly increasing variance on the performance of double sampling (DS)- X ¯ chart. We study the capability of multiple measurements procedure to reduce the undesired effect of imprecise measurements on detection capability of DS- X ¯ chart. Using simulation experiments, we compare the performance of DS- X ¯ and classical X ¯ charts in terms of average run length (ARL) and standard deviation of run length (SDRL) metrics. The results show that the measurement errors negatively affect the performance of both DS- X ¯ and classical X ¯ charts. The comparison results also confirm that under measurement errors, the DS- X ¯ control chart outperforms the classical X ¯ chart in all out-of-control scenarios. Moreover, the results indicate that taking several measurements on each item can effectively reduce the undesired impact of error on chart's performance. Finally, the undesired impact of measurement errors on detection capability of DS- X ¯ control chart is illustrated using a real-life example. [ABSTRACT FROM AUTHOR]

The ratio, product, difference estimators, and unbiased estimator under systematic sampling scheme has been studied in the presence of measurement error. The methods of estimation have been proposed for the estimation of the finite population mean. To exhibit the effect of measurement error, the study variable and auxiliary variable are supposed to be observed with measurement error. The properties of estimators' viz. bias and MSE have been obtained. The simulation study has been conducted to compute the effect of measurement error on the MSE for the different levels of correlation coefficient and different levels of error variance. [ABSTRACT FROM AUTHOR]

The present investigation deals with the estimation of population variance in successive sampling in presence and absence of measurement error. We have suggested a chain type estimator of population variance and compared its performances with natural sample variance estimator in presence and absence of measurement errors. The dominance of the proposed strategies over conventional ones has been demonstrated through numerical investigation carried over the dataset of natural and artificially generated population. Suitable recommendations have been made for the application of proposed strategy in real life. [ABSTRACT FROM AUTHOR]