Panel-corrected

standard errors performed excellently in these experiments.

Thus, it is easier for a survey user to multiply the

standard error computed from the data collected in a particular sampling method by the design factor to make it suitable for statistical analysis.

Approximate

standard errors and normal-based confidence intervals for [alpha] and [beta] are obtained from the observed inverse information matrix and are based on asymptotic properties of MLE's (Cox 1970).

In these situations, modeling of the dependent variable must account for the nested data structure in order to ensure that

standard errors and model parameters are accurately estimated (Snijders & Bosker, 2012).

Moreover, MI provides more valid estimations, such as

standard error, regression coefficient, and average, compared to other value imputation methods (Twisk and de Vente 2002; Fichman and Cummings 2003).

Dowd, Greene, and Norton (2014) opine that inclusion of B in equation (6) "seems incorrect to us" and exclude it from the suggested formulation of the asymptotic

standard error of [??] given in their equation (18).

Table 3 shows the resulting estimates of [[beta].sub.1] for the treatment condition in the linear model (3) and the corresponding asymptotic

standard errors and p-values using the different models.

The

standard error statistic is a measurement of sampling error.

The missing data simulation, multiple imputation with the RF method, pooling of the disability estimates and their

standard errors, and scatter plots were performed using functions written in the R software package version 2.13.0 (The R Foundation for Statistical Computing).

The instrument that is omitted from the IV combination is utilized as an explanatory variable and its coefficient and

standard error is reported.

In this study we estimate

standard errors of month on month (MoM) and YoY inflation in Pakistan using the stochastic approach, following Selvanathan and Selvanathan (2006).

Appendix A--Technical Notes and Glossary provides more information about the statistical tests used, and Appendix B--Standard Error Tables provides the

standard errors of the table estimates.