No abstract

The confidence interval is an important statistical estimator of population location and dispersion parameters. The paper considers a robust modified confidence interval, which is an adjustment of the Student’s t confidence interval based on the decile mean and decile standard deviation for estimating the population mean of a skewed distribution. The efficiency of the proposed interval estimator is evaluated on the basis of an extensive Monte Carlo simulation study. The coverage ratio and average width of the proposed confidence interval are compared with certain existing and widely used confidence intervals. The simulation results show that, in general, the proposed interval estimator’s performance is highly effective. For illustrative purposes, three real-life data sets are analyzed, which, to a certain extent, support the findings obtained from the simulation study. Thus, we recommend that practitioners use the robust modified confidence interval for estimating the population mean when the data are generated by a normal or skewed distribution.

Abstract. The objective of this research was to propose a composite correlation coefficient to estimate the rank correlation coefficient of two variables. A simulation study was conducted using 228 situations for a bivariate normal distribution to compare the robustness properties of the proposed rank correlation coefficient with three estimators, namely, Spearman's rho, Kendall's tau and Plantagenet's correlation coefficients when the data were contaminated with outliers. In both cases of non-outliers and outliers in the data, it was found that the composite correlation coefficient seemed to be the most robust estimator for all sample sizes, whatever the level of the correlation coefficient.

Confidence intervals are important statistical methods used to estimate the location and dispersion parameters of the population. A new robust interval estimator, which is an adjustment of the Student-t confidence interval for estimating population mean based on the decile mean and standard deviation is consider in this research. The efficiency of this proposed interval estimator is evaluated using an extensive Monte-Carlo simulation study. The coverage probabilities and average widths of the proposed interval estimator are compared with some existing widely used interval estimators under normal and contaminated normal distributions. The simulation results show that the proposed interval estimator performs very well in terms of attaining high coverage probability and shorter average width. For illustration purposes, real-life data sets are analyzed which supported the findings obtained from the simulation study to some extent. In summary, our results confirmed that the type of estimator used to construct the confidence interval affects the performance of the interval estimator, and the proposed version of the interval estimator performs better than the other estimators evaluated herein. Consequently, we recommend the new robust confidence interval for the practitioners to be used for estimating of the population mean when the contamination in the data of the distribution is present. The proposed confidence interval of the population mean can be easily calculated by using R program which is providing in this appendix.Mathematics Subject Classification 62F10; 62F35.

In this research, the authors were interested in an efficiency comparison study of new adjusted nonparametric and parametric statistics interval estimation methods in the simple linear regression model. The independent variable and the error came from normal, scale-contaminated normal, and gamma distributions. Six point estimations were performed, for example, least squares, Bayesian, Jack knife, Theil, optimum-type Theil, and new adjusted Theil–Sen and Siegel methods in the simple linear regression model with 1,000 iterations. The criteria used to consider in this study were the coefficient of the confidence interval and the average width of the confidence interval used to compare and determine the optimal effectiveness for six interval estimations of the simple linear regression model. In the interval estimation for normal and scale-contaminated normal distributions of β 0 , the least squares method had the narrowest average width of confidence interval. For the interval estimation of β 1 , the Bayesian method had the narrowest average width of confidence interval in a small variance of 1, followed by the same of optimum-type Theil and new adjusted Theil–Sen and Siegel methods, and Theil method, respectively. In the interval estimation for gamma distribution of β 1 , the Bayesian method had the narrowest average width of confidence interval, followed by optimum-type Theil, new adjusted Theil–Sen and Siegel, and Theil methods, respectively. The optimum-type Theil method was good for medium sample size, while Theil and new adjusted Theil–Sen and Siegel methods were good for small and large sample sizes. Therefore, new adjusted Theil–Sen and Siegel method can be used in many situations and can be used in place of optimum-type Theil and Theil methods for nonparametric statistics interval estimation.