Abstract
There are many bootstrap methods that can be used for statistical analysis especially in econometrics, biometrics, Statistics, Sampling and so on. The sole aim of this paper is to ascertain the accuracy and efficiency of the estimates from the independent and identically distributed (iid) simple linear regression (SLR) model under a variety of assessment conditions using bootstrap techniques. Analysis was carried out using S-plus statistical package on hypothetical data sets from a normal distribution with different group proficiency levels to buttress the arguments in the paper. In the course of the analysis, 268,800 scenarios were replicated 1000 times. The result shows a significant difference between the performances of the bootstrap methods used, namely; residual and parametric bootstrap techniques. From the analysis, the largest bias and standard error were always associated with model HP311 while the smallest bias and standard error values were associated with models HR311. The exception was found in the group proficiency level 3- N (1, 0.25), when the sample sizes were 200, 1000 and 10000 instead of model HR311 producing the smallest bias and standard error, model RP311 did. The significantly better performance of the residual bootstrap indicates the possible use of this technique in assessment of comparative performance and the capability of yielding very accurate, consistent, faster and extra-ordinarily reliable statistical inference under several assessment conditions.
Highlights
Bootstrap is not another statistical technique but is rather a general approach to statistical inference with very broad applicability and very mild modeling assumptions
In Test 1, across the three different sample sizes and the three different group proficiency levels, the largest the bias and standard error were always associated with model HP311 while the smallest bias and standard error values were associated with models HR311
The largest bias and standard error were always associated with model HP311 while the smallest bias and standard error values were associated with models HR311
Summary
Bootstrap is not another statistical technique but is rather a general approach to statistical inference with very broad applicability and very mild modeling assumptions. It is the result from the way the sample information is processed. In most econometric applications, where there is no readily available finite sample distribution of the test statistics that’s when one gets the most mileage out of the bootstrap methods. Even though, it is computationally more demanding than other sampling techniques. To estimate the test statistics of the functional models and to determine the best model under those conditions
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