What problems can bootstrap solve in statistics

Editor to share with you what problems bootstrap can solve in statistics, I believe most people do not know much about it, so share this article for your reference, I hope you can learn a lot after reading this article, let's go to know it!

The Bootstrap method makes statistical inference on the distribution characteristics of the population based on the copied observation information of the given original sample, and no additional information is needed.

Efron (1979) believes that this method is also a nonparametric statistical method.

The Bootstrap method starts from the observed data without any distribution assumptions. Aiming at the problems of parameter estimation and hypothesis testing in statistics, the data set of a statistic calculated by bootstrapping samples generated by the Bootstrap method can be used to reflect the sampling distribution of the statistic, that is, to generate an empirical distribution. In this way, even if we are uncertain about the population distribution, we can approximately estimate the statistic and its confidence interval. From this distribution, the quantiles corresponding to different confidence levels can be obtained, that is, the so-called critical value, which can be further used in the hypothesis test.

Therefore, Bootstrap method can solve many problems that can not be solved by traditional statistical analysis methods.

In the implementation of Bootstrap, the status of computer can not be ignored (Diaconis et al.,1983), because Bootstrap involves a large number of simulation calculations.

It can be said that without computers, Bootstrap theory can only be empty talk. With the rapid development of computer and the improvement of computing speed, the computing time is greatly reduced.

When the data distribution hypothesis is too far-fetched or the analytical formula is too difficult to derive, Bootstrap provides us with another effective way to solve the problem. Therefore, this method has certain value and practical significance in bioscience research.

Reasons for applying bootstrap:

In fact, in the analysis, the first thing to do is to determine the type of random variables, and then to determine what distribution the data of random variables obey.

What distribution is important because it directly determines whether it can be analyzed or not. For example: if the analysis of variance, first of all requires the normal distribution, if not normal distribution, there must be remedial measures, this remedial measure is bootstrap.

Bootstrap is also useful because classical statistics are perfect for centralized trends, but the interval estimates of other distribution parameters, such as median, quartile, standard deviation, coefficient of variation, etc., are not perfect, so bootstrap is needed.

Bootstrap is similar to classical statistical methods. In general, the efficiency of parametric method is higher than that of non-parametric method. However, the biggest disadvantage of parametric method is that it needs a distribution model in advance. If the model is not consistent, the analysis results may be wrong, that is, white analysis.

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