What problem is statistical bootstrap used to solve?

The Bootstrap method makes statistical inferences about the distribution characteristics of the population based on the given original sample copy observation information, without requiring additional information.

Efron (1979) believes that this method is also a non-parametric statistical method. (Recommended learning: Bootstrap video tutorial)

The Bootstrap method starts from the observation data and does not require any distribution assumptions. It uses the Bootstrap method to address parameter estimation and hypothesis testing problems in statistics. The data set of a certain statistic calculated by bootstrapping samples 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 overall distribution, we can approximately estimate the statistic and its confidence interval. From this distribution, quantiles corresponding to different confidence levels can be obtained—the so-called critical values, which can be further used for hypothesis testing.

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

In the implementation process of Bootstrap, the status of computers cannot 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 computers, the calculation speed has increased and the calculation time has been greatly reduced.

When the data distribution assumption 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 utilization value and practical significance in biological research.

Reasons for applying bootstrap:

In fact, when performing analysis, the first thing to do is to determine the type of random variable, and then to determine the random variable What distribution does the data of the variable obey?

What distribution is crucial, because it directly determines whether it can be analyzed. For example: If you perform variance analysis, you must first require a normal distribution. If it is not a normal distribution, you must take remedial measures. This remedial measure is bootstrap.

bootstrap also has another use, because classic statistics is relatively perfect for central tendency, but for some other distribution parameters, such as median, quartile, standard deviation, coefficient of variation, etc. It is estimated to be imperfect, so bootstrap is needed.

bootstrap is similar to the classic statistical method. Generally, the parametric method is more efficient than the non-parametric method. However, the biggest drawback of the parametric method is that it requires a distribution model in advance. If the model does not meet the requirements, the analysis results It may be wrong, which is a white analysis.

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