The Comparison Of Sampling Methods Based On The Loss Functions

Due to the huge range of data sets,there are many different sampling methods appearing,which differs from the traditional ones.Therefore,it is particularly important to evaluate different sampling methods,but most of studies focus on the features of estimator.This method just can ensure estimators maintain stable.However,it is unclear that how many loss this estimator would bring,so specific values just can be got during the production.In this paper,loss functions are introduced to evaluate different sampling methods,and the loss function are regarded as the objective function.According to information we have gotten,we can obtain a new estimator.During this process,by loosing hypothesis this method can be applied in practice.At first assuming that the distribution is known including the parameters in the distribution,the gap between estimators and real value can be calculated.However in practice,it is impossible to get parameter value in distribution,thus loosing hypothesis is necessary.Finally,in order to improve the reliability,risk function also be used to evaluate the loss function.According to the classification of sampling methods,five sampling methods and four loss functions are selected in this paper,including the absolute loss function,the square loss function,the inverse normal loss function and the inverse Gamma loss function,which is used to measure the loss caused by estimator.In addition,a certain loss functions based on sample distribution are constructed to measure the difference between the sample distribution and the distribution obtained by different sampling methods.By estimating the average call time according to a mobile communication data,loss functions are used to evaluate different sampling methods,like random sampling,PaiPS sampling,Quota sampling,jackknife and bootstrap resampling.This study compares the advantages and disadvantages of various sampling methods from loss of function.Overall,the resampling method based on random sampling have the least loss value;Bayes estimator based on loss function could correct the original estimator,and risk function varies with sampling methods,loss function and data set.