Research On The Multidimensional Expansion Of Bonferroni Index And The Imbalance Of People’s Livelihood

With the rapid development of the economy,various unbalanced development issues have become increasingly prominent while people’s living standards improve steady.Therefore research on the imbalance has attracted a lot of attention.At present,a series of indicators that evaluate the inequality level,can only evaluate whether single social resource allocation is balanced,such as the Bonferroni index.But social resources are increasingly diversified,and the Bonferroni index is not applicable when we consider evaluating the inequality level using more than one social resources.In this paper,the Bonferroni index is extended from single into multi dimensions within the new framework.It is based on a hyper-surface and can be used to measure the imbalance of multiple indicators.As China always attach great importance to the development of people’s livelihood,although there are many studies in the field of people’s livelihood,few articles have focused on the imbalanced development of people’s livelihood.Therefore,this paper applies the multidimensional Bonferroni index to the field of people’s livelihood,in order to measure the imbalance of people’s livelihood development and analyze the differences in people’s livelihood in different regions.The content of this paper can be divided into the following parts:In the first part,we introduce the People’s Livelihood index briefly.The People’s Livelihood index selected in this paper is composed of the Social Security index and the Engel index,which measure the social security level and people’s living standards in each place,respectively.In the second part,the Bonferroni index is extended from single into multi dimensions.First,the Bonferroni curve is represented as an implicit function.Then we exchange the vertical and horizontal axes of the curve,and derive algorithms for multidimensional Bonferroni index as well as sample-empirical Bonferroni index within the new framework.Then we use Monte Carlo simulation to explain the nature as well as the influential factors of the multidimensional Bonferroni index,and prove that the multidimensional index can more accurately reflect the imbalance of multiple indicators than the one-dimensional index.In the third part,we expand samples based on non-parametric method.Few samples will affect the accuracy of the results when we calculate the value of multidimensional Bonferroni index.Therefore,this paper uses kernel density estimation to estimate the density function of the samples and then generates new samples through the density function to achieve the purpose of expanding the original data.The fourth part analyzes the imbalance of people’s livelihood.First,we analyze the trend of the People’s Livelihood index from 1990 to 2018.Then the multidimensional Bonferroni index was used to calculate the imbalance of people’s livelihood.It is found that the multidimensional Bonferroni index not only considers the high-level complex information in the people’s livelihood data comprehensively but also gives more attention to low-level areas.Finally,the development trend of the imbalance of people’s livelihood is analyzed from the perspective of time,and the causes of the imbalance are analyzed from the perspective of space.The main conclusions are as follows: First,the national standard of living is steadily improving,and both the Social Security index and the Engel index show an upward trend.Among them,the starting point of the Social Security index is lower and the Engel index grows faster.Secondly,from the perspective of the whole country,the degree of imbalance in the people’s livelihood shows a downward trend in general,and the development of people’s livelihood between provinces become more and more balanced.In 1990,the level of social security across the country was extremely unbalanced.As the coverage of the social security system expands,the imbalance has dropped a lot but is still high.Third,from the perspective of the four economic regions,the imbalance in people’s livelihood has declined,the West has fallen the most.In 2018,the imbalances in people’s livelihood shows the characteristics of the East>West>Central>Northeast.Fourth,from 1990 to 2018,the development of people’s livelihood between the regions has become more and more balanced,and the imbalance is lower than the overall national level.