浅议众数

在统计学文献中，众数扮演很小的角色。然而，在许多应用中，众数被证明是个有用的统计参数。本文介绍了众数在实际中的一些应用，并提出了三种概率密度 f(x)的众数估计方法。     

分流居民储蓄存款的难题与对策

一、我国城乡居民人均储蓄存款、人均定期储蓄存款、人均可支配收入增长的对比分析 我国居民的金融投资大多集中在储蓄存款上,研究居民储蓄存款的变化,不能只观察余额总量的增长,还需结合人口总量的增长以及消除价格变化影响来分析它的实际增长,特别是其中居民人均定期储蓄存款的变化.因此,本文采用按1978年可比价格计算的历年我国城乡居民人均储蓄存款(Y3)、人均定期储蓄存款(Y4)、人均可支配收入(X3)来进行分析(参见表1).     

众数回归森林模型及其在收入分配研究中的应用

为解决传统非参数众数回归模型没有考虑解释变量间复杂交互影响的局限，文章将众数回归与机器学习方法相结合，提出了一个新的非参数众数回归模型：众数回归森林模型。该模型一方面充分考虑了各个解释变量之间的交互影响；另一方面采用Bagging技术汇总多个众数回归树的结果，提高了预测性能。数值模拟结果表明：第一，与线性众数回归模型和众数回归树模型相比，众数回归森林模型极大地提高了估计和预测精度；第二，当数据为偏态分布时，众数回归森林模型的估计和预测精度显著优于中位数回归森林和均值回归森林模型。此外，将众数回归森林模型应用于收入分配研究中，得到了与中位数回归森林和均值回归森林模型不同的结果。     

基于极差的条件自回归极差模型

本文介绍了一种在固定时间区间上资产价格极差的动态模型:条件自回归极差(CARR)模型。CARR模型的条件极差十分类似GARCH模型中的条件方差,而且CARR模型也相似于ACD(Autoregressive Conditional Duration)模型。极端值理论(Extreme value theory)暗示极差是波动的一种有效估计,因此CARR模型可以看作是波动模型,并通过实证分析发现CARR模型的样本期外波动的预测效果比标准的GARCH波动模型要好。     

居民收支:人均可支配收入较上年增长1819元

2020年,四川城乡居民收入经受住疫情考验,二季度以来逐季恢复增长。全年全省居民人均可支配收入26522元,较上年增加1819元,增长7.4%。其中,城镇居民人均可支配收入38253元,增长5.8%;农村居民人均可支配收入15929元,增长8.6%。收入增速稳步回升2020年全省居民人均可支配收入扣除价格因素,实际增长4.1%,增速比前三季度、上半年和一季度分别加快1.3、3.3和7.2个百分点。     

国民经济核算与人均收入指标关系

随着国家对民生和收入分配领域重视力度的加大,社会各界对人均国内生产总值(GDP)、职工平均工资、居民人均可支配收入等统计指标的关注度日益提高。本文从指标概念内涵以及核算的角度出发,阐述了人均GDP与平均工资、人均可支配收入指标之间的联系和区别,并以我国1995-2009年数据为基础,对各指标之间内在关系进行实证分析。     

遇到平均数与大多数

遇到对人均可支配收入高低的质疑,我们总是解释人均可支配收入是平均数,强调是按照国家规定的方法制度,严格实施抽样调查。然而解释和强调总是难以消除质疑,还是你解释你的,我认为我的。细想一下,人家的质疑还是可以理解的。人均可支配收入毕竟是一个量化的收入水平,不同的收入群体感受同一个平均水平肯定是有不同的感觉的。收入水平高的认为低了,收入水平低的认为高了,这是     

居民收支:收入恢复性增长 消费持续改善

2021年,面对复杂严峻的国际环境和国内省内疫情散发等多重挑战,四川持续做好“六稳、六保”工作,民生保障有力,全省城乡居民收入保持恢复性增长,居民消费支出持续改善。城乡居民可支配收入保持恢复性增长2021年,四川全体居民人均可支配收入29080元(预计数,下同),同比增长9.6%,与2019年相比两年平均增长8.5%。分城乡看,城镇居民人均可支配收入41444元,同比增长8.3%,两年平均增长7.1%;农村居民人均可支配收入17575元,同比增长10.3%,两年平均增长9.5%(见表1)。     

我国各省市城镇居民消费与收入关系的实证研究

本文运用面板数据模型，利用了1991—2007年的人均消费和人均可支配收入的统计数据。对我国29个省市城镇居民的消费水平进行了比较研究。研究表明，消费水平与人均可支配收入密切相关，其中居民自发消费与人均可支配收入呈同方向变动，而边际消费倾向与人均可支配收入呈反方向变动，并且城镇居民的自发消费呈现不断增加的趋势。     

西部民族地区城镇化进程与经济发展的实证分析

文章采用2005年-2012年我国西部民族地区川、滇、黔3省46个市(州)的城镇化率、人均GDP和农民人均可支配收入的面板数据,利用横截面、时间和变量三维信息对城镇化率、人均GDP和农民人均可支配收入之间的关系进行分析.通过对面板数据的单位根检验和协整检验,得出46个市(州)的城镇化率、人均GDP和农民人均可支配收入之间存在长期稳定的均衡关系,进一步建立面板数据固定效应变系数模型,并提出相应对策.     

A comparison of sampling grids,cut-off distance and type of residuals in parametric variogram estimation

In spatial statistics, the correct identification of a variogram model when fitted to an empirical variogram depends on many factors. Here, simulation experiments show fitting based on the variogram cloud is preferable to that based on Matheron's and Cressie–Hawkins empirical variogram estimators. For correct model specification, a number of models should be fitted to the empirical variogram using a grid of cut-off values, and recommendations are given for best choice. A design where roughly half the maximum distance between points equals the practical range works well for correct variogram identification of any model, with varying nugget sizes and sample sizes.     

Finite sample correction factors for several simple robust estimators of normal standard deviation

Estimation of the standard deviation of a normal population is an important practical problem that in industrial practice must often be done from small and possibly contaminated data sets. Using multiple estimators is useful, as differences in the estimates may indicate whether the data set is contaminated and the form of the contamination. In this paper, finite sample correction factors have been estimated by simulation for several simple robust estimators of the standard deviation of a normal population. The estimators are the median absolute deviation, interquartile range, shortest half interval (Shorth), and median moving range. Finite sample correction factors have also been estimated for the commonly used non-robust estimators: mean absolute deviation and mean moving range. The simulation has been benchmarked against finite sample correction factors for the sample standard deviation and the sample range.     

A note on effective sample size for constructing confidence intervals for the difference of two proportions

Proportion differences are often used to estimate and test treatment effects in clinical trials with binary outcomes. In order to adjust for other covariates or intra-subject correlation among repeated measures, logistic regression or longitudinal data analysis models such as generalized estimating equation or generalized linear mixed models may be used for the analyses. However, these analysis models are often based on the logit link which results in parameter estimates and comparisons in the log-odds ratio scale rather than in the proportion difference scale. A two-step method is proposed in the literature to approximate the calculation of confidence intervals for the proportion difference using a concept of effective sample sizes. However, the performance of this two-step method has not been investigated in their paper. On this note, we examine the properties of the two-step method and propose an adjustment to the effective sample size formula based on Bayesian information theory. Simulations are conducted to evaluate the performance and to show that the modified effective sample size improves the coverage property of the confidence intervals.     

Disaggregate-level estimates of indebtedness in the state of Uttar Pradesh in India: an application of small-area estimation technique

The National Sample Survey Organisation (NSSO) surveys are the main source of official statistics in India, and generate a range of invaluable data at the macro level (e.g. state and national levels). However, the NSSO data cannot be used directly to produce reliable estimates at the micro level (e.g. district or further disaggregate level) due to small sample sizes. There is a rapidly growing demand of such micro-level statistics in India, as the country is moving from centralized to more decentralized planning system. In this article, we employ small-area estimation (SAE) techniques to derive model-based estimates of the proportion of indebted households at district or at other small-area levels in the state of Uttar Pradesh in India by linking data from the Debt–Investment Survey 2002–2003 of NSSO and the Population Census 2001 and the Agriculture Census 2003. Our results show that the model-based estimates are precise and representative. For many small areas, it is even not possible to produce estimates using sample data alone. The model-based estimates generated using SAE are still reliable for such areas. The estimates are expected to provide invaluable information to policy analysts and decision-makers.     

Statistical analysis of non-inferiority via non-zero risk difference in stratified matched-pair studies

A stratified study is often designed for adjusting several independent trials in modern medical research. We consider the problem of non-inferiority tests and sample size determinations for a nonzero risk difference in stratified matched-pair studies, and develop the likelihood ratio and Wald-type weighted statistics for testing a null hypothesis of non-zero risk difference for each stratum in stratified matched-pair studies on the basis of (1) the sample-based method and (2) the constrained maximum likelihood estimation (CMLE) method. Sample size formulae for the above proposed statistics are derived, and several choices of weights for Wald-type weighted statistics are considered. We evaluate the performance of the proposed tests according to type I error rates and empirical powers via simulation studies. Empirical results show that (1) the likelihood ratio and the Wald-type CMLE test based on harmonic means of the stratum-specific sample size (SSIZE) weight (the Cochran's test) behave satisfactorily in the sense that their significance levels are much closer to the prespecified nominal level; (2) the likelihood ratio test is better than Nam's [2006. Non-inferiority of new procedure to standard procedure in stratified matched-pair design. Biometrical J. 48, 966–977] score test; (3) the sample sizes obtained by using SSIZE weight are smaller than other weighted statistics in general; (4) the Cochran's test statistic is generally much better than other weighted statistics with CMLE method. A real example from a clinical laboratory study is used to illustrate the proposed methodologies.     

Taylor linearization sampling errors and design effects for poverty measures and other complex statistics

A systematic procedure for the derivation of linearized variables for the estimation of sampling errors of complex nonlinear statistics involved in the analysis of poverty and income inequality is developed. The linearized variable extends the use of standard variance estimation formulae, developed for linear statistics such as sample aggregates, to nonlinear statistics. The context is that of cross-sectional samples of complex design and reasonably large size, as typically used in population-based surveys. Results of application of the procedure to a wide range of poverty and inequality measures are presented. A standardized software for the purpose has been developed and can be provided to interested users on request. Procedures are provided for the estimation of the design effect and its decomposition into the contribution of unequal sample weights and of other design complexities such as clustering and stratification. The consequence of treating a complex statistic as a simple ratio in estimating its sampling error is also quantified. The second theme of the paper is to compare the linearization approach with an alternative approach based on the concept of replication, namely the Jackknife repeated replication (JRR) method. The basis and application of the JRR method is described, the exposition paralleling that of the linearization method but in somewhat less detail. Based on data from an actual national survey, estimates of standard errors and design effects from the two methods are analysed and compared. The numerical results confirm that the two alternative approaches generally give very similar results, though notable differences can exist for certain statistics. Relative advantages and limitations of the approaches are identified.     

Recurrence relations for single and product moments of order statistics from a generalized half logistic distribution with applications to inference

In this paper, we derive several recurrence relations satisfied by the single and product moments of order statistics from a generalized half logistic distribution. These generalize the corresponding results for the half logistic distribution established by Balakrishnan (1985). The relations established in this paper will enable one to compute the single and product moments of all order statistics for all sample sizes in a simple recursive manner; this may be done for any choice of the shape parameter k. These moments can then be used to determine the best linear unbiased estimators of location and scale parameters from complete as well as Type-I1 censored samples.     

Sample size for estimating a binomial proportion: comparison of different methods

The poor performance of the Wald method for constructing confidence intervals (CIs) for a binomial proportion has been demonstrated in a vast literature. The related problem of sample size determination needs to be updated and comparative studies are essential to understanding the performance of alternative methods. In this paper, the sample size is obtained for the Clopper–Pearson, Bayesian (Uniform and Jeffreys priors), Wilson, Agresti–Coull, Anscombe, and Wald methods. Two two-step procedures are used: one based on the expected length (EL) of the CI and another one on its first-order approximation. In the first step, all possible solutions that satisfy the optimal criterion are obtained. In the second step, a single solution is proposed according to a new criterion (e.g. highest coverage probability (CP)). In practice, it is expected a sample size reduction, therefore, we explore the behavior of the methods admitting 30% and 50% of losses. For all the methods, the ELs are inflated, as expected, but the coverage probabilities remain close to the original target (with few exceptions). It is not easy to suggest a method that is optimal throughout the range (0, 1) for p. Depending on whether the goal is to achieve CP approximately or above the nominal level different recommendations are made.     

县域城乡居民消费结构与收入关系分析

 本文利用福建省县域居民消费样本调查数据,基于空间相关性和扩展线性支出系统,对我国县域居民消费结构与收入关系进行实证分析。结果表明：可支配(纯)收入对居民的各类消费具有显著的影响,而且对八类消费的作用强度不同;旨在提高居民收入的收入分配制度改革能够促进消费需求,针对不同边际消费倾向的政策可以更有效地引导居民消费。本文的分析不同于以往对居民消费结构的研究在于：一是直接使用居民生活状况调查的微观数据进行ELES模型的参数估计,改变了仅使用七类收入群体数据的局限;二是在ELES模型中引入空间因素,考虑了因地理相邻对居民消费结构的影响,分析更为客观合理。     

中国城乡居民收入差距影响因素分析

目前,过大的城乡收入差距已成为中国经济发展的重要瓶颈,影响了社会的公正与稳定,故将城乡二元结构系数、外贸依存度以及城镇居民人均可支配收入发展速度作为城乡居民收入差距变动的影响变量,通过建立协整回归和误差修正模型得到反映它们之间长期均衡与短期波动的表达式。实证分析结果表明：城镇居民人均可支配收入发展速度是影响中国城乡居民收入差距变动的主要因素。