多阶模型在地区消费差异研究中的应用

 当组间差异显著时，应该运用多阶模型纳入更高阶的场景变量进行分析。对2007年广东省11市7县、区的1600个家庭的消费数据研究表明，不同城市之间居民的消费水平、边际消费倾向都存在显著差异。文章引入微观层面的家庭人均可支配收入（PDI）和是否拥有住房（HOUSE）虚拟变量来解释微观层面的家庭消费差异；引入宏观层面的地区人均可支配收入（GPDI）和是否为发达地区（D）虚拟变量作为场景变量解释家庭消费跨地区的差异。实证结果表明，微观层面变量对家庭消费差异（组内差异）的解释程度达48％以上，两个场景变量对城镇居民消费跨地区差异（组间差异）的解释程度达99％以上。     

Generalized binomial distributions

In many cases where the binomial dismbution fails to apply to real world data it is because of more variability in the data than can be explained by that dismbution. Several authors have proposed models that are useful in explaining extra-binomial variation. In this paper we point out a characterization of sequences of exchangeable Bernoulli random variables which can be used to develop models which show more variability than the binomial. We give sufficient conditions which will yield such models and show how existig models can be combined to generate further models. The usefulness of some of these models is illustrated by fitting them to sets of real data.     

Is it Cash that the Deprived are Short of?

SUMMARY
In using census data, a range of indicators is commonly used to indicate deprivation. This paper examines the validity of these indicators by exploring how well they predict income in surveys (the Family Expenditure Surveys of 1983 and 1990 and the General Household Survey of 1984) which also collect income data. A reasonably parsimonious set of seven socioeconomic variables (as well as controls for age, sex and region) explains about 40% of the variation in log-income. Our results provide a set of weights for a deprivation index and offer no support for the practice of assigning equal weights to the indicators. A census-based proxy would miss a sizable minority of the actual poor and misclassify some with higher incomes. A majority of the `deprived' are poor by a cash yardstick, but some are not.     

人口分布的相对变化对我国地区间收入趋同的影响研究

本文利用省级面板数据研究了人口分布的相对变化对我国地区间收入趋同的影响。修正后的 -趋同分析结果显示,1978-2010年,我国地区间总收入和人均收入都表现为趋同模式,但人均收入的趋同速度比总收入趋同速度大约快16%。为了考察这一趋同速度上的差异,我们使用偏离—份额分析法考察了人口分布的相对变化对地区人均收入趋同过程的影响。分析结果表明,地区间人均收入趋同与人口分布的相对变化有显著关系。     

THE EPIDEMIOLOGY OF A DISEASE USING HAZARD FUNCTIONS1

A prime objective of this paper is to mathematically quantify certain epidemiological concepts and show how some of these can be applied to certain registry type data. Usually epidemiological quantities are expressed in terms of density functions. However it is often more natural to estimate hazard functions in practical situations. Hence the emphasis will be on expressing various measures in terms of hazard functions. This contrasts with the useful paper of Albert, Gertman & Louis (1978) where density functions are used throughout. The definitions of some key concepts such as cohort effect are also different which gives rise to an alternative analysis and some new results. Initially, incidence, mortality and prevalence are discussed and this is followed by a treatment of initiation which is a less commonly used measure. The results are applied to the lung cancer data in the South Australian Central Cancer Registry.     

Problems in estimating non-linear Engel parameters in the absence of appropriate grouped means and average elasticity of variable elasticity Engel functions

Household Expenditure Survey (HES) data are widely reported in grouped form for a number of reasons. Only within-group arithmetic means (AMs) of the household expenditures on various consumption items, total expenditure, income . and other variables are reported in the tabular form. However, the use of such within-group AMs introduces biases when the parameters of various commonly used non-linear Engel functions are estimated by the Aitken's generalized least squares (GLS) method. This is because the within-group geometric means (GMs)/harmonic means (HMs) are needed in order to estimate unbiased parameters of those non-linear Engel functions. Kakwani (1977) estimated the within-group GMs/HMs from the Kakwani-Podder (1976) Lorenz curve for Indonesian data. We have extended his method to estimate within-group GMs/HMs to a set of variables, based on a general type of concentration curve. It is shown that our estimated within-group GMs/HMs based on concentration curves are not entirely suitable for the Australian HES data. However, these GMs/HMs are then used to estimate Engel parameters for various non-linear Engel functions and it is seen that these elasticities are different for some items of certain non-linear Engel functions than those when the reported within-group AMs are used as proxies for within-group GMs/HMs in order to estimate those non-linear Engel functions. The concept of the average elasticity of a variable elasticity Engel function is discussed and computed for various Australian household consumption items. It is empirically demonstrated that the average elasticities are more meaningful than the traditional elasticity estimates computed at some representative values for certain functions.     

Sure explained variability and independence screening

In the era of Big Data, extracting the most important exploratory variables available in ultrahigh-dimensional data plays a key role in scientific researches. Existing researches have been mainly focusing on applying the extracted exploratory variables to describe the central tendency of their related response variables. For a response variable, its variability characteristic is as much important as the central tendency in statistical inference. This paper focuses on the variability and proposes a new model-free feature screening approach: sure explained variability and independence screening (SEVIS). The core of SEVIS is to take the advantage of recently proposed asymmetric and nonlinear generalised measures of correlation in the screening. Under some mild conditions, the paper shows that SEVIS not only possesses desired sure screening property and ranking consistency property, but also is a computational convenient variable selection method to deal with ultrahigh-dimensional data sets with more features than observations. The superior performance of SEVIS, compared with existing model-free methods, is illustrated in extensive simulations. A real example in ultrahigh-dimensional variable selection demonstrates that the variables selected by SEVIS better explain not only the response variables, but also the variables selected by other methods.     

Prediction Regions for Bivariate Extreme Events

This paper suggests using a mixture of parametric and non‐parametric methods to construct prediction regions in bivariate extreme‐value problems. The non‐parametric part of the technique is used to estimate the dependence function, or copula, and the parametric part is employed to estimate the marginal distributions. A bootstrap calibration argument is suggested for reducing coverage error. This combined approach is compared with a more parametric one, relative to which it has the advantages of being more flexible and simpler to implement. It also enjoys these features relative to predictive likelihood methods. The paper shows how to construct both compact and semi‐infinite bivariate prediction regions, and it treats the problem of predicting the value of one component conditional on the other. The methods are illustrated by application to Australian annual maximum temperature data.     

Influence Diagnostics for Simultaneous Equations Models

This paper presents influence diagnostics for simultaneous equations models. It proposes residuals, leverage and other influence measures. A missing data method is adopted to minimize the masking effect due to case deletions. The assessment of local influence is also considered. The paper shows how to evaluate the effects that perturbations to the endogenous variables, predetermined variables and case weights may have on the parameter estimates. The diagnostics are illustrated with two examples.     

Conditional versus unconditional analysis in some regression models

This paper discusses extensions of the variability of the parameters (or functions of parameters) in a recursive system of regression models, and shows that conditioning on the carriers may lead to drastically different conclusions than when the carriers are viewed as stochastic. The relationships among the variables in these models are derived by a sequence of regressions, in which the dependent variable of one equation may reappear as a carrier in a later equation. The model to be fitted need not be identical with the generating equations. In these recursive systems of equations, when the models are miss-specified, or when functions of parameters from different equations are to be estimated, the variability of the estimators is shown to depend critically on the level of conditioning assumed. Various jackknife and bootstrap methods of estimating the variability of the estimators are suggested. In particular the bootstrap estimators of variability can be adopted to captured the correct level of conditioning, by mimicking the conditioning in their design. Two problems in which the level of conditioning matters are described and analysed under the general chained regression models. A real data problem. Omission of variables is sometimes advocated for reducting the variance of the remaining estimators. In both cases the effectiveness of the nonparametric variance estimators is demonstrated using simulation studies.     

农民收入与金融财政支持的实证研究:陕西例证

利用陕西省1978-2007年的时序数据,对农民收入与金融、财政支持的关系进行了实证研究。结果表明：一,农民增收与财政支农水平长期正向相关,并在未来对财政支农水平存在较强的依赖性;二,金融支农水平在过去和未来对农民增收的促进影响均十分微弱;三,金融和财政支农均无法对农民收入的短期波动起到有效的调整作用,同时,二者支农效率较低,对农民增收难以产生直接的因果影响。在此基础上,就陕西省农民增收提出了简要的政策建议。     

基尼加权回归分析：概念、方法及应用

普通最小二乘法是进行回归分析最常用的基本方法,但该方法要求满足若干经典假设,对于小样本或在与收入相关回归分析的参数估计中易受奇异值、高收入群体的影响。本文试图利用基尼加权回归弥补以上不足。基尼加权回归可分为参数方法与非参数方法两类,参数方法基于样本残差的基尼平均差最小原则对参数进行估计;非参数方法则是直接由两点间的斜率加权得到。基尼加权回归分析可以进行参数假设检验并定义拟合优度,其中的假设检验在实际应用中采用Jackknife重抽样方法估计方差。文中提出的样本拓展基尼平均差算法,弥补了现有算法对样本数据只能提供近似计算的不足,极大简化相应的计算公式。利用我国2015年省域截面数据、1994至2015年总量时间序列数据分别讨论入境旅游收入对收入基尼系数的影响,发现使用基尼加权回归的结果不仅符合理论预期,而且可以通过不平等厌恶参数的变化反映入境旅游收入对不同群体收入公平性的影响。     

Two simple measures of variability for categorical data

This paper proposes two new variability measures for categorical data. The first variability measure is obtained as one minus the square root of the sum of the squares of the relative frequencies of the different categories. The second measure is obtained by standardizing the first measure. The measures proposed are functions of the variability measure proposed by Gini [Variabilitá e Mutuabilitá Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche, C. Cuppini, Bologna, 1912] and approximate the coefficient of nominal variation introduced by Kvålseth [Coefficients of variation for nominal and ordinal categorical data, Percept. Motor Skills 80 (1995), pp. 843–847] when the number of categories increases. Different mathematical properties of the proposed variability measures are studied and analyzed. Several examples illustrate how the variability measures can be interpreted and used in practice.     

Application of ridge regression and factor analysis in design and production of alloy wheels

This study proposes using statistical approaches to help with both the design and manufacture of wheels. The quality of a wheel is represented by the mechanical properties of spokes. Variation in the mechanical properties of different wheels is attributed to two sources, i.e. between-model variation and within-model variation. The between-model variation is due to different shapes of different wheel models. To model the effect of shapes on the mechanical properties, we first specify eight shape variables potentially critical to the mechanical properties, and then we collect relevant data on 18-wheel models and perform ridge regression to find the effects of these variables on the mechanical properties. These results are linked to the solidification theory of the A356 alloy. The within-model variation is due to natural variability and process abnormality. We extract mechanical data of a particular wheel model from the database. Factor analysis is employed to analyze the data with a view to identifying the latent factors behind the mechanical properties. We then look into the microstructure of the alloy to corroborate the fact that these two latent factors are essentially the Si phase and the Mg₂Si phase, respectively. These results can be used to efficiently identify the root cause when the manufacturing process goes wrong.     

Ratio index variables or ANCOVA? Fisher's cats revisited

Over 60 years ago Ronald Fisher demonstrated a number of potential pitfalls with statistical analyses using ratio variables. Nonetheless, these pitfalls are largely overlooked in contemporary clinical and epidemiological research, which routinely uses ratio variables in statistical analyses. This article aims to demonstrate how very different findings can be generated as a result of less than perfect correlations among the data used to generate ratio variables. These imperfect correlations result from measurement error and random biological variation. While the former can often be reduced by improvements in measurement, random biological variation is difficult to estimate and eliminate in observational studies. Moreover, wherever the underlying biological relationships among epidemiological variables are unclear, and hence the choice of statistical model is also unclear, the different findings generated by different analytical strategies can lead to contradictory conclusions. Caution is therefore required when interpreting analyses of ratio variables whenever the underlying biological relationships among the variables involved are unspecified or unclear. Copyright © 2009 John Wiley & Sons, Ltd.     

Statistical matching and uncertainty analysis in combining household income and expenditure data

Among the goals of statistical matching, a very important one is the estimation of the joint distribution of variables not jointly observed in a sample survey but separately available from independent sample surveys. The absence of joint information on the variables of interest leads to uncertainty about the data generating model since the available sample information is unable to discriminate among a set of plausible joint distributions. In the present paper a short review of the concept of uncertainty in statistical matching under logical constraints, as well as how to measure uncertainty for continuous variables is presented. The notion of matching error is related to an appropriate measure of uncertainty and a criterion of selecting matching variables by choosing the variables minimizing such an uncertainty measure is introduced. Finally, a method to choose a plausible joint distribution for the variables of interest via iterative proportional fitting algorithm is described. The proposed methodology is then applied to household income and expenditure data when extra sample information regarding the average propensity to consume is available. This leads to a reconstructed complete dataset where each record includes measures on income and expenditure.     

A distribution-free approach to inducing rank correlation among input variables

A method for inducing a desired rank correlation matrix on a multivariate input random variable for use in a simulation study is introduced in this paper. This method is simple to use, is distribution free, preserves the exact form of the marginal distributions on the input variables, and may be used with any type of sampling scheme for which correlation of input variables is a meaningful concept. A Monte Carlo study provides an estimate of the bias and variability associated with the method. Input variables used in a model for study of geologic disposal of radioactive waste provide an example of the usefulness of this procedure. A textbook example shows how the output may be affected by the method presented in this paper.     

Heterogeneity,Aggregate Uncertainty,and the Short-Term Interest Rate

This article analyzes the relationship between the short-term interest rate and diversity (i.e., the number of types) in models with heterogeneous agents and incomplete markets. The number of types needed to approximate a continuum varies across examples. In all cases, however, the number of types has little effect on the average interest rate and consumption variability. In these models, the set of state variables is large because the equilibrium law of motion depends on the cross-sectional wealth distribution. The article shows how to solve these models numerically by approximating the distribution using moments or percentiles.     

农产品电商会影响我国家庭农场的收入吗?

农产品电商作为数字经济直接催生的新业态,为农民增收提供了新渠道。本文以家庭农场为研究对象,基于全国农村固定观察点新型农业经营主体发展指数专项调查的微观数据,对农产品电商的增收效应进行了实证检验。研究结果表明,农产品电商对家庭农场农业经营性收入的提高有明显的促进作用,但农产品电商的增收效应具有异质性。条件分位数处理效应的估计结果显示,农产品电商对中低收入水平家庭农场的增收效果要明显好于中高收入水平的家庭农场,更进一步的中介效应检验证实了自有品牌和产品认证在农产品电商增收效应中的部分中介作用。未来应该提升农村电商的配套服务水平,努力为农产品电商营造良好的电商氛围,以期更好地发挥农产品电商的增收效应。     

Illuminate the unknown: evaluation of imputation procedures based on the SAVE survey

Questions about monetary variables (such as income, wealth or savings) are key components of questionnaires on household finances. However, missing information on such sensitive topics is a well-known phenomenon which can seriously bias any inference based only on complete-case analysis. Many imputation techniques have been developed and implemented in several surveys. Using the German SAVE data, a new estimation technique is necessary to overcome the upward bias of monetary variables caused by the initially implemented imputation procedure. The upward bias is the result of adding random draws to the implausible negative values predicted by OLS regressions until all values are positive. To overcome this problem the logarithm of the dependent variable is taken and the predicted values are retransformed to the original scale by Duan’s smearing estimate. This paper evaluates the two different techniques for the imputation of monetary variables implementing a simulation study, where a random pattern of missingness is imposed on the observed values of the variables of interest. A Monte-Carlo simulation based on the observed data shows the superiority of the newly implemented smearing estimate to construct the missing data structure. All waves are consistently imputed using the new method.