Factors influencing Soay sheep survival

We present a survival analysis of Soay sheep mark recapture and recovery data. Unlike previous conditional analyses, it is not necessary to assume equality of recovery and recapture probabilities; instead these are estimated by maximum likelihood. Male and female sheep are treated separately, with the higher numbers and survival probabilities of the females resulting in a more complex model than that used for the males. In both cases, however, age and time aspects need to be included and there is a strong indication of a reduction in survival for sheep aged 7 years or more. Time variation in survival is related to the size of the population and selected weather variables, by using logistic regression. The size of the population significantly affects the survival probabilities of male and female lambs, and of female sheep aged 7 or more years. March rainfall and a measure of the North Atlantic oscillation are found to influence survival significantly for all age groups considered, for both males and females. Either of these weather variables can be used in a model. Several phenotypic and genotypic individual covariates are also fitted. The only covariate which is found to influence survival significantly is the type of horn of first-year female sheep. There is a substantial variation in the recovery probabilities over time, reflecting in part the increased effort when a population crash was expected. The goodness of fit of the model is checked by using graphical procedures.     

Bootstrapping regression models with BLUS residuals

To bootstrap a regression problem, pairs of response and explanatory variables or residuals can be resam‐pled, according to whether we believe that the explanatory variables are random or fixed. In the latter case, different residuals have been proposed in the literature, including the ordinary residuals (Efron 1979), standardized residuals (Bickel & Freedman 1983) and Studentized residuals (Weber 1984). Freedman (1981) has shown that the bootstrap from ordinary residuals is asymptotically valid when the number of cases increases and the number of variables is fixed. Bickel & Freedman (1983) have shown the asymptotic validity for ordinary residuals when the number of variables and the number of cases both increase, provided that the ratio of the two converges to zero at an appropriate rate. In this paper, the authors introduce the use of BLUS (Best Linear Unbiased with Scalar covariance matrix) residuals in bootstrapping regression models. The main advantage of the BLUS residuals, introduced in Theil (1965), is that they are uncorrelated. The main disadvantage is that only n —p residuals can be computed for a regression problem with n cases and p variables. The asymptotic results of Freedman (1981) and Bickel & Freedman (1983) for the ordinary (and standardized) residuals are generalized to the BLUS residuals. A small simulation study shows that even though only n — p residuals are available, in small samples bootstrapping BLUS residuals can be as good as, and sometimes better than, bootstrapping from standardized or Studentized residuals.     

Correlation in a Bayesian framework

The authors consider the correlation between two arbitrary functions of the data and a parameter when the parameter is regarded as a random variable with given prior distribution. They show how to compute such a correlation and use closed form expressions to assess the dependence between parameters and various classical or robust estimators thereof, as well as between p‐values and posterior probabilities of the null hypothesis in the one‐sided testing problem. Other applications involve the Dirichlet process and stationary Gaussian processes. Using this approach, the authors also derive a general nonparametric upper bound on Bayes risks.     

Differential equation models for statistical functions

Differential equations have been used in statistics to define functions such as probability densities. But the idea of using differential equation formulations of stochastic models has a much wider scope. The author gives several examples, including simultaneous estimation of a regression model and residual density, monotone smoothing, specification of a link function, differential equation models of data, and smoothing over complicated multidimensional domains. This paper aims to stimulate interest in this approach to functional estimation problems, rather than provide carefully worked out methods.     

Transformation using ( x + 0.5) to stabilize the variance of populations

Transformation is required to achieve homo-scedasticity when we perform ANOVA to test the effect of factors on population abundance. The effectiveness of transformations decreases when the data contain zeros. Especially, the logarithmic transformation or the Box–Cox transformation is not applicable in such a case. For the logarithmic transformation, 1 is traditionally added to avoid such problems. However, there is no concrete foundation as to why 1 is added rather than other constants, such as 0.5 or 2, although the result of ANOVA is much influenced by the added constant. In this paper, I suggest that 0.5 is preferable to 1 as an added constant, because a discrete distribution defined in {0, 1, 2, . . .} is approximately described by a corresponding continuous distribution defined in (0, ≧) if we add 0.5. Numerical investigation confirms this prediction. Received: October 16, 1998 / Accepted: June 10, 1999     

农户土地流转有助于农户群体“提低扩中”吗?

提高中低收入农户群体的收入水平是缩小居民收入差距、实现共同富裕的关键任务。利用CFPS 2018数据,使用基于RIF的ITE模型等计量方法进行分析研究发现：(1)土地流转的增收效应具有非对称性,转出土地的中低收入农户能显著增收,但转入土地的中低收入农户增收不明显;(2)东部和西部地区转出土地的中低收入农户收入增长显著;(3)土地流转(尤其是转出)有助于缩小农户间收入差距、优化农户群体的收入分配结构。实证结果稳健地说明农户土地流转对实现农户群体“提低扩中”目标具有积极意义,在此基础上提出在西部和东中部欠发达农村地区,鼓励和支持中低收入农户流转土地,以增加其兼业和非农收入等政策建议。     

A new heteroscedastic regression to analyze mass loss of wood in civil construction in Brazil

A heteroscedastic regression based on the odd log-logistic Marshall–Olkin normal (OLLMON) distribution is defined by extending previous models. Some structural properties of this distribution are presented. The estimation of the parameters is addressed by maximum likelihood. For different parameter settings, sample sizes and some scenarios, various simulations investigate the performance of the heteroscedastic OLLMON regression. We use residual analysis to detect influential observations and to check the model assumptions. The new regression explains the mass loss of different wood species in civil construction in Brazil.     

福建省科技资源配置效率影响因素分析

针对前期研究成果所测算出的值,从结构和社会环境两方面选取解释变量,运用多元回归分析法,对影响福建省科技资源配置效率水平的因素进行定量分析,研究确定了主要影响因素,为福建省制定合理的科技资源配置政策提供参考依据。     

M-quantile models with application to poverty mapping

Over the last decade there has been growing demand for estimates of population characteristics at small area level. Unfortunately, cost constraints in the design of sample surveys lead to small sample sizes within these areas and as a result direct estimation, using only the survey data, is inappropriate since it yields estimates with unacceptable levels of precision. Small area models are designed to tackle the small sample size problem. The most popular class of models for small area estimation is random effects models that include random area effects to account for between area variations. However, such models also depend on strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow for outlier robust inference. An alternative approach to small area estimation that is based on the use of M-quantile models was recently proposed by Chambers and Tzavidis (Biometrika 93(2):255–268, 2006) and Tzavidis and Chambers (Robust prediction of small area means and distributions. Working paper, 2007). Unlike traditional random effects models, M-quantile models do not depend on strong distributional assumption and automatically provide outlier robust inference. In this paper we illustrate for the first time how M-quantile models can be practically employed for deriving small area estimates of poverty and inequality. The methodology we propose improves the traditional poverty mapping methods in the following ways: (a) it enables the estimation of the distribution function of the study variable within the small area of interest both under an M-quantile and a random effects model, (b) it provides analytical, instead of empirical, estimation of the mean squared error of the M-quantile small area mean estimates and (c) it employs a robust to outliers estimation method. The methodology is applied to data from the 2002 Living Standards Measurement Survey (LSMS) in Albania for estimating (a) district level estimates of the incidence of poverty in Albania, (b) district level inequality measures and (c) the distribution function of household per-capita consumption expenditure in each district. Small area estimates of poverty and inequality show that the poorest Albanian districts are in the mountainous regions (north and north east) with the wealthiest districts, which are also linked with high levels of inequality, in the coastal (south west) and southern part of country. We discuss the practical advantages of our methodology and note the consistency of our results with results from previous studies. We further demonstrate the usefulness of the M-quantile estimation framework through design-based simulations based on two realistic survey data sets containing small area information and show that the M-quantile approach may be preferable when the aim is to estimate the small area distribution function.     

ADE-4: a multivariate analysis and graphical display software

We present ADE-4, a multivariate analysis and graphical display software. Multivariate analysis methods available in ADE-4 include usual one-table methods like principal component analysis and correspondence analysis, spatial data analysis methods (using a total variance decomposition into local and global components, analogous to Moran and Geary indices), discriminant analysis and within/between groups analyses, many linear regression methods including lowess and polynomial regression, multiple and PLS (partial least squares) regression and orthogonal regression (principal component regression), projection methods like principal component analysis on instrumental variables, canonical correspondence analysis and many other variants, coinertia analysis and the RLQ method, and several three-way table (k-table) analysis methods. Graphical display techniques include an automatic collection of elementary graphics corresponding to groups of rows or to columns in the data table, thus providing a very efficient way for automatic k-table graphics and geographical mapping options. A dynamic graphic module allows interactive operations like searching, zooming, selection of points, and display of data values on factor maps. The user interface is simple and homogeneous among all the programs; this contributes to making the use of ADE-4 very easy for non- specialists in statistics, data analysis or computer science.