超越对数生产函数的半参数变系数估计模型

提出超越对数生产函数的半参数变系数模型,利用Profile方法给出产出弹性函数系数的局部加权最小二乘估计,并利用非参数条件自助法对有限样本的近似分布进行模拟,给出相对精确的广义似然比检验。规模报酬约束下中国1953--2008年的实证结果拒绝超越对数生产函数模型假设,产出弹性不可简单线性化而是对数劳均资本的非线性函数,时变资本弹性表现为倒U型变化趋势,时变劳动力弹性表现为U型变化趋势。     

Estimation in large cross random-effect models by data augmentation

Estimation in mixed linear models is, in general, computationally demanding, since applied problems may involve extensive data sets and large numbers of random effects. Existing computer algorithms are slow and/or require large amounts of memory. These problems are compounded in generalized linear mixed models for categorical data, since even approximate methods involve fitting of a linear mixed model within steps of an iteratively reweighted least squares algorithm. Only in models in which the random effects are hierarchically nested can the computations for fitting these models to large data sets be carried out rapidly. We describe a data augmentation approach to these computational difficulties in which we repeatedly fit an overlapping series of submodels, incorporating the missing terms in each submodel as 'offsets'. The submodels are chosen so that they have a nested random-effect structure, thus allowing maximum exploitation of the computational efficiency which is available in this case. Examples of the use of the algorithm for both metric and discrete responses are discussed, all calculations being carried out using macros within the MLwiN program.     

On convergence of the EM algorithmand the Gibbs sampler

In this article we investigate the relationship between the EM algorithm and the Gibbs sampler. We show that the approximate rate of convergence of the Gibbs sampler by Gaussian approximation is equal to that of the corresponding EM-type algorithm. This helps in implementing either of the algorithms as improvement strategies for one algorithm can be directly transported to the other. In particular, by running the EM algorithm we know approximately how many iterations are needed for convergence of the Gibbs sampler. We also obtain a result that under certain conditions, the EM algorithm used for finding the maximum likelihood estimates can be slower to converge than the corresponding Gibbs sampler for Bayesian inference. We illustrate our results in a number of realistic examples all based on the generalized linear mixed models.     

On a class of m out of n bootstrap confidence intervals

It is widely known that bootstrap failure can often be remedied by using a technique known as the ' m out of n ' bootstrap, by which a smaller number, m say, of observations are resampled from the original sample of size n . In successful cases of the bootstrap, the m out of n bootstrap is often deemed unnecessary. We show that the problem of constructing nonparametric confidence intervals is an exceptional case. By considering a new class of m out of n bootstrap confidence limits, we develop a computationally efficient approach based on the double bootstrap to construct the optimal m out of n bootstrap intervals. We show that the optimal intervals have a coverage accuracy which is comparable with that of the classical double-bootstrap intervals, and we conduct a simulation study to examine their performance. The results are in general very encouraging. Alternative approaches which yield even higher order accuracy are also discussed.     

Estimating the Relative Density of Snapper in and around a Marine Reserve Using a Log-Linear Mixed-Effects Model

Angling from small recreational fishing boats was used as a sampling method to quantify the relative density of snapper ( Pagrus auratus ) in six areas within the Cape Rodney-Okakari Point Marine Reserve (New Zealand) and four areas adjacent to the reserve. Penalized quasi-likelihood was used to fit a log-linear mixed-effects model having area and date as fixed effects and boat as a random effect. Simulation and first-order bias correction formulae were employed to assess the validity of the estimates of the area effects. The bias correction is known to be unsuitable for general use because it typically over-estimatesbias, and this was observed here. However, it was qualitatively useful for indicating the direction of bias and for indicating when estimators were approximately unbiased. The parameter of primary interest was the ratio of snapper density in the marine reserve versus snapper density outside the reserve, and the estimator of this parameter was first-order asymptotically unbiased. This ratio of snapper densities was estimated to be 11 (±3).     

District-level poverty estimation: a proposed method

This paper develops a method of estimating micro-level poverty in cases where data are scarce. The method is applied to estimate district-level poverty using the household level Indian national sample survey data for two states, viz., West Bengal and Madhya Pradesh. The method involves estimation of state-level poverty indices from the data formed by pooling data of all the districts (each time excluding one district) and multiplying this poverty vector with a known weight matrix to obtain the unknown district-level poverty vector. The proposed method is expected to yield reliable estimates at the district level, because the district-level estimate is now based on a much larger sample size obtained by pooling data of several districts. This method can be an alternative to the “small area estimation technique” for estimating poverty at sub-state levels in developing countries.     

Spatio-temporal modelling using B-spline for disease mapping: analysis of childhood cancer trends

To examine childhood cancer diagnoses in the province of Alberta, Canada during 1983–2004, we construct a generalized additive mixed model for the analysis of geographic and temporal variability of cancer ratios. In this model, spatially correlated random effects and temporal components are adopted. The interaction between space and time is also accommodated. Spatio-temporal models that use conditional autoregressive smoothing across the spatial dimension and B-spline over the temporal dimension are considered. We study the patterns of incidence ratios over time and identify areas with consistently high ratio estimates as areas for potential further investigation. We apply the method of penalized quasi-likelihood to estimate the model parameters. We illustrate this approach using a yearly data set of childhood cancer diagnoses in the province of Alberta, Canada during 1983–2004.     

A non-stationary spatial generalized linear mixed model approach for studying plant diversity

We analyze the multivariate spatial distribution of plant species diversity, distributed across three ecologically distinct land uses, the urban residential, urban non-residential, and desert. We model these data using a spatial generalized linear mixed model. Here plant species counts are assumed to be correlated within and among the spatial locations. We implement this model across the Phoenix metropolis and surrounding desert. Using a Bayesian approach, we utilized the Langevin–Hastings hybrid algorithm. Under a generalization of a spatial log-Gaussian Cox model, the log-intensities of the species count processes follow Gaussian distributions. The purely spatial component corresponding to these log-intensities are jointly modeled using a cross-convolution approach, in order to depict a valid cross-correlation structure. We observe that this approach yields non-stationarity of the model ensuing from different land use types. We obtain predictions of various measures of plant diversity including plant richness and the Shannon–Weiner diversity at observed locations. We also obtain a prediction framework for plant preferences in urban and desert plots.     

Relative risk regression for current status data in case‐cohort studies

We propose using the weighted likelihood method to fit a general relative risk regression model for the current status data with missing data as arise, for example, in case‐cohort studies. The missingness probability is either known or can be reasonably estimated. Asymptotic properties of the weighted likelihood estimators are established. For the case of using estimated weights, we construct a general theorem that guarantees the asymptotic normality of the M‐estimator of a finite dimensional parameter in a class of semiparametric models, where the infinite dimensional parameter is allowed to converge at a slower than parametric rate, and some other parameters in the objective function are estimated a priori. The weighted bootstrap method is employed to estimate the variances. Simulations show that the proposed method works well for finite sample sizes. A motivating example of the case‐cohort study from an HIV vaccine trial is used to demonstrate the proposed method. The Canadian Journal of Statistics 39: 557–577; 2011. © 2011 Statistical Society of Canada     

Non‐parametric Copula Estimation Under Bivariate Censoring

In this paper, we consider non‐parametric copula inference under bivariate censoring. Based on an estimator of the joint cumulative distribution function, we define a discrete and two smooth estimators of the copula. The construction that we propose is valid for a large range of estimators of the distribution function and therefore for a large range of bivariate censoring frameworks. Under some conditions on the tails of the distributions, the weak convergence of the corresponding copula processes is obtained in l^∞([0,1]²). We derive the uniform convergence rates of the copula density estimators deduced from our smooth copula estimators. Investigation of the practical behaviour of these estimators is performed through a simulation study and two real data applications, corresponding to different censoring settings. We use our non‐parametric estimators to define a goodness‐of‐fit procedure for parametric copula models. A new bootstrap scheme is proposed to compute the critical values.