Empirical likelihood weighted composite quantile regression with partially missing covariates

This paper develops a novel weighted composite quantile regression (CQR) method for estimation of a linear model when some covariates are missing at random and the probability for missingness mechanism can be modelled parametrically. By incorporating the unbiased estimating equations of incomplete data into empirical likelihood (EL), we obtain the EL-based weights, and then re-adjust the inverse probability weighted CQR for estimating the vector of regression coefficients. Theoretical results show that the proposed method can achieve semiparametric efficiency if the selection probability function is correctly specified, therefore the EL weighted CQR is more efficient than the inverse probability weighted CQR. Besides, our algorithm is computationally simple and easy to implement. Simulation studies are conducted to examine the finite sample performance of the proposed procedures. Finally, we apply the new method to analyse the US news College data.     

Modeling material stress using integrated Gaussian Markov random fields

The equations of a physical constitutive model for material stress within tantalum grains were solved numerically using a tetrahedrally meshed volume. The resulting output included a scalar vonMises stress for each of the more than 94,000 tetrahedra within the finite element discretization. In this paper, we define an intricate statistical model for the spatial field of vonMises stress which uses the given grain geometry in a fundamental way. Our model relates the three-dimensional field to integrals of latent stochastic processes defined on the vertices of the one- and two-dimensional grain boundaries. An intuitive neighborhood structure of the said boundary nodes suggested the use of a latent Gaussian Markov random field (GMRF). However, despite the potential for computational gains afforded by GMRFs, the integral nature of our model and the sheer number of data points pose substantial challenges for a full Bayesian analysis. To overcome these problems and encourage efficient exploration of the posterior distribution, a number of techniques are now combined: parallel computing, sparse matrix methods, and a modification of a block update strategy within the sampling routine. In addition, we use an auxiliary variables approach to accommodate the presence of outliers in the data.     

Optimal Change-point Estimation in Inverse Problems

We develop a method of estimating a change-point of an otherwise smooth function in the case of indirect noisy observations. As two paradigms we consider deconvolution and non-parametric errors-in-variables regression. In a similar manner to well-established methods for estimating change-points in non-parametric regression, we look essentially at the difference of one-sided kernel estimators. Because of the indirect nature of the observations we employ deconvoluting kernels. We obtain an estimate of the change-point by the extremal point of the differences between these two-sided kernel estimators. We derive rates of convergence for this estimator. They depend on the degree of ill-posedness of the problem, which derives from the smoothness of the error density. Analysing the Hellinger modulus of continuity of the problem we show that these rates are minimax     

有限域Fq上矩阵的广义逆及矩阵Kronecker积

给出了Fq上矩阵群逆和E-P逆和E-P逆及矩阵Kronecker积的弱广义Schur补定义,并讨论了其相应的特殊性质.     

On best affine prediction

The theory of best affine prediction (BAP) is extended to the vector case with possibly singular variance matrix of the predictor variable. The theory is then applied to derive Thomson’s classical predictor for factor scores, allowing for a singular variance matrix of the factors. The results are formulated in a free distribution setting. Further, Bartlett’s estimator is considered and compared with Thomson’s predictor. The authors are thankful to the two referees, one for a suggestion that led to the Addendum of the paper, and the other one for several very useful remarks. Research supported by the Spanish grant BEC2000-0983.     

A theory of statistical models for Monte Carlo integration

Summary. The task of estimating an integral by Monte Carlo methods is formulated as a statistical model using simulated observations as data. The difficulty in this exercise is that we ordinarily have at our disposal all of the information required to compute integrals exactly by calculus or numerical integration, but we choose to ignore some of the information for simplicity or computational feasibility. Our proposal is to use a semiparametric statistical model that makes explicit what information is ignored and what information is retained. The parameter space in this model is a set of measures on the sample space, which is ordinarily an infinite dimensional object. None-the-less, from simulated data the base-line measure can be estimated by maximum likelihood, and the required integrals computed by a simple formula previously derived by Vardi and by Lindsay in a closely related model for biased sampling. The same formula was also suggested by Geyer and by Meng and Wong using entirely different arguments. By contrast with Geyer's retrospective likelihood, a correct estimate of simulation error is available directly from the Fisher information. The principal advantage of the semiparametric model is that variance reduction techniques are associated with submodels in which the maximum likelihood estimator in the submodel may have substantially smaller variance than the traditional estimator. The method is applicable to Markov chain and more general Monte Carlo sampling schemes with multiple samplers.     

Fitting and comparing seed germination models with a focus on the inverse normal distribution

This paper reviews current methods for fitting a range of models to censored seed germination data and recommends adoption of a probability‐based model for the time to germination. It shows that, provided the probability of a seed eventually germinating is not on the boundary, maximum likelihood estimates, their standard errors and the resultant deviances are identical whether only those seeds which have germinated are used or all seeds (including seeds ungerminated at the end of the experiment). The paper recommends analysis of deviance when exploring whether replicate data are consistent with a hypothesis that the underlying distributions are identical, and when assessing whether data from different treatments have underlying distributions with common parameters. The inverse normal distribution, otherwise known as the inverse Gaussian distribution, is discussed, as a natural distribution for the time to germination (including a parameter to measure the lag time to germination). The paper explores some of the properties of this distribution, evaluates the standard errors of the maximum likelihood estimates of the parameters and suggests an accurate approximation to the cumulative distribution function and the median time to germination. Additional material is on the web, at http://www.agric.usyd.edu.au/staff/oneill/ .     

分块结式矩阵逆阵的快速算法

利用结式矩阵求逆矩阵的多项式快速算法,给出了具有结式矩阵块的分块矩阵逆矩阵的一种快速算法。该算法仅用结式矩阵的第一行元素进行计算,在计算机上实现时只有舍入误差,故在理论上是精确的。最后给出了应用该算法的数值例子。     

Bayesian analysis of covariance under inverse Gaussian model

This paper considers the problem of analysis of covariance (ANCOVA) under the assumption of inverse Gaussian distribution for response variable from the Bayesian point of view. We develop a fully Bayesian model for ANCOVA based on the conjugate prior distributions for parameters contained in the model. The Bayes estimator of parameters, ANCOVA model and adjusted effects for both treatments and covariates along with predictive distribution of future observations are developed. We also provide the essentials for comparing adjusted treatments effects and adjusted factor effects. A simulation study and a real world application are also performed to illustrate and evaluate the proposed Bayesian model.     

Systematic handling of missing data in complex study designs – experiences from the Health 2000 and 2011 Surveys

We present a systematic approach to the practical and comprehensive handling of missing data motivated by our experiences of analyzing longitudinal survey data. We consider the Health 2000 and 2011 Surveys (BRIF8901) where increased non-response and non-participation from 2000 to 2011 was a major issue. The model assumptions involved in the complex sampling design, repeated measurements design, non-participation mechanisms and associations are presented graphically using methodology previously defined as a causal model with design, i.e. a functional causal model extended with the study design. This tool forces the statistician to make the study design and the missing-data mechanism explicit. Using the systematic approach, the sampling probabilities and the participation probabilities can be considered separately. This is beneficial when the performance of missing-data methods are to be compared. Using data from Health 2000 and 2011 Surveys and from national registries, it was found that multiple imputation removed almost all differences between full sample and estimated prevalences. The inverse probability weighting removed more than half and the doubly robust method 60% of the differences. These findings are encouraging since decreasing participation rates are a major problem in population surveys worldwide.