Frailty Models for Arbitrarily Censored and Truncated Data

In this paper, we propose a frailty model for statistical inference in the case where we are faced with arbitrarily censored and truncated data. Our results extend those of Alioum and Commenges (1996), who developed a method of fitting a proportional hazards model to data of this kind. We discuss the identifiability of the regression coefficients involved in the model which are the parameters of interest, as well as the identifiability of the baseline cumulative hazard function of the model which plays the role of the infinite dimensional nuisance parameter. We illustrate our method with the use of simulated data as well as with a set of real data on transfusion-related AIDS.     

The Efficacy of Different Methods for Informing the Public About the Range Dependency of Magnetic Fields from High Voltage Power Lines

The AC electric and magnetic fields associated with high voltage power lines have become a concern as a possible health risk. In most cases the strength of these fields decreases as the inverse square of the distance from the line. In earlier work, we found that laypeople do not understand how rapidly field strength decreases with distance. Most believe that any high voltage power line they can see is exposing them to strong fields. This paper confirms the earlier finding and explores a number of strategies which might be used in risk communications to correct this misperception. We found it relatively easy to provide subjects with a better understanding of the range-dependency of magnetic field strength. Moreover, the quality of this acquisition was apparently independent of the manner in which they were instructed. Such successful instruction is markedly different from the well-established difficulty of teaching people about many qualitative domains, such as physics or ideas in probability. Clearly, while some erroneous beliefs are highly resistant to change, others can be altered quite readily. We suspect that an important distinction between knowledge about the range-dependency of power-frequency magnetic fields and less tractable topics involves the presence or absence of prior folk-theories or "mental models" of the domain.     

Generalized Inverse Gaussian Distributions and their Wishart Connections

The matrix generalized inverse Gaussian distribution (MGIG) is shown to arise as a conditional distribution of components of a Wishart distributio n. In the special scalar case, the characterization refers to members of the class of generalized inverse Gaussian distributions (GIGs) and includes the inverse Gaussian distribution among others     

Variable selection for high-dimensional generalized linear model with block-missing data

In modern scientific research, multiblock missing data emerges with synthesizing information across multiple studies. However, existing imputation methods for handling block-wise missing data either focus on the single-block missing pattern or heavily rely on the model structure. In this study, we propose a single regression-based imputation algorithm for multiblock missing data. First, we conduct a sparse precision matrix estimation based on the structure of block-wise missing data. Second, we impute the missing blocks with their means conditional on the observed blocks. Theoretical results about variable selection and estimation consistency are established in the context of a generalized linear model. Moreover, simulation studies show that compared with existing methods, the proposed imputation procedure is robust to various missing mechanisms because of the good properties of regression imputation. An application to Alzheimer's Disease Neuroimaging Initiative data also confirms the superiority of our proposed method.     

Bayesian inverse problems with heterogeneous variance

We consider inverse problems in Hilbert spaces under correlated Gaussian noise, and use a Bayesian approach to find their regularized solution. We focus on mildly ill-posed inverse problems with fractional noise, using a novel wavelet-based vaguelette–vaguelette approach. It allows us to apply sequence space methods without assuming that all operators are simultaneously diagonalizable. The results are proved for more general bases and covariance operators. Our primary aim is to study posterior contraction rate in such inverse problems over Sobolev classes and compare it to the derived minimax rate. Secondly, we study effect of plugging in a consistent estimator of variances in sequence space on the posterior contraction rate. This result is applied to the problem with error in forward operator. Thirdly, we show that empirical Bayes posterior distribution with a plugged-in maximum marginal likelihood estimator of the prior scale contracts at the optimal rate, adaptively, in the minimax sense.     

Empirical likelihood and Wilks phenomenon for data with nonignorable missing values

Wilks's theorem is useful for constructing confidence regions. When applying the popular empirical likelihood to data with nonignorable nonresponses, Wilks's phenomenon does not hold. This paper unveils that this is caused by the extra estimation of the nuisance parameter in the nonignorable nonresponse propensity. Motivated by this result, we propose an adjusted empirical likelihood for which Wilks's theorem holds. Asymptotic results are presented and supplemented by simulation results for finite sample performance of the point estimators and confidence regions. An analysis of a data set is included for illustration.     

Performance of ridge estimator in inverse Gaussian regression model

The presence of multicollinearity among the explanatory variables has undesirable effects on the maximum likelihood estimator (MLE). Ridge estimator (RE) is a widely used estimator in overcoming this issue. The RE enjoys the advantage that its mean squared error (MSE) is less than that of MLE. The inverse Gaussian regression (IGR) model is a well-known model in the application when the response variable positively skewed. The purpose of this paper is to derive the RE of the IGR under multicollinearity problem. In addition, the performance of this estimator is investigated under numerous methods for estimating the ridge parameter. Monte Carlo simulation results indicate that the suggested estimator performs better than the MLE estimator in terms of MSE. Furthermore, a real chemometrics dataset application is utilized and the results demonstrate the excellent performance of the suggested estimator when the multicollinearity is present in IGR model.     

The mixture of left–right truncated normal distributions

This paper introduces the mixture of left–right truncated normal distributions, from the spreads between bid and ask prices, as a statistical model for handle non-normality of asset price returns. It has been proved that there is only one maximum for the likelihood function of the new model.     

非线性反问题同伦反演的一般格式

针对非线性算子参数识别反问题,引入具有大范围收敛特性的同伦算法,构造了同伦反演求解的一般格式。     

Dynamic approach to linear statistical calibration with an application in microwave radiometry

The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the ‘classical’ approach and the ‘inverse’ regression approach. Both of these models are static models and are used to estimate exact measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe it. The Bayesian time series analysis method of Dynamic Linear Models can be used to monitor the evolution of the measures, thus introducing a dynamic approach to statistical calibration. The research presented employs a new approach to performing statistical calibration. A simulation study in the context of microwave radiometry is conducted that compares the dynamic model to traditional static frequentist and Bayesian approaches. The focus of the study is to understand how well the dynamic statistical calibration method performs under various signal-to-noise ratios, r.