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     

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.     

Statistical inference on the drift parameter in fractional Brownian motion with a deterministic drift

In statistical inference on the drift parameter a in the fractional Brownian motion W^H_t with the Hurst parameter H ∈ (0, 1) with a constant drift Y^H_t = at + W^H_t, there is a large number of options how to do it. We may, for example, base this inference on the properties of the standard normal distribution applied to the differences between the observed values of the process at discrete times. Although such methods are very simple, it turns out that more appropriate is to use inverse methods. Such methods can be generalized to non constant drift. For the hypotheses testing about the drift parameter a, it is more proper to standardize the observed process, and to use inverse methods based on the first exit time of the observed process of a pre-specified interval until some given time. These procedures are illustrated, and their times of decision are compared against the direct approach. Other generalizations are possible when the random part is a symmetric stochastic integral of a known, deterministic function with respect to fractional Brownian motion.     

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.     

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.     

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.     

对综合类文化期刊“一稿多投”现象的理性分析

本文试图从作者队伍、刊物自身机制、市场经济学、市场传播学以及著作权法等方面入手,对“一稿多投”这种“不甚光彩”的社会灰色现象,进行一些力图客观公正的理性分析,并对刊物今后怎样做才能真正杜绝“一稿多投”现象的产生,提出了一些自己的看法。     

LEVERAGE ADJUSTMENTS FOR DISPERSION MODELLING IN GENERALIZED NONLINEAR MODELS

For normal linear models, it is generally accepted that residual maximum likelihood estimation is appropriate when covariance components require estimation. This paper considers generalized linear models in which both the mean and the dispersion are allowed to depend on unknown parameters and on covariates. For these models there is no closed form equivalent to residual maximum likelihood except in very special cases. Using a modified profile likelihood for the dispersion parameters, an adjusted score vector and adjusted information matrix are found under an asymptotic development that holds as the leverages in the mean model become small. Subsequently, the expectation of the fitted deviances is obtained directly to show that the adjusted score vector is unbiased at least to O(1/n) . Exact results are obtained in the single‐sample case. The results reduce to residual maximum likelihood estimation in the normal linear case.     

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.