TEST

We consider two families of short-tailed distributions (kurtosis less than 3) and discuss their usefulness in modeling numerous real life data sets. We develop estimation and hypothesis testing procedures which are efficient and robust to short-tailed distributions and inliers.

Robust Bayesian analysis is the study of the sensitivity of Bayesian answers to uncertain inputs. This paper seeks to provide an overview of the subject, one that is accessible to statisticians outside the field. Recent developments in the area are also reviewed, though with very uneven emphasis.

We develop a procedure for monitoring changes in the error distribution of autoregressive time series while controlling the overall size of the sequential test. The proposed procedure, unlike standard procedures which are also referred to, utilizes the empirical characteristic function of properly estimated residuals. The limit behavior of the test statistic is investigated under the null hypothesis as well as under alternatives. Since the asymptotic null distribution contains unknown parameters, a bootstrap procedure is proposed in order to actually perform the test and corresponding results on the finite–sample performance of the new method are presented. As it turns out the procedure is not only able to detect distributional changes but also changes in the regression coefficient.

This paper proposes a new model-based approach to estimate small areas that extends the Fay–Herriot methodology. The new model is additive, with a random term to characterize the inter-area variability and a nonparametric mean function specification, defined using the information on an auxiliary variable. The most significant advantage of the proposal is that it avoids the model misspecification problem. The monotonicity is the only assumption about the functional form of the relationship between the variable of interest and the auxiliary one. Estimators for the area means are derived combining “Order Restricted Inference” and standard mixed model approaches. A large simulation experiment shows how the new approach outperforms the Fay–Herriot methodology in many scenarios. Besides, the new method is applied to the Australian farms data.

We propose a “NOVEL Integration of the Sample and Thresholded covariance” (NOVELIST) estimator to estimate the large covariance (correlation) and precision matrix. NOVELIST estimator performs shrinkage of the sample covariance (correlation) towards its thresholded version. The sample covariance (correlation) component is non-sparse and can be low rank in high dimensions. The thresholded sample covariance (correlation) component is sparse, and its addition ensures the stable invertibility of NOVELIST. The benefits of the NOVELIST estimator include simplicity, ease of implementation, computational efficiency and the fact that its application avoids eigenanalysis. We obtain an explicit convergence rate in the operator norm over a large class of covariance (correlation) matrices when the dimension p and the sample size n satisfy log $$ p/n\rightarrow 0$$ , and its improved version when $$p/n \rightarrow 0$$ . In empirical comparisons with several popular estimators, the NOVELIST estimator performs well in estimating covariance and precision matrices over a wide range of models and sparsity classes. Real-data applications are presented.