Point-symmetry models and decomposition for collapsed square contingency tables

For square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed tables with some adjacent categories combined in the original table. This paper proposes three kinds of new models which have the structure of point-symmetry (PS), quasi point-symmetry and marginal point-symmetry for collapsed square tables. This paper also gives a decomposition of the PS model for collapsed square tables. The father's and his daughter's occupational mobility data are analyzed using new models.     

Asymptotic normality of the deconvolution kernel density estimator under the vanishing error variance

Let $X_1,\dots ,X_n$ be i.i.d. observations, where $X_i=Y_i+{\sigma }_n{Z}_i$ and the $Y$’s and $Z$’s are independent. Assume that the $Y$’s are unobservable and that they have the density $f$ and also that the $Z$’s have a known density $k$. Furthermore, let ${\sigma }_n$ depend on $n$ and let ${\sigma }_n\to 0$ as $n\to \infty$. We consider the deconvolution problem, i.e. the problem of estimation of the density $f$ based on the sample $X_1,\dots ,X_n$. A popular estimator of $f$ in this setting is the deconvolution kernel density estimator. We derive its asymptotic normality under two different assumptions on the relation between the sequence ${\sigma }_n$ and the sequence of bandwidths $h_n$. We also consider several simulation examples which illustrate different types of asymptotics corresponding to the derived theoretical results and which show that there exist situations where models with ${\sigma }_n\to 0$ have to be preferred to the models with fixed $\sigma$.     

A New Test on High-Dimensional Mean Vector Without Any Assumption on Population Covariance Matrix

In this paper, a new test for the equality of the mean vectors between a two groups with the same number of the observations in high-dimensional data. The existing tests for this problem require a strong condition on the population covariance matrix. The proposed test in this paper does not require such conditions for it. This test will be obtained in a general model, that is, the data need not be normally distributed.     

Decompounding discrete distributions: A nonparametric Bayesian approach

Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a nonparametric Bayesian approach to estimate the intensity of the underlying Poisson process and the distribution of the jumps. We provide a Markov chain Monte Carlo scheme for obtaining samples from the posterior. We apply our method on both simulated and real data examples, and compare its performance with the frequentist plug-in estimator proposed by Buchmann and Grübel. On a theoretical side, we study the posterior from the frequentist point of view and prove that as the sample size n→∞, it contracts around the “true,” data-generating parameters at rate $1/\sqrt{n}$, up to a $\log n$ factor.     

Analyzing Collision,Grounding, and Sinking Accidents Occurring in the Black Sea Utilizing HFACS and Bayesian Networks

This study examines and analyzes marine accidents that have occurred over the past 20 years in the Black Sea. Geographic information system, human factor analysis and classification system (HFACS), and Bayesian network models are used to analyze the marine accidents. The most important feature distinguishing this study from other studies is that this is the first study to analyze accidents that have occurred across the whole Black Sea. Another important feature is the application of a new HFACS structure to reveal accident formation patterns. The results of this study indicate that accidents occurred in high concentrations in coastal regions of the Black Sea, especially in the Kerch Strait, Novorossiysk, Kilyos, Constanta, Riva, and Batumi regions. The formation of grounding and sinking accidents has been found to be similar in nature; the use of inland and old vessels has been highlighted as important factors in sinking and grounding incidents. However, the sequence of events leading to collision-contact accidents differs from the sequence of events resulting in grounding and sinking accidents. This study aims to provide information to the maritime industry regarding the occurrence of maritime incidents in the Black Sea, in order to assist with reduction and prevention of the marine accidents.     

Positive-definite modification of a covariance matrix by minimizing the matrix $$\ell_{\infty}$$ ℓ ∞ norm with applications to portfolio optimization

AStA Advances in Statistical Analysis - The covariance matrix, which should be estimated from the data, plays an important role in many multivariate procedures, and its positive definiteness...     

Asymptotic properties of the maximum smoothed partial likelihood estimator in the change-plane Cox model

The change-plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the finite-dimensional parameter. Particularly, the convergence rate, not to mention the asymptotic distribution, has not been fully characterized for the general model where classification is based on multiple covariates. To bridge this theoretical gap, this study proposes a maximum smoothed partial likelihood estimator and establishes the following asymptotic properties. First, it shows that the convergence rate for the classification parameter can be arbitrarily close to $n^{-1}$ up to a logarithmic factor under a certain condition on covariates and the choice of tuning parameter. Given this convergence rate result, it also establishes the asymptotic normality for the regression parameter.