A volume based approach to establish B-spline based expressions for density functions and its application to progressive hybrid censoring

We propose an approach to determine the distribution of particular linear combinations of hybrid censored order statistics which is based on the calculation of volumes of polytopes. For this purpose, we establish efficient and compact volume formulas in terms of B-splines. Further, we illustrate our approach for ten different progressive hybrid censoring schemes under an exponential assumption.     

Nonparametric estimation of multivariate extreme-value copulas

Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to certain shape constraints that arise from an integral transform of an underlying measure called spectral measure. Multivariate extensions are provided of certain rank-based nonparametric estimators of the Pickands dependence function. The shape constraint that the estimator should itself be a Pickands dependence function is enforced by replacing an initial estimator by its best least-squares approximation in the set of Pickands dependence functions having a discrete spectral measure supported on a sufficiently fine grid. Weak convergence of the standardized estimators is demonstrated and the finite-sample performance of the estimators is investigated by means of a simulation experiment.     

Mixture experiments with mixing errors

In mixture experiments the properties of mixtures are usually studied by mixing the amounts of the mixture components that are required to obtain the necessary proportions. This paper considers the impact of inaccuracies in discharging the required amounts of the mixture components on the statistical analysis of the data. It shows how the regression calibration approach can be used to minimize the resulting bias in the model and in the estimates of the model parameters, as well as to find correct estimates of the corresponding variances. Its application is made difficult by the complex structure of these errors. We also show how knowledge of the form of the model bias allows for choosing a manufacturing setting for a mixture product that is not biased and has smaller signal to noise ratio.     

Computing monotone disjoint paths on polytopes

The Holt-Klee Condition states that there exist at least d vertex-disjoint strictly monotone paths from the source to the sink of a polytopal digraph consisting of the set of vertices and arcs of a polytope P directed by a linear objective function in general position. The study of paths on polytopal digraphs stems from a long standing problem, that of designing a polynomial-time pivot method, or proving none exists. To study disjoint paths it would be useful to have a tool to compute them. Without explicitly computing the digraph we develop an algorithm to compute a maximum cardinality set of source to sink paths in a polytope, even in the presence of degeneracy. The algorithm uses a combination of networks flows, the simplex method, and reverse search. An implementation is available.     

REGRESSION DIAGNOSTICS FOR THE LEAST ABSOLUTE DEVIATIONS AND THE MINIMAX METHODS

Abstract

In this article, we extend the concept of univariate frailty to a bivariate case to quantify and visualize the loss of efficiency of the log-rank test when a dependence structure between failure and censoring times is being ignored. We assume that an unobservable frailty influences the risk of failure and the other affects the risk of censoring, and those two frailties are correlated. Under the model being compared as a benchmark, the dependence structure between failure and censoring times is assumed to be completely observed. Under the model where the log-rank test is constructed without considering the dependency between failure and censoring times, it is assumed that the unobservable dependence structure has been absorbed into the baseline distributions. We note in our particular example that the loss of efficiency is minimal under the proportional hazards model even when the correlation between potential failure and censoring times is strong unless the dependence censorship induces a severe nonproportionality.     

Tucker3 Model for Compositional Data

For the exploratory analysis of three-way data, the Tucker3 is one of the most applied models to study three-way arrays when the data are quadrilinear. When the data consist of vectors of positive values summing to a unit, as in the case of compositional data, this model should consider the specific problems that compositional data analysis brings. The main purpose of this paper is to describe how to do a Tucker3 analysis of compositional data, and to show the relationships between the loading matrices when different preprocessing procedures are used.     

Simplex representation of insurance performance analysis

The general belief in the insurance industry is that underwriting is a loss-making segment but is essential as it generates cash flow. The underwriting losses are cross-subsidized by investment income resulting in overall profits. In this paper, we investigate if the same is true in the Indian context. For this Simplex representation, (also known as trilinear plot or Saari Triangle) a tool in the field of political science, is adapted. Simplex representation can give an instant understanding of the relative performance of a company in any segment/domain. The study reveals that, contrary to expectation, it is reinsurance that has contributed more to overall aggregate performance as against investment.     

求解一类特殊线性规划问题的多最优解的围墙法

用单纯形法求解线性规划问题的多最优解,对一类特殊的可行域,有时会导致失效。对此,在单纯形法的基础上,本文提出了一种行之有效的围墙法,弥补了单纯形法的缺陷。     

Implementation of saddlepoint approximations in resampling problems

In many situations saddlepoint approximations can replace the Monte Carlo simulation typically used to find the bootstrap distribution of a statistic. We explain how bootstrap and permutation distributions can be expressed as conditional distributions and how methods for linear programming and for fitting generalized linear models can be used to find saddlepoint approximations to these distributions. The ideas are illustrated using an example from insurance.