Winding Stairs: A sampling tool to compute sensitivity indices

Sensitivity analysis aims to ascertain how each model input factor influences the variation in the model output. In performing global sensitivity analysis, we often encounter the problem of selecting the required number of runs in order to estimate the first order and/or the total indices accurately at a reasonable computational cost. The Winding Stairs sampling scheme (Jansen M.J.W., Rossing W.A.H., and Daamen R.A. 1994. In: Gasman J. and van Straten G. (Eds.), Predictability and Nonlinear Modelling in Natural Sciences and Economics. pp. 334–343.) is designed to provide an economic way to compute these indices. The main advantage of it is the multiple use of model evaluations, hence reducing the total number of model evaluations by more than half. The scheme is used in three simulation studies to compare its performance with the classic Sobol' LP. Results suggest that the Jansen Winding Stairs method provides better estimates of the Total Sensitivity Indices at small sample sizes.     

Calculation of marginal densities for parameters of multinomial distributions

The full Bayesian analysis of multinomial data using informative and flexible prior distributions has, in the past, been restricted by the technical problems involved in performing the numerical integrations required to obtain marginal densities for parameters and other functions thereof. In this paper it is shown that Gibbs sampling is suitable for obtaining accurate approximations to marginal densities for a large and flexible family of posterior distributions—the family. The method is illustrated with a three-way contingency table. Two alternative Monte Carlo strategies are also discussed.     

Smooth Estimation of the Reliability Function

Problems with censored data arise quite frequently in reliability applications. Estimation of the reliability function is usually of concern. Reliability function estimators proposed by Kaplan and Meier (1958), Breslow (1972), are generally used when dealing with censored data. These estimators have the known properties of being asymptotically unbiased, uniformly strongly consistent, and weakly convergent to the same Gaussian process, when properly normalized. We study the properties of the smoothed Kaplan-Meier estimator with a suitable kernel function in this paper. The smooth estimator is compared with the Kaplan-Meier and Breslow estimators for large sample sizes giving an exact expression for an appropriately normalized difference of the mean square error (MSE) of the two estimators. This quantifies the deficiency of the Kaplan-Meier estimator in comparison to the smoothed version. We also obtain a non-asymptotic bound on an expected ₁-type error under weak conditions. Some simulations are carried out to examine the performance of the suggested method.     

Sample Size Calculation for Rank Tests Comparing K Survival Distributions

Rank tests, such as logrank or Wilcoxon rank sum tests, have been popularly used to compare survival distributions of two or more groups in the presence of right censoring. However, there has been little research on sample size calculation methods for rank tests to compare more than two groups. An existing method is based on a crude approximation, which tends to underestimate sample size, i.e., the calculated sample size has lower power than projected. In this paper we propose an asymptotically correct method and an approximate method for sample size calculation. The proposed methods are compared to other methods through simulation studies.     

A two-sample test for mean functions with increasing number of projections

We propose a test for equality of two means when data are functions and obtain the asymptotic properties of the test statistic as data dimension increases with the sample size. We also derive the asymptotic power of the test under some local alternatives and show that the test statistic is root-n consistent. A simulation study is conducted to evaluate the performance of the test numerically and to compare the proposed test with other existing four popular tests.     

Simultaneous inference on diversity of biological communities

In environmental statistics, surveys on the structure of biological communities are generally carried out by focusing on diversity indexes. A more complete analysis may be performed by means of an appropriate function giving a spectrum of different measures of diversity: diversity profiles. They can be expressed as a function of the unknown abundance vector of the ecological population. In this paper we develop a non parametric approach based on bootstrap in order to make inference on diversity profiles. The proposed procedure is applied on biological data of four parks in Milan, Italy.     

Convexity-based clustering criteria: theory,algorithms, and applications in statistics

This paper deals with the construction of optimum partitions of for a clustering criterion which is based on a convex function of the class centroids as a generalization of the classical SSQ clustering criterion for n data points. We formulate a dual optimality problem involving two sets of variables and derive a maximum-support-plane (MSP) algorithm for constructing a (sub-)optimum partition as a generalized k-means algorithm. We present various modifications of the basic criterion and describe the corresponding MSP algorithm. It is shown that the method can also be used for solving optimality problems in classical statistics (maximizing Csiszárs -divergence) and for simultaneous classification of the rows and columns of a contingency table.     

A tool to facilitate the production of control charts within a spreadsheet

Abstract

The adoption of control charts can be traced to the classic text by Shewhart (1931 Shewhart, W. A. 1931. Economic control of quality of manufactured product. London: Macmillan. ISBN: 1614278115. [Google Scholar]) and championed by many writers since then, including Deming (1982 Deming, W. E. 1982. Out of the crisis: Quality, productivity and competitive position. Cambridge: Cambridge University Press. ISBN: 0521305535. [Google Scholar]). Numerous other texts and publications stress the continuing importance of this area. While tables of key Shewhart control chart parameters are extremely useful they are easily lost or mislaid and can sometimes be difficult to interpret. To address this issue spreadsheet code is implemented to produce all the key control chart factors.     

Power comparison of data depth-based nonparametric tests for testing equality of locations

In the recent years, the notion of data depth has been used in nonparametric multivariate data analysis since it gives natural ‘centre-outward’ ordering of multivariate data points with respect to the given data cloud. In the literature, various nonparametric tests are developed for testing equality of location of two multivariate distributions based on data depth. Here, we define two nonparametric tests based on two different test statistic for testing equality of locations of two multivariate distributions. In the present work, we compare the performance of these tests with the tests developed by Li and Liu [New nonparametric tests of multivariate locations and scales using data depth. Statist Sci. 2004;(1):686–696] for testing equality of locations of two multivariate distributions. Comparison in terms of power is done for multivariate symmetric and skewed distributions using simulation for three popular depth functions. Application of tests to real life data is provided. Conclusion and recommendations are also provided.