A theoretical basis for perturbation methods

In this paper we discuss a new theoretical basis for perturbation methods. In developing this new theoretical basis, we define the ideal measures of data utility and disclosure risk. Maximum data utility is achieved when the statistical characteristics of the perturbed data are the same as that of the original data. Disclosure risk is minimized if providing users with microdata access does not result in any additional information. We show that when the perturbed values of the confidential variables are generated as independent realizations from the distribution of the confidential variables conditioned on the non-confidential variables, they satisfy the data utility and disclosure risk requirements. We also discuss the relationship between the theoretical basis and some commonly used methods for generating perturbed values of confidential numerical variables.     

Understanding racial literacy through acts of (un)masking: Latinx teachers in a new Latinx diaspora community

As Latinx teachers are recruited to work in U.S. schools, a continued agenda to understand their experiences is warranted. This multiple case study considers the storytelling of six Latinx teachers in a new Latinx diaspora community. It documents both their racial literacy (the ability to resolve racially stressful issues) and their experiences with (un)masking (literal and figurative ways to cover or embrace racial markers). This study reveals the tensions that arise when Latinx teachers attempt to define their identity in social spaces where their languages, bodies, and names, among other markers, are racialized when read by others. Implications for teacher education include a call to include storytelling as a pedagogical tool to develop Latinx teachers’ racial literacy skills. By experiencing storytelling in their own schooling, Latinx teachers are more likely to model such racial literacy skills in their schooling communities; thereby, empowering a generation of students to enact more humanizing behaviors.     

Parametric Modeling for Survival with Competing Risks and Masked Failure Causes

We consider a life testing situation in which systems are subject to failure from independent competing risks. Following a failure, immediate (stage-1) procedures are used in an attempt to reach a definitive diagnosis. If these procedures fail to result in a diagnosis, this phenomenon is called masking. Stage-2 procedures, such as failure analysis or autopsy, provide definitive diagnosis for a sample of the masked cases. We show how stage-1 and stage-2 information can be combined to provide statistical inference about (a) survival functions of the individual risks, (b) the proportions of failures associated with individual risks and (c) probability, for a specified masked case, that each of the masked competing risks is responsible for the failure. Our development is based on parametric distributional assumptions and the special case for which the failure times for the competing risks have a Weibull distribution is discussed in detail.     

Dependent masking and system life data analysis: Bayesian inference for two-component systems

Data from field operations of a system is often used to estimate the reliability of components. Under ideal circumstances, this system field data contains the time to failure along with information on the exact component responsible for the system failure. However, in many cases, the exact component causing the failure of the system cannot be identified, and is considered to be masked. Previously developed models for estimation of component reliability from masked system life data have been based upon the assumption that masking occurs independently of the true cause of system failure. In this paper we develop a Bayesian methodology for estimating component reliabilities from masked system life data when the probability of masking is dependent upon the true cause of system failure. The Bayesian approach is illustrated for the case of a two-component system of exponentially distributed components.     

Locally best invariant test for outliers in a gamma type distribution

It is shown that the locally best invariant test for the existence of outliers for scale parameters of the gamma distribution is given by Bartholomew's test for exponentiality which is the ratio of the sum of squares of the data to the square of the sample mean. The optimality robustness, including null and nonnull robustness of the test is shown. A small simulation study to compare the power among the other eight competitive tests for testing exponentiality is performed. It is seen that the locally best invariant test is not always best but is reasonably good. It is slightly better than Cochran's test and suffers less from the limiting masking effect.     

Should an OEM Retain Component Procurement when the CM Produces Competing Products?

We consider a large original equipment manufacturer (OEM) who relies on a contract manufacturer (CM) to produce her product. In addition to the OEM's product, the CM also produces for a smaller OEM. Both the larger OEM and the CM can purchase the component from the supplier, but their purchase prices may differ and remain unknown to each other. The main question we address is whether the larger OEM should retain component procurement by purchasing components from the supplier and reselling to the CM (buy–sell), or outsource component procurement by letting the CM purchase directly from the supplier (turnkey). We show that, under buy–sell, the larger OEM's optimal strategy is to resell components at the highest possible component purchase price of the CM (i.e., the street price). By comparing buy–sell and turnkey, we find that a CM with low component price is better off under turnkey, even though under buy–sell he receives more profits through the products sold to the smaller OEM. Furthermore, the larger OEM's preference between buy–sell and turnkey depends on her component price, the volatility of the CM's component price and substitutability between the two products.     

The stalactite plot for the detection of multivariate outliers

Detection of multiple outliers in multivariate data using Mahalanobis distances requires robust estimates of the means and covariance of the data. We obtain this by sequential construction of an outlier free subset of the data, starting from a small random subset. The stalactite plot provides a cogent summary of suspected outliers as the subset size increases. The dependence on subset size can be virtually removed by a simulation-based normalization. Combined with probability plots and resampling procedures, the stalactite plot, particularly in its normalized form, leads to identification of multivariate outliers, even in the presence of appreciable masking.     

Cluster-based multivariate outlier identification and re-weighted regression in linear models

A cluster methodology, motivated by a robust similarity matrix is proposed for identifying likely multivariate outlier structure and to estimate weighted least-square (WLS) regression parameters in linear models. The proposed method is an agglomeration of procedures that begins from clustering the n-observations through a test of ‘no-outlier hypothesis’ (TONH) to a weighted least-square regression estimation. The cluster phase partition the n-observations into h-set called main cluster and a minor cluster of size n?h. A robust distance emerge from the main cluster upon which a test of no outlier hypothesis’ is conducted. An initial WLS regression estimation is computed from the robust distance obtained from the main cluster. Until convergence, a re-weighted least-squares (RLS) regression estimate is updated with weights based on the normalized residuals. The proposed procedure blends an agglomerative hierarchical cluster analysis of a complete linkage through the TONH to the Re-weighted regression estimation phase. Hence, we propose to call it cluster-based re-weighted regression (CBRR). The CBRR is compared with three existing procedures using two data sets known to exhibit masking and swamping. The performance of CBRR is further examined through simulation experiment. The results obtained from the data set illustration and the Monte Carlo study shows that the CBRR is effective in detecting multivariate outliers where other methods are susceptible to it. The CBRR does not require enormous computation and is substantially not susceptible to masking and swamping.     

Stepwise local influence in generalized autoregressive conditional heteroskedasticity models

Detection of outliers or influential observations is an important work in statistical modeling, especially for the correlated time series data. In this paper we propose a new procedure to detect patch of influential observations in the generalized autoregressive conditional heteroskedasticity (GARCH) model. Firstly we compare the performance of innovative perturbation scheme, additive perturbation scheme and data perturbation scheme in local influence analysis. We find that the innovative perturbation scheme give better result than other two schemes although this perturbation scheme may suffer from masking effects. Then we use the stepwise local influence method under innovative perturbation scheme to detect patch of influential observations and uncover the masking effects. The simulated studies show that the new technique can successfully detect a patch of influential observations or outliers under innovative perturbation scheme. The analysis based on simulation studies and two real data sets show that the stepwise local influence method under innovative perturbation scheme is efficient for detecting multiple influential observations and dealing with masking effects in the GARCH model.     

A Perturbation Approach to Outlier Detection in Two-Way Contingency Tables

In order to identify outliers in contingency tables, we evaluate the derivatives of the perturbation-formed surface of the Pearson goodness-of-fit statistic. The resulting diagnostics are shown to be less susceptible to masking and swamping problems than residual-based measures. A Monte Carlo study further confirms the effectiveness of the proposed diagnostics.