Diana Kelmansky

A Class of Locally and Globally Robust Regression Estimates

Abstract We present a new class of regression estimates called generalized τ estimates. These estimates are defined by minimizing the τ scale of the weighted residuals, with weights that penalize high-leverage observations. Like the τ estimates, the generalized τ estimates utilize for their definition two loss functions, ρ1 and ρ2, which together with the weights can be chosen to achieve simultaneously high breakdown point, finite gross error sensitivity, and high efficiency. We recommend, however, choosing these functions so as to control the bias behavior of the estimate for a large range of possible contaminations and then boosting the efficiency by a simple least squares reweighting step. The generalized τ estimate with loss functions ρ1 and ρ2 is related to the Hill–Ryan GM estimate with a loss function ρ, which is a linear combination of ρ1 and ρr. In fact, both estimates have the same influence function and asymptotic distribution under the central model. We show that a certain generalized τ estima...

Estimators based on ranks for ARMA models

In this paper we introduce a new family of robust estimators for ARMA models. These estimators are defined by replacing the residual sample autocovariances in the least squares equations by autocovariances based on ranks. The asymptotic normality of the proposed estimators is provided. The efficiency and robustness properties of these estimators are studied. An adequate choice of the score functions gives estimators which have high efficiency under normality and robustness in the presence of outliers. The score functions can also be chosen so that the resulting estimators are asymptotically as efficient as the maximum likelihood estimators for a given distribution.

A New Goodness-of-Fit Test for Censored Data with an Application in Monitoring Processes

In this article, we propose a new goodness-of-fit test for Type I or Type II censored samples from a completely specified distribution. This test is a generalization of Michaels test for censored data, which is based on the empirical distribution and a variance stabilizing transformation. Using Monte Carlo methods, the distributions of the test statistics are analyzed under the null hypothesis. Tables of quantiles of these statistics are also provided. The power of the proposed test is studied and compared to that of other well-known tests also using simulation. The proposed test is more powerful in most of the considered cases. Acceptance regions for the PP, QQ, and Michaels stabilized probability plots are derived, which enable one to visualize which data contribute to the decision of rejecting the null hypothesis. Finally, an application in quality control is presented as illustration.

On the glog-normal distribution and its application to the gene expression problem

In this article, we characterized the glog-normal distribution and present a comprehensive treatment of the properties of this model. Specifically, we present the probability density function as well as a graphical analysis of this density, the cumulative distribution function and the moments for this statistical distribution. Additionally, by using likelihood methods, we estimate the parameters, carry out asymptotic inference and discuss influence diagnostics of this model. Finally, we show the usefulness of the glog-normal distribution for modeling gene expression microarray intensity data by means of a real numerical example.

On a goodness-of-fit test for normality with unknown parameters and type-II censored data

We propose a new goodness-of-fit test for normal and lognormal distributions with unknown parameters and type-II censored data. This test is a generalization of Michaels test for censored samples, which is based on the empirical distribution and a variance stabilizing transformation. We estimate the parameters of the model by using maximum likelihood and Guptas methods. The quantiles of the distribution of the test statistic under the null hypothesis are obtained through Monte Carlo simulations. The power of the proposed test is estimated and compared to that of the Kolmogorov–Smirnov test also using simulations. The new test is more powerful than the Kolmogorov–Smirnov test in most of the studied cases. Acceptance regions for the PP, QQ and Michaels stabilized probability plots are derived, making it possible to visualize which data contribute to the decision of rejecting the null hypothesis. Finally, an illustrative example is presented.

A new variance stabilizing transformation for gene expression data analysis

Abstract In this paper, we introduce a new family of power transformations, which has the generalized logarithm as one of its members, in the same manner as the usual logarithm belongs to the family of Box-Cox power transformations. Although the new family has been developed for analyzing gene expression data, it allows a wider scope of mean-variance related data to be reached. We study the analytical properties of the new family of transformations, as well as the mean-variance relationships that are stabilized by using its members. We propose a methodology based on this new family, which includes a simple strategy for selecting the family member adequate for a data set. We evaluate the finite sample behavior of different classical and robust estimators based on this strategy by Monte Carlo simulations. We analyze real genomic data by using the proposed transformation to empirically show how the new methodology allows the variance of these data to be stabilized.

Does serum cause lipid-droplet accumulation in bovine embryos produced in vitro, during developmental days 1 to 4?

SummaryPurposeSerum supplementation has shown to have beneficial effects on in vitro bovine embryo development. However, it is often assumed that serum supplementation may produce mitochondrial damage and this damage would generate lipid accumulation, a major obstacle for cryopreservation. The aim of the present study is to investigate the previous assumptions in early embryonic stages.MethodsWe considered in vitro produced bovine embryos from day 1 to 4 of development, which were grown in presence of serum from days 1, 2 or 3 or in absence of it. Electron transmission micrographs allowed us to quantify the area occupied by lipid droplets and by the different mitochondrial types to evaluate serum effect. Using confocal microscopy we analyzed mitochondrial activity and location.ResultsWe found no evidence of lipid droplets accumulation or mitochondrial degeneration or reduction of mitochondrial area in serum supplemented media. Further, our results suggest that events of mitochondrial proliferation are taking place even in serum supplemented media.ConclusionsSerum does not produce lipid accumulation or mitochondrial damage in bovine embryos from 2 to 16 cells. When serum was added to embryo culture medium on day 3 of development, there were ultrastructural signs of a beneficial effect for embryo development. The lack of serum until day 3 may also avoid the unnecessary exposure to potentially inhibitory factors present on it.

Assessment of child psychomotor development in population groups as a positive health indicator

INTRODUCTION It is necessary to use health indicators describing the conditions of all individuals in a population, not just of those who have a disease or die. OBJECTIVES To introduce a method to collect population indicators of psychomotor development in children younger than 6 years old and show its results. POPULATION AND METHODS Data were obtained from a cross-sectional assessment regarding compliance with 13 developmental milestones (selected from the national reference) conducted in 5465 children using five surveys administered by the Matanza-Riachuelo River Basin Authority in areas of this basin where a high proportion of families with unmet basic needs live. For each survey, a logistic regression analysis was used to estimate the median age at attainment of the 13 developmental milestones. A linear regression model between the estimated age at attainment of the 13 milestones was adjusted for each survey based on the corresponding age at attainment of the national reference. Based on this model, three indicators were defined: overall developmental quotient, developmental quotient at 4 years old, and developmental trend. RESULTS Results from the five surveys ranged between 0.74 and 0.85, 0.88 and 0.81, and -0.15 and -0.26 for the overall developmental quotient, developmental quotient at 4 years old, and developmental trend, respectively. A distinct developmental delay and an increasing trend in delay with age were observed. CONCLUSIONS Indicators are easily interpreted and related to social indicators (unmet basic needs, etc.). Collecting the information necessary to make estimations takes little time and can be applied to population groups, but not on an individual level.