Tommaso Gastaldi

A least-squares approach to fuzzy linear regression analysis

This paper deals with a new approach to fuzzy linear regression analysis. A doubly linear adaptive fuzzy regression model is proposed, based on two linear models: a core regression model and a spread regression model. The first one “explains” the centers of the fuzzy observations, while the second one is for their spreads. As dependence between centers and spreads is often encountered in real world applications, our model is defined in such a way as to take into account a possible linear relationship among centers and spreads. Illustrative examples are also discussed, and a computer program which implements our procedure is enclosed.

An orderwise polynomial regression procedure for fuzzy data

A procedure for polynomial fit with fuzzy data is presented. As in real case studies, there is often dependence between modes and spreads, we propose a regression polynomial model capable to take into account possible interactions between the estimated spreads and modes. This method finds applications in several fields such as reliability, quality control, psychometrics, marketing, image processing, etc. An application to a software reliability problem is also presented.

A kolmogorov-smirnov test procedure involving a possibly censored or truncated sample

We present a procedure to carry out the Kolmogorov-Smimov (K-S) tests of identity in the case when one possibly censored or truncated sample is involved. The form of censoring we allow is the most general one. Some applications are given.

Linear Fuzzy Regression Analysis with Asymmetric Spreads

We discuss a regression model for the study of asymmetrical fuzzy data and provide a method for numerical estimation of the relevant regression parameters. The proposed model is based on a new approach and has the capability to take into account the possible relationships between the size of the spreads and the magnitude of the centers of the fuzzy observations. Two illustrative examples are also presented.

Optimal reconstruction of a generally censored sample

Some order statistics from a univariate random sample of known size, drawn from a random variable X, are censored or lost. We are concerned with the problem of estimating how many observations we have lost within each interval between the remaining (observed) order statistics (including - [infinity] and + [infinity] among the remaining order statistics), in order to infer the unknown structure of the original sample.

Note on closed-form MLEs of failure rates in a fully parametric random censorship model with incomplete data

Closed-form maximum likelihood estimators (MLEs) of the failure rates in the competing risk model with masked data and an arbitrary number, say r, of exponentially distributed competing causes of failure are unknown at the present. Miyakawa (1984) gives closed-form MLEs for r = 2 and Usher and Hodgson (1988) find closed-form MLEs for r = 3 under certain assumptions on the data. In every other case, the MLEs have to be computed through numerical methods. The object of the present note consists of: (a) giving closed-form MLEs under assumptions that are either weaker or different as compared with the assumptions under which closed-form MLEs are currently known, (b) showing that general closed-form expressions of such estimators for arbitrary data sets do not exist. It is also indicated that the particular conditions under which closed-form estimators are obtained are easily met, at least approximately, in common frameworks.

Interpolating missing values in a censored sample

Abstract Given a sample from which a number of contiguous order statistics have been lost (or censored), some problems, and possible solutions, related with this situation, and concerning the reconstruction of the structure of the original sample, are discussed.

A Life Test Procedure with Right Censored Data Based on the Wald–Wolfowitz Run Test

Abstract One of the most common types of acceleration of tests, along with high usage rate, overstress, degradation and specimen design (Nelson, W. (1990). Accelerated Testing. New York: Wiley & Sons) is right censoring, which occurs when tests are terminated before all specimens placed on test run to failure. In this article, a test procedure in sequential setting based on the Wald–Wolfowitz (Wald, A., Wolfowitz, J. (1940). On a test whether two samples are from the same population. The Annals of Mathematical Statistics 11:147–162) run test with possibly right censored data is discussed. Simulation results are also included.

A constrained clusterwise procedure for segmentation

A procedure for segmentation by a constrained hierarchical clustering algorithm is proposed, using a criterion (or response) variable X and k structural factors or predictors, which yields classes different mainly as to the (conditional) distributions of X, computed within each segment. Since the procedure works on combinations of factor levels (and only indirectly on individuals), the methodology can be employed even for very large populations, with no increase of computational complexity.

Reconstructive estimation in a parametric random censorship model with incomplete data

We explore theoretically an approach to estimation, in a multivariate random censorship model with incomplete data, based on the reconstruction of the missing information. Simulation results are also presented.