Symmetry Of Errors Research Articles

Rapid and lean multifactorial screening methods for robust product lifetime improvement

Reliability enhancement is indispensable in modern operations. It aims to ensure the viability of complex functionalities in competitive products. We propose a full-robust screening/optimization method that promotes the rapid multi-factorial profiling of censored highly-fractionated lifetime datasets. The method intends to support operational conditions that demand quick, practical and economical experimentation. The innovative part of this proposal includes the robust split and quantification of structured lifetime information in terms of location and dispersion tendencies. To accomplish the robust data-reduction of lifetimes, maximum breakdown-point estimators are introduced to stabilize potential external-noise intrusions, which might be manifested as outliers or extremities. The novel solver provides resilience by robustifying the location (median) and dispersion (Rousseeuw-Croux Qn) estimations. The proposed profiler fuses dichotomized and homogenized lifetime information in a distribution-free manner. The converted and consolidated lifetime dataset is non-parametrically pre-screened to ensure error balances across effects. Consequently, any strong effects that maximize the lifetime response are diagnosed as long as the error symmetry has been previously established. We discuss problems that may be encountered in comparison to other multi-factorial profilers/optimizers upon application to densely-fractionated-and-saturated experimental schemes. We comment on the lean and agile advantages of the proposed technique with respect to several traditional treatments for the difficult case that implicates small and censored survival datasets. The robust screening procedure is illustrated on an industrial-level paradigm that concerns the multi-factorial reliability improvement of a thermostat; the trial units have been subjected to conditions of censoring and use-rate acceleration.

Tests for validity of the semiparametric heteroskedastic transformation model

There exist a number of tests for assessing the nonparametric heteroskedastic location-scale assumption. The goodness-of-fit tests considered are for the more general hypothesis of the validity of this model under a parametric functional transformation on the response variable, specifically testing for independence between the regressors and the errors in a model where the transformed response is just a location/scale shift of the error is considered. The proposed criteria use the familiar factorization property of the joint characteristic function under independence. The difficulty is that the errors are unobserved and hence one needs to employ properly estimated residuals in their place. The limit distribution of the test statistics is studied under the null hypothesis as well as under alternatives, and also a resampling procedure is suggested in order to approximate the critical values of the tests. This resampling is subsequently employed in a series of Monte Carlo experiments that illustrate the finite-sample properties of the new test. The performance of related test statistics for normality and symmetry of errors is also investigated, and application of our methods on real data sets is provided.

On ecological aspects of dynamics for zero slope regression for water pollution in Chile

Zero slope regression is an important problem in chemometrics, ranging from challenges of intercept-bias and slope ‘corrections’ in spectrometry, up to analysis of administrative data on chemical pollution in water in the region of Arica and Parinacota. Such issue is really complex and it integrates problems of optimal design, symmetry of errors, stabilization of the variability of estimators, dynamical system for errors up to an administrative data challenges. In this article we introduce a realistic approach to zero slope regression problem from dynamical point of view. Linear regression is a widely used approach for data fitting under assumption of normally distributed residuals. Many times non-normal residuals are observed and also theoretically justified. Our solution to such problem uses the recently introduced inference function called score function of distribution. As a minimization criterion, the minimum information of residuals criterion is used. The score regression appears to be a direct generalization of the least-squares regression for an arbitrary known (believed) distribution of residuals. The score estimation is also distribution sensitive version of M-estimation. The capability of the method is demonstrated by water pollution data examples.

Semiparametric Bayesian measurement error modeling

This work presents a Bayesian semiparametric approach for dealing with regression models where the covariate is measured with error. Given that (1) the error normality assumption is very restrictive, and (2) assuming a specific elliptical distribution for errors (Student- t for example), may be somewhat presumptuous; there is need for more flexible methods, in terms of assuming only symmetry of errors (admitting unknown kurtosis). In this sense, the main advantage of this extended Bayesian approach is the possibility of considering generalizations of the elliptical family of models by using Dirichlet process priors in dependent and independent situations. Conditional posterior distributions are implemented, allowing the use of Markov Chain Monte Carlo (MCMC), to generate the posterior distributions. An interesting result shown is that the Dirichlet process prior is not updated in the case of the dependent elliptical model. Furthermore, an analysis of a real data set is reported to illustrate the usefulness of our approach, in dealing with outliers. Finally, semiparametric proposed models and parametric normal model are compared, graphically with the posterior distribution density of the coefficients.

A Regression Technique Accounting for Heteroscedastic and Asymmetric Errors

Regression models are often used for estimating net outputs of a biological system. In many cases both heteroscedasticity and asymmetry of the errors are encountered. Properly accounting for the effects of these types of errors can substantially improve the estimation of regression coefficients and prediction intervals. Transformations, such as those proposed by Box and Cox (1964), are used extensively to obtain homoscedasticity and symmetry of errors. One of the major drawbacks of transformation methods is that when both heteroscedasticity and asymmetry are present, a transformation that corrects for both may not exist. A regression method based on modeling the error distribution using Johnson's (1949) Su distribution is proposed and referred to as Su regression. This new regression technique is compared with the weighted and unweighted transformation of both sides methods using two forestry datasets. For both datasets the assumption of Su distributed errors was appropriate, but neither of the transformation of both sides methods was able to achieve symmetric residuals. Clear improvements in the prediction intervals for Su regression were demonstrated in a cross-validated simulation.

Forecast Error Symmetry in ARIMA Models

Abstract Forecasts and residuals from estimated autoregressive integrated moving average (ARIMA) models are investigated with respect to the symmetry of their distributions. For models estimated with and without intercept terms and, more generally, for regression models with correlated errors, it is shown that both the set of residuals and the set of forecast errors at leads 1, 2, …, l have joint distributions that are symmetric about 0 under mild symmetry conditions on the true process generating the observations. We consider most common estimation methods including maximum likelihood, conditional least squares, and unconditional least squares. We also show that the forecast error t statistics are symmetrically distributed about 0.