Self-tuning regulators with restricted inputs
Sensitivity analysis in linear models
In this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators’ sensitivity results.We include brief remarks...
Sensitivity analysis in singular mixed linear models with constraints
The singular mixed linear model with constraints is investigated with respect to an influence of inaccurate variance components on a decrease of the confidence level. The algorithm for a determination of the boundary of the insensitivity region is given. It is a set of all shifts of variance components values which make the tolerated decrease of the confidence level only. The problem about geometrical characterization of the confidence domain is also presented.
Sensitivity analysis of -estimators of non-linear regression models
An asymptotic formula for the difference of the -estimates of the regression coefficients of the non-linear model for all observations and for observations is presented under conditions covering the twice absolutely continuous -functions. Then the implications for the -estimation of the regression model are discussed.
Sensitivity studies of pollutant concentrations calculated by the UNI-DEM with respect to the input emissions
The influence of emission levels on the concentrations of four important air pollutants (ammonia, ozone, ammonium sulphate and ammonium nitrate) over three European cities (Milan, Manchester, and Edinburgh) with different geographical locations is considered. Sensitivity analysis of the output of the Unified Danish Eulerian Model according to emission levels is provided. The Sobol’ variance-based approach for global sensitivity analysis has been applied to compute the corresponding sensitivity measures....
Separable least squares, variable projection, and the Gauss-Newton algorithm.
Sequential and iterative designs of experiments
Sequential estimation method for the minimum of a quadratic regression function
Sequential monitoring for change in scale
We propose a sequential monitoring scheme for detecting a change in scale. We consider a stable historical period of length . The goal is to propose a test with asymptotically small probability of false alarm and power 1 as the length of the historical period tends to infinity. The asymptotic distribution under the null hypothesis and consistency under the alternative hypothesis is derived. A small simulation study illustrates the finite sample performance of the monitoring scheme.
Shrinkage strategies in some multiple multi-factor dynamical systems
In this paper, we are interested in estimation problem for the drift parameters matrices of m independent multivariate diffusion processes. More specifically, we consider the case where the m-parameters matrices are supposed to satisfy some uncertain constraints. Given such an uncertainty, we develop shrinkage estimators which improve over the performance of the maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, we study the relative dominance of the...
Shrinkage strategies in some multiple multi-factor dynamical systems
In this paper, we are interested in estimation problem for the drift parameters matrices of m independent multivariate diffusion processes. More specifically, we consider the case where the m-parameters matrices are supposed to satisfy some uncertain constraints. Given such an uncertainty, we develop shrinkage estimators which improve over the performance of the maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, we study the relative dominance of the...
Sign and Wilcoxon tests for quadratic versus cubic regression.
In this paper sign and Wilcoxon tests for testing the null hypothesis of quadratic regression versus the alternative, cubic regression are proposed. It is shown that in the case of a simple design consisting of multiple Y observations at each of the four levels of x, the proposed tests perform reasonably well as compared to their parametric competitors, while in the case of a general design consisting of a large number of levels of x, the loss in Pitman efficiency is considerable. However their...
Significance testing in exact logistic multiple regression.
Sobre la robustificación interna del algoritmo de Plackett-Kalman para la estimación recursiva del modelo de regresión lineal.
Este trabajo presenta un procedimiento para hacer robusto el algoritmo recursivo de Plackett-Kalman para el modelo lineal, incorporándole medidas diagnósticas que indiquen la influencia potencial y real de cada nueva observación en los parámetros del modelo. Se describe cómo calcular recursivamente el estadístico D2 de Cook, la distancia de Mahalanobis de cada nueva observación al centro de gravedad de la ya incluidas, y un contraste, basado en los residuos recursivos, de que la nueva observación...
Some Applications of Anderson's Inequality to Some Optimality Criteria of the Generalized Least Squares Estimator.
Some asymptotic results for robust procedures for testing the constancy of regression models over time
Some Diagnostic Tools in Robust Econometrics
Highly robust statistical and econometric methods have been developed not only as a diagnostic tool for standard methods, but they can be also used as self-standing methods for valid inference. Therefore the robust methods need to be equipped by their own diagnostic tools. This paper describes diagnostics for robust estimation of parameters in two econometric models derived from the linear regression. Both methods are special cases of the generalized method of moments estimator based on implicit...
Some inferential questions in regard to analysing two-way Layouts and associated linear model theory and practice
In analysing a well known data set from the literature which can be thought of as a two-way layout it transpires that a robust adaptive regression approach for identifying outliers fails to be sensitive enough to detect the possible interchange of two observations. On the other hand if one takes the classical approach of diagnostic checking one may also stop too early and be satisfied with a model that falls short of a more detailed analysis that takes account of heteroscedasticity in the data....
Some invariant test procedures for detection of structural changes; behavior under alternatives
Regression- and scale-invariant -test procedures for detection of structural changes in linear regression model was developed and their limit behavior under the null hypothesis was studied in Hušková [9]. In the present paper the limit behavior under local alternatives is studied. More precisely, it is shown that under local alternatives the considered test statistics have asymptotically normal distribution.
Some invariant test procedures for detection of structural changes
Regression and scale invariant -test procedures are developed for detection of structural changes in linear regression model. Their limit properties are studied under the null hypothesis.