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A Comparative Simulation Study of Robust Estimators of Standard ErrorsJohnson, Natalie 10 July 2007 (has links) (PDF)
The estimation of standard errors is essential to statistical inference. Statistical variability is inherent within data, but is usually of secondary interest; still, some options exist to deal with this variability. One approach is to carefully model the covariance structure. Another approach is robust estimation. In this approach, the covariance structure is estimated from the data. White (1980) introduced a biased, but consistent, robust estimator. Long et al. (2000) added an adjustment factor to White's estimator to remove the bias of the original estimator. Through the use of simulations, this project compares restricted maximum likelihood (REML) with four robust estimation techniques: the Standard Robust Estimator (White 1980), the Long estimator (Long 2000), the Long estimator with a quantile adjustment (Kauermann 2001), and the empirical option of the MIXED procedure in SAS. The results of the simulation show small sample and asymptotic properties of the five estimators. The REML procedure is modelled under the true covariance structure, and is the most consistent of the five estimators. The REML procedure shows a slight small-sample bias as the number of repeated measures increases. The REML procedure may not be the best estimator in a situation in which the covariance structure is in question. The Standard Robust Estimator is consistent, but it has an extreme downward bias for small sample sizes. The Standard Robust Estimator changes little when complexity is added to the covariance structure. The Long estimator is unstable estimator. As complexity is introduced into the covariance structure, the coverage probability with the Long estimator increases. The Long estimator with the quantile adjustment works as designed by mimicking the Long estimator at an inflated quantile level. The empirical option of the MIXED procedure in SAS works well for homogeneous covariance structures. The empirical option of the MIXED procedure in SAS reduces the downward bias of the Standard Robust Estimator when the covariance structure is homogeneous.
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Pairwise Multiple Comparisons Under Short-tailed Symmetric DistributionBalci, Sibel 01 May 2007 (has links) (PDF)
In this thesis, pairwise multiple comparisons and multiple comparisons with a control are studied when the observations have short-tailed symmetric distributions.
Under non-normality, the testing procedure is given and Huber estimators, trimmed mean with winsorized standard deviation, modified maximum likelihood estimators and ordinary sample mean and sample variance used in this procedure are reviewed.
Finally, robustness properties of the stated estimators are compared with each other and it is shown that the test based on the modified maximum likelihood estimators has better robustness properties under short-tailed symmetric distribution.
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Investigating the performance of process-observation-error-estimator and robust estimators in surplus production model: a simulation studyHe, Qing 15 September 2010 (has links)
This study investigated the performance of the three estimators of surplus production model including process-observation-error-estimator with normal distribution (POE_N), observation-error-estimator with normal distribution (OE_N), and process-error-estimator with normal distribution (PE_N). The estimators with fat-tailed distributions including Student's t distribution and Cauchy distribution were also proposed and their performances were compared with the estimators with normal distribution. This study used Bayesian method, revised Metropolis Hastings within Gibbs sampling algorithm (MHGS) that was previously used to solve POE_N (Millar and Meyer, 2000), developed the MHGS for the other estimators, and developed the methodologies which enabled all the estimators to deal with data containing multiple indices based on catch-per-unit-effort (CPUE). Simulation study was conducted based on parameter estimation from two example fisheries: the Atlantic weakfish (Cynoscion regalis) and the black sea bass (Centropristis striata) southern stock.
Our results indicated that POE_N is the estimator with best performance among all six estimators with regard to both accuracy and precision for most of the cases. POE_N is also the robust estimator to outliers, atypical values, and autocorrelated errors. OE_N is the second best estimator. PE_N is often imprecise. Estimators with fat-tailed distribution usually result in some estimates more biased than estimators with normal distribution. The performance of POE_N and OE_N can be improved by fitting multiple indices. Our study suggested that POE_N be used for population dynamic models in future stock assessment. Multiple indices from valid surveys should be incorporated into stock assessment models. OE_N can be considered when multiple indices are available. / Master of Science
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[en] ELECTRICAL ENERGY CONDITIONAL DEMAND ANALYSIS USING ROBUST REGRESSION: APLICATION TO A REAL CASE / [pt] ANÁLISE CONDICIONADA DA DEMANDA DE ENERGIA ELÉTRICA: APLICAÇÃO A UM CASO REALERICK ROMARIO DE PAULA 11 October 2006 (has links)
[pt] Este trabalho tem como objetivo avaliar o uso da técnica
Análise
Condicionada da Demanda, que é uma metodologia que quebra
o consumo de
energia elétrica (neste trabalho do setor residencial) em
suas partes por
equipamento e por uso final, via Regressão Robusta em
contrapartida à utilização
da regressão clássica, na estimação do consumo de energia
elétrica por uso final
do setor residencial. Para isto foram realizadas análises
via regressão linear
múltipla e também análises via regressão robusta
(estimadores robustos). Serão
realizadas as duas análises para efeito de comparação
entre o método clássico
MQO - Mínimos Quadrados Ordinários, que não é o ideal,
pois os dados violam
os pressupostos para utilização desta técnica, e o método
robusto, menos sensível
a desvios de pressupostos / [en] This work has the purpose of evaluating the use of the
technique
Conditional Demand Analysis - CDA, which is a methodology
that segregates the
consumption of electric energy (on this work about the
residential sector) is its
parts per equipment and per final use through the Robust
Regression, in
counterpart of using the classic regression, in the
estimation of the electric energy
consumption for final use on the residential sector. For
this purpose analyses will
be made using the multiple linear regression and also
analyses using the robust
regression (robust estimators). The two analyses will be
made for comparing the
classic method Squared Minimums Usual - MQO, which is not
the ideal one
because the data violates the requirements for using this
kind of method, and the
robust method, less sensible to detours of the
requirements.
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Two statistical problems related to credit scoring / Tanja de la Rey.De la Rey, Tanja January 2007 (has links)
This thesis focuses on two statistical problems related to credit scoring. In credit scoring of individuals, two classes are distinguished, namely low and high risk individuals (the so-called "good" and "bad" risk classes). Firstly, we suggest a measure which may be used to study the nature of a classifier for distinguishing between the two risk classes. Secondly, we derive a new method DOUW (detecting outliers using weights) which may be used to fit logistic regression models robustly and for the detection of outliers.
In the first problem, the focus is on a measure which may be used to study the nature of a classifier. This measure transforms a random variable so that it has the same distribution as another random variable. Assuming a linear form of this measure, three methods for estimating the parameters (slope and intercept) and for constructing confidence bands are developed and compared by means of a Monte Carlo study. The application of these estimators is illustrated on a number of datasets. We also construct statistical hypothesis to test this linearity assumption. In the second problem, the focus is on providing a robust logistic regression fit and
the identification of outliers. It is well-known that maximum likelihood estimators of
logistic regression parameters are adversely affected by outliers. We propose a robust approach that also serves as an outlier detection procedure and is called DOUW. The approach is based on associating high and low weights with the observations as a result of the likelihood maximization. It turns out that the outliers are those observations to which low weights are assigned. This procedure depends on two tuning constants. A simulation study is presented to show the effects of these constants on the performance of the proposed methodology. The results are presented in terms of four benchmark datasets as well as a large new dataset from the application area of retail marketing campaign analysis.
In the last chapter we apply the techniques developed in this thesis on a practical credit scoring dataset. We show that the DOUW method improves the classifier performance and that the measure developed to study the nature of a classifier is useful in a credit scoring context and may be used for assessing whether the distribution of the good and the bad risk individuals is from the same translation-scale family. / Thesis (Ph.D. (Risk Analysis))--North-West University, Potchefstroom Campus, 2008.
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Two statistical problems related to credit scoring / Tanja de la Rey.De la Rey, Tanja January 2007 (has links)
This thesis focuses on two statistical problems related to credit scoring. In credit scoring of individuals, two classes are distinguished, namely low and high risk individuals (the so-called "good" and "bad" risk classes). Firstly, we suggest a measure which may be used to study the nature of a classifier for distinguishing between the two risk classes. Secondly, we derive a new method DOUW (detecting outliers using weights) which may be used to fit logistic regression models robustly and for the detection of outliers.
In the first problem, the focus is on a measure which may be used to study the nature of a classifier. This measure transforms a random variable so that it has the same distribution as another random variable. Assuming a linear form of this measure, three methods for estimating the parameters (slope and intercept) and for constructing confidence bands are developed and compared by means of a Monte Carlo study. The application of these estimators is illustrated on a number of datasets. We also construct statistical hypothesis to test this linearity assumption. In the second problem, the focus is on providing a robust logistic regression fit and
the identification of outliers. It is well-known that maximum likelihood estimators of
logistic regression parameters are adversely affected by outliers. We propose a robust approach that also serves as an outlier detection procedure and is called DOUW. The approach is based on associating high and low weights with the observations as a result of the likelihood maximization. It turns out that the outliers are those observations to which low weights are assigned. This procedure depends on two tuning constants. A simulation study is presented to show the effects of these constants on the performance of the proposed methodology. The results are presented in terms of four benchmark datasets as well as a large new dataset from the application area of retail marketing campaign analysis.
In the last chapter we apply the techniques developed in this thesis on a practical credit scoring dataset. We show that the DOUW method improves the classifier performance and that the measure developed to study the nature of a classifier is useful in a credit scoring context and may be used for assessing whether the distribution of the good and the bad risk individuals is from the same translation-scale family. / Thesis (Ph.D. (Risk Analysis))--North-West University, Potchefstroom Campus, 2008.
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