Symmetric Trimming Research Articles

Estimation of panel data partly specified Tobit regression with fixed effects

This paper presents an estimation of a partly specified Tobit model with fixed effects by extending the symmetric trimming procedure proposed in Honoré (1992). Under some sufficient conditions, we present conditions to identify both the parametric and the nonparametric component of the unknown parameter. Under some sufficient conditions, we establish that the proposed estimates are consistent and the estimates of the parametric component are asymptotically normally consistent. Finally, we present some consistent covariance matrix for the estimates of the parametric component.

Type I Error Rates of Ft Statistic with Different Trimming Strategies for Two Groups Case

When the assumptions of normality and homoscedasticity are met, researchers should have no doubt in using classical test such as t-test and ANOVA to test for the equality of central tendency measures for two and more than two groups respectively. However, in real life we do not often encounter with this ideal situation. A robust method known as Ft statistic has been identified as an alternative to the above methods in handling the problem of nonnormality. Motivated by the good performance of the method, in this study we proposed to use Ft statistic with three different trimming strategies, namely, i) fixed symmetric trimming (10%, 15% and 20%), ii) fixed asymmetric trimming (10%, 15% and 20%) and iii) empirically determined trimming, to simultaneously handle the problem of nonnormality and heteroscedasticity. To test for the robustness of the procedures towards the violation of the assumptions, several variables were manipulated. The variables are types of distributions and heterogeneity of variances. Type I error for each procedures were then be calculated. This study will be based on simulated data with each procedure been simulated 5000 times. Based on the Type I error rates, we were able to identify which procedures (Ft with different trimming strategies) are robust and have good control of Type I error. The best procedure that should be taken into consideration is the Ft with MOM - Tn for normal distribution, 15% fixed trimming for skewed normal-tailed distribution and MOM - MADn for skewed leptokurtic distribution. This is because, all of the procedures produced the nearest Type I error rates to the nominal level.

THE DISTRIBUTION OF THE INFLATION IN TURKEY

This paper investigates distribution of inflation items using various measures of skewness and kurtosis for Turkey covering the period 1996-2007. Considering sensitivity of traditional distribution measures to outlying observations robust skewness and kurtosis are also computed as a novelty. Analysis results mainly reveal that inflation components are right skewed and fat tailed as documented by the previous studies. However due to possible effects of the outliers traditional measures, in particular skewness, are lagging behind the robust measures in identifying underlying dispersion. Therefore one can say that weighted mean inflation used to measure general price changes is not trustworthy and a biased estimator of central location. Our results further suggest that core measures based on constant and symmetric trimming applied by the previous studies for Turkey is somewhat deficient since skewness of the data is ignored in the estimation process. Therefore, to obtain more reliable information in monitoring general price movements we suggest use of asymmetric trimmed means estimators which allows trimming different percentages from each tail of the distribution

Assessing when a sample is mostly normal

The use of trimming procedures constitutes a natural approach to robustifying statistical methods. This is the case of goodness-of-fit tests based on a distance, which can be modified by choosing trimmed versions of the distributions minimizing that distance. The L 2 -Wasserstein distance is used to introduce the trimming methodology for assessing when a data sample can be considered mostly normal. The method can be extended to other location and scale models, introducing a robust approach to model validation, and allows an additional descriptive analysis by determining the subset of the data with the best improved fit to the model. This is a consequence of the use of data-driven trimming methods instead of the more classical symmetric trimming procedures.

A comparative study of robust tests for spread: Asymmetric trimming strategies

We examined 633 procedures that can be used to compare the variability of scores across independent groups. The procedures, except for one, were modifications of the procedures suggested by Levene (1960) and O'Brien (1981). We modified their procedures by substituting robust measures of the typical score and variability, rather than relying on classical estimators. The robust measures that we utilized were either based on a priori or empirically determined symmetric or asymmetric trimming strategies. The Levene-type and O'Brien-type transformed scores were used with either the ANOVA F test, a robust test due to Lee and Fung (1985), or the Welch (1951) test. Based on four measures of robustness, we recommend a Levene-type transformation based upon empirically determined 20% asymmetric trimmed means, involving a particular adaptive estimator, where the transformed scores are then used with the ANOVA F test.

Multiple Comparison Procedures, Trimmed Means And Transformed Statistics

Multiple Comparison Procedures, Trimmed Means And Transformed Statistics

Comparing the "typical score" across independent groups based on different criteria for trimming

Nonnormality and variance heterogeneity affect the validity of the traditional tests for treatment group equality (e.g. ANOVA F-test and t-test), particularly when group sizes are unequal. Adopting trimmed means instead of the usual least squares estimator has been shown to be mostly affective in combating the deleterious effects of nonnormality. There are, however, practical concerns regarding trimmed means, such as the predetermined amount of symmetric trimming that is typically used. Wilcox and Keselman proposed the Modified One- Step M-estimator (MOM) which empirically determines the amount of trimming. Othman et al. found that when this estimator is used with Schrader and Hettmansperger's H statistic, rates of Type I error were well controlled even though data were nonnormal in form. In this paper, we modified the criterion for choosing the sample values for MOM by replacing the default scale estimator, MADn, with two robust scale estimators, Sn and Tn , suggested by Rousseeuw and Croux (1993). To study the robustness of the modified methods, conditions that are known to negatively affect rates of Type I error were manipulated. As well, a bootstrap method was used to generate a better approximate sampling distribution since the null distribution of MOM-H is intractable. These modified methods resulted in better Type I error control especially when data were extremely skewed.

Multiple comparisons based on a modified one-step M-estimator

Although many methods are available for performing multiple comparisons based on some measure of location, most can be unsatisfactory in at least some situations, in simulations when sample sizes are small, say less than or equal to twenty. That is, the actual Type I error probability can substantially exceed the nominal level, and for some methods the actual Type I error probability can be well below the nominal level, suggesting that power might be relatively poor. In addition, all methods based on means can have relatively low power under arbitrarily small departures from normality. Currently, a method based on 20% trimmed means and a percentile bootstrap method performs relatively well (Wilcox, in press). However, symmetric trimming was used, even when sampling from a highly skewed distribution and a rigid adherence to 20% trimming can result in low efficiency when a distribution is sufficiently heavy-tailed. Robust M-estimators are more flexible but they can be unsatisfactory in terms of Type I errors when sample sizes are small. This paper describes an alternative approach based on a modified one-step M-estimator that introduces more flexibility than a trimmed mean but provides better control over Type I error probabilities compared with using a one-step M-estimator.

A Test Of Symmetry

When data are nonnormal in form classical procedures for assessing treatment group equality are prone to distortions in rates of Type I error and power to detect effects. Replacing the usual means with trimmed means reduces rates of Type I error and increases sensitivity to detect effects. If data are skewed, say to the right, then it has been postulated that asymmetric trimming, to the right, should be better at controlling rates of Type I error and power to detect effects than symmetric trimming from both tails of the data distribution. Keselman, Wilcox, Othman and Fradette (2002) found that Babu, Padmanabhan and Puri's (1999) test for symmetry when combined with a heteroscedastic statistic which compared either symmetrically or asymmetrically determined means provided excellent Type I error control even when data were extremely heterogeneous and very nonnormal in form. In this paper, we present a detailed discussion of the Babu et al. procedure as well as a numerical example demonstrating its use.

Effect of Trimming on LP III Flood Quantile Estimates

In the fields of statistics and hydrology, a considerable amount of research has been directed toward robust methods of estimation. This paper broadly reviews these methods and presents results of the application of a specific robust estimation procedure, namely trimming, in flood frequency analysis. Using simulation, the effect of various proportions of symmetric trimming on the estimation of moments, distribution parameters, and quantiles is examined. The influence of the sample size and parent distribution parameters on the estimation performance is also investigated for several return periods and for three different fitting methods for the log-Pearson Type III distribution. While the results point to the potential usefulness of robust estimators in hydrological analysis, they also serve as a precaution that certain distribution fitting techniques may be overly robust to extreme observations in the sample (those in the tails).

Generalized method of moment estimation of truncated or censored regression

This paper proposes the generalized method of moment estimation of truncated or censored regression model, and applies this procedure to the recreational demand model estimation. In a typical limited dependent variable regression, the conditional mean of error distribution is no longer zero. However, by symmetric trimming of error distribution, we can obtain zero conditional mean, and the orthogonality conditions for GMM estimation. Travel cost model (TOM) is estimated using the symmetrically trimmed GMM estimation. Bootstrap is used to simulate the finite sample distribution of GMM estimates.

Estimation of Type 3 Tobit models using symmetric trimming and pairwise comparisons

This paper considers estimation of the semiparametric Type 3 Tobit model. We construct two-step estimators that use the ideas of symmetric trimming and pairwise comparisons which have been proposed for the censored regression model by Powell (1986) and Honoré and Powell (1994). The estimators are consistent and asymptotically normal under two identifying assumptions: conditional symmetry and independence between the errors and regressors. The ideas and techniques are also implementable in other selection models that are variations of the basic Type 3 Tobit model. We demonstrate this by applying the proposed method in estimating an empirical model considered by Udry (1994).

Modelling and prediction of travel distance by car

A theoretical basis and empirical modelling and prediction results for Swedish travelling distances by car are given. The results form the basis for an assessment of the economic consequences of Swedish petrol price adjustments by region and travel type. Truncated regression models are estimated using a general distribution class specification and a robust estimator based on symmetric trimming. Predictors and prediction variances are given. The study confirms the hypothesis of a positive income effect for work and business travel distances. The effect is negative and significant for recreation distances. Travel distances tend to be shorter in less densely populated regions, i.e. a positive density effect. Males have significantly longer work and shopping trips. The differences between estimators and corresponding predictions are small. The financial support from the Swedish Transport Research Board (Dnr 21/88–82) is gratefully acknowledged.