Problems in estimating non-linear Engel parameters in the absence of appropriate grouped means and average elasticity of variable elasticity Engel functions

Household Expenditure Survey (HES) data are widely reported in grouped form for a number of reasons. Only within-group arithmetic means (AMs) of the household expenditures on various consumption items, total expenditure, income . and other variables are reported in the tabular form. However, the use of such within-group AMs introduces biases when the parameters of various commonly used non-linear Engel functions are estimated by the Aitken's generalized least squares (GLS) method. This is because the within-group geometric means (GMs)/harmonic means (HMs) are needed in order to estimate unbiased parameters of those non-linear Engel functions. Kakwani (1977) estimated the within-group GMs/HMs from the Kakwani-Podder (1976) Lorenz curve for Indonesian data. We have extended his method to estimate within-group GMs/HMs to a set of variables, based on a general type of concentration curve. It is shown that our estimated within-group GMs/HMs based on concentration curves are not entirely suitable for the Australian HES data. However, these GMs/HMs are then used to estimate Engel parameters for various non-linear Engel functions and it is seen that these elasticities are different for some items of certain non-linear Engel functions than those when the reported within-group AMs are used as proxies for within-group GMs/HMs in order to estimate those non-linear Engel functions. The concept of the average elasticity of a variable elasticity Engel function is discussed and computed for various Australian household consumption items. It is empirically demonstrated that the average elasticities are more meaningful than the traditional elasticity estimates computed at some representative values for certain functions.     

A review of the seasonal affective disorder hypothesis

This review of the SAD hypothesis of Kamstra et al. (2003), hereafter KKL (2003), isolates four new problems. First, the KKL (2003) statistical model does not test the KKL (2003) SAD hypothesis. Second, KKL (2003) do not properly interpret their results. Third, KKL (2003) incorrectly specify the sign of the SAD effect in the winter. The revised SAD hypothesis is that hours of night have a negative influence on stock returns in the fall and in the winter. Fourth, the statistical tests do not support either the KKL (2003) hypothesis or the revised SAD hypothesis.     

Criteria for selecting a suitable method for producing post-2000 county population estimates: A case study of population estimates in Illinois

We compared 2000 county population estimates for Illinois against 2000 census counts. Administrative records (ADREC) and ratio correlation (Ratio-CORR) methods were used to produce two sets of controlled county estimates for 2000; a third set represented an average of the estimates reached using these methods. Another set using the ADREC method was not controlled to any estimate. Also, the 2000 estimates were adjusted for undercount in the 1990 census. We compared performance of these methods with the performance of two naive models: (i) do nothing and (ii) constant growth rate. ADREC estimates were more accurate than estimates from the Ratio-CORR or Average method in terms of Mean Absolute Percent (MAPE) or weighted MAPE. Undercount adjustment in general improved the accuracy of the estimates for all three methods. A top-down or bottom-up approach worked equally well. As a single method, ADREC performed best.     

Some Uniform Limit Results in Additive Regression Model

In the setting of additive regression model components estimation, we establish some uniform limit results in probability. Our results allow to give an asymptotic simultaneous 100% confidence band for these components. These results are stated in the framework of i.i.d random vectors when the marginal integration estimation method is used.     

Asymptotic Distribution of Robust Estimator for Functional Nonparametric Models

We propose a family of robust nonparametric estimators for regression function based on kernel method. We establish the asymptotic normality of the estimator under the concentration properties on small balls of the probability measure of the functional explanatory variables. Useful applications to prediction, discrimination in a semi-metric space, and confidence curves are given. In addition, to highlight the generality of our purpose and to emphasize the role of each of our hypotheses, several special cases of our general conditions are also discussed. Finally, some numerical study in chemiometrical real data are carried out to compare the sensitivity to outliers between the classical and robust regression.     

Detection of outliers in high-dimensional data using nu-support vector regression

Support Vector Regression (SVR) is gaining in popularity in the detection of outliers and classification problems in high-dimensional data (HDD) as this technique does not require the data to be of full rank. In real application, most of the data are of high dimensional. Classification of high-dimensional data is needed in applied sciences, in particular, as it is important to discriminate cancerous cells from non-cancerous cells. It is also imperative that outliers are identified before constructing a model on the relationship between the dependent and independent variables to avoid misleading interpretations about the fitting of a model. The standard SVR and the μ-ε-SVR are able to detect outliers; however, they are computationally expensive. The fixed parameters support vector regression (FP-ε-SVR) was put forward to remedy this issue. However, the FP-ε-SVR using ε-SVR is not very successful in identifying outliers. In this article, we propose an alternative method to detect outliers i.e. by employing nu-SVR. The merit of our proposed method is confirmed by three real examples and the Monte Carlo simulation. The results show that our proposed nu-SVR method is very successful in identifying outliers under a variety of situations, and with less computational running time.