A Geometric Examination of Linear Model Assumptions

From a geometric perspective, linear model theory relies on a single assumption, that (‘corrected’) data vector directions are uniformly distributed in Euclidean space. We use this perspective to explore pictorially the effects of violations of the traditional assumptions (normality, independence and homogeneity of variance) on the Type I error rate. First, for several non‐normal distributions we draw geometric pictures and carry out simulations to show how the effects of non‐normality diminish with increased parent distribution symmetry and continuity, and increased sample size. Second, we explore the effects of dependencies on Type I error rate. Third, we use simulation and geometry to investigate the effect of heterogeneity of variance on Type I error rate. We conclude, in a fresh way, that independence and homogeneity of variance are more important assumptions than normality. The practical implication is that statisticians and authors of statistical computing packages need to pay more attention to the correctness of these assumptions than to normality.     

An efficient algorithm for Harrison-Stevens forecasting using the multi-process multivariate dynamic linear model

This paper develops a computationally efficient algorithm for Harrison-Stevens forecasting in a multivariate time series which has correlated errors. The algorithm uses the observation vector one component at a time on the multiprocess multivariate dynamic linear model. This gives a computationally efficient, robust, quick adapting forecasting method for non stationary multivariate time series.     

A Note on Support Vector Density Estimation for the Deconvolution Problem

The problem of support vector density estimation is studied when the sample observations are contaminated with random noise. A procedure based on support vector method and the Fourier transform is presented and is compared with kernel density estimators by the simulation study.     

On additive and block decompositions of WLSEs under a multiple partitioned regression model

While considering the mechanism of weighted least-squares estimators (WLSEs) of regression coefficients in a partitioned linear model, Tian and Takane [On sum decompositions of weighted least-squares estimators under the partitioned linear model, Comm. Statist. Theory Methods 37 (2008), pp. 55–69] gave some identifying conditions for the WLSEs to be the sum of WLSEs under its two small models based on orthogonality of regressors with respect to the given weight matrix. The purpose of this paper is to show how to establish additive and block decompositions of WLSEs under a multiple partitioned linear model and its k small models based on orthogonality of regressors with respect to a given weight matrix.     

Limit theorems for random maximum of independent and non-identically distributed random vectors

In this paper, we study the weak convergence of the random maximum of independent and non-identical random vectors. When the random sample size is assumed to be independent of the basic variables and its distribution function is assumed to converge weakly to a non-degenerate limit, the necessary and sufficient conditions for the weak convergence of the random maximum are derived. An illustrative example is given.     

Using adaptively weighted large margin classifiers for robust sufficient dimension reduction

In this paper, we combine adaptively weighted large margin classifiers with Support Vector Machine (SVM)-based dimension reduction methods to create dimension reduction methods robust to the presence of extreme outliers. We discuss estimation and asymptotic properties of the algorithm. The good performance of the new algorithm is demonstrated through simulations and real data analysis.     

Comparison of Support Vector Machines to Other Classifiers Using Gene Expression Data

The efficiency of independent controling variates in simulation of activity networks will be evaluated in the sense of mean square deviation of the estimator from the true value. The given result is asymptotic     

Measuring Time Series Predictability Using Support Vector Regression

Most studies involving statistical time series analysis rely on assumptions of linearity, which by its simplicity facilitates parameter interpretation and estimation. However, the linearity assumption may be too restrictive for many practical applications. The implementation of nonlinear models in time series analysis involves the estimation of a large set of parameters, frequently leading to overfitting problems. In this article, a predictability coefficient is estimated using a combination of nonlinear autoregressive models and the use of support vector regression in this model is explored. We illustrate the usefulness and interpretability of results by using electroencephalographic records of an epileptic patient.     

Forecasting Contemporaneously Aggregated Vector ARMA Processes

Given a multiple time series that is generated by a multivariate ARMA process and assuming the objective is to forecast a weighted sum of the individual variables, then under a mean squared error measure of forecasting precision, it is preferable to forecast the disaggregated multiple time series and aggregate the forecasts, rather than forecast the aggregated series directly, if the involved processes are known. This result fails to hold if the processes used for forecasting are estimated from a given set of time series data. The implications of these results for empirical research are investigated using different sets of economic data.     

Testing normalization and overidentification of cointegrating vectors in vector autoregressive processes

This paper develops test procedures for testing the validity of general linear identifying restrictions imposed on cointegrating vectors in the context of a vector autoregressive model. In addition to overidentifying restrictions the considered restrictions may also involve normalizing restrictions. Tests for both types of restrictions are developed and their asymptotic properties are obtained. Under the null hypothesis tests for normalizing restrictions have an asymptotic "multivariate unit root distribution", similar to that obtained for the likelihood ratio test for cointegration, while tests for overidentifying restrictions have a standard chi-square limiting distribution. Since these two types of tests are asymptotically independent they are easy to cotnbine to an overall test for the spccifed identifying restrictions. An overall test of this kind can consistently reveal the failure of the identifying restrictions in a wider class of cases than previous tests which only test for overidentifying restrictions.