A test statistic for homogeneity of two or more covariance matrices is presented when the distributions may be non-normal and the dimension may exceed the sample size. Using the Frobenius norm of the difference of null and alternative hypotheses, the statistic is constructed as a linear combination of consistent, location-invariant, estimators of trace functions that constitute the norm. These estimators are defined as U-statistics and the corresponding theory is exploited to derive the normal limit of the statistic under a few mild assumptions as both sample size and dimension grow large. Simulations are used to assess the accuracy of the statistic.
The laws of gravity and mass interactions inspire the gravitational search algorithm (GSA), which finds optimal regions of complex search spaces through the interaction of individuals in a population of particles. Although GSA has proven effective in both science and engineering, it is still easy to suffer from premature convergence especially facing complex problems. In this paper, we proposed a new hybrid algorithm by integrating genetic algorithm (GA) and GSA (GA-GSA) to avoid premature convergence and to improve the search ability of GSA. In GA-GSA, crossover and mutation operators are introduced from GA to GSA for jumping out of the local optima. To demonstrate the search ability of the proposed GA-GSA, 23 complex benchmark test functions were employed, including unimodal and multimodal high-dimensional test functions as well as multimodal test functions with fixed dimensions. Wilcoxon signed-rank tests were also utilized to execute statistical analysis of the results obtained by PSO, GSA, and GA-GSA. Experimental results demonstrated that the proposed algorithm is both efficient and effective.
Time series consists of complex nonlinear and chaotic patterns that are difficult to forecast. This paper proposes a novel hybrid forecasting model which combines the group method of data handling (GMDH) and the least squares support vector machine (LSSVM), known as GLSSVM. The GMDH is used to determine the useful input variables for the LSSVM model and the LSSVM model that works as time series forecasting. Three well-known time series data sets are used in this study to demonstrate the effectiveness of the forecasting model. These data are utilized to forecast through an application aimed to handle real life time series. The results found by the proposed model were compared with the results of the GMDH and LSSVM models. Experiment result indicates that the hybrid model was a powerful tool to model time series data and provides a promising technique in time series forecasting methods.
Let $q \ge 3$ be a positive integer. For any integers $m$ and $n$, the two-term exponential sum $C(m,n,k;q)$ is defined by $C(m,n,k;q) = \sum _{a=1}^q e ({(ma^k +na)}/{q})$, where $e(y)={\rm e}^{2\pi {\rm i} y}$. In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.
The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.
The main purpose of this paper is using the mean value formula of Dirichlet L-functions and the analytic methods to study a hybrid mean value problem related to certain Hardy sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.
The main purpose of this paper is to study a hybrid mean value problem related to the Dedekind sums by using estimates of character sums and analytic methods.
Bankruptcy has long been an important topic in finance and accounting research. Recent headline bankruptcies have included Enron, Fannie Mae, Freddie Mac, Washington Mutual, Merrill Lynch, and Lehman Brothers. These bankruptcies and their financial fallout have become a serious public concern due to huge influence these companies play in the real economy. Many researchers began investigating bankruptcy predictions back in the early 1970s. However, until recently, most research used prediction models based on traditional statistics. In recent years, however, newly-developed data mining techniques have been applied to various fields, including performance prediction systems. This research applies particle swarm optimization (PSO) to obtain suitable parameter settings for a support vector machine (SVM) model and to select a subset of beneficial features without reducing the classification accuracy rate. Experiments were conducted on an initial sample of 80 electronic companies listed on the Taiwan Stock Exchange Corporation (TSEC).
This paper makes four critical contributions: (1) The results indicate the business cycle factor mainly affects financial prediction performance and has a greater influence than financial ratios. (2) The closer we get to the actual occurrence of financial distress, the higher the accuracy obtained both with and without feature selection under the business cycle approach. For example, PSO-SVM without feature selection provides 89.37% average correct cross-validation for two quarters prior to the occurrence of financial distress. (3) Our empirical results show that PSO integrated with SVM provides better classification accuracy than the Grid search, and genetic algorithm (GA) with SVM approaches for companies as normal or under threat. (4) The PSO-SVM model also provides better prediction accuracy than do the Grid-SVM, GA-SVM, SVM, SOM, and SVR-SOM approaches for seven well-known UCI datasets. Therefore, this paper proposes that the PSO-SVM approach could be a more suitable method for predicting potential financial distress.