Average group effect of strongly correlated predictor variables is estimable

It is well known that individual parameters of strongly correlated predictor variables in a linear model cannot be accurately estimated by the least squares regression due to multicollinearity generated by such variables. Surprisingly, an average of these parameters can be extremely accurately estimated. We find this average and briefly discuss its applications in the least squares regression.Comment: 1

A group-based approach to the least squares regression for handling multicollinearity from strongly correlated variables

Multicollinearity due to strongly correlated predictor variables is a long-standing problem in regression analysis. It leads to difficulties in parameter estimation, inference, variable selection and prediction for the least squares regression. To deal with these difficulties, we propose a group-based approach to the least squares regression centered on the collective impact of the strongly correlated variables. We discuss group effects of such variables that represent their collective impact, and present the group-based approach through real and simulated data examples. We also give a condition more precise than what is available in the literature under which predictions by the least squares estimated model are accurate. This approach is a natural way of working with multicollinearity which resolves the difficulties without altering the least squares method. It has several advantages over alternative methods such as ridge regression and principal component regression.Comment: 36 pages, 1 figur

Bounds on coverage probabilities of the empirical likelihood ratio confidence regions

This paper studies the least upper bounds on coverage probabilities of the empirical likelihood ratio confidence regions based on estimating equations. The implications of the bounds on empirical likelihood inference are also discussed

Efficient Portfolio Selection

Merak believed that an efficient frontier analysis method that combined the robustness of the Monte Carlo approach with the confidence of the Markowitz approach would be a very powerful tool for any industry. However, it soon became clear that there are other ways to address the problem that do not require a Monte Carlo component. Three subgroups were formed, and each developed a different approach for solving the problem. These were the Portfolio Selection Algorithm Approach, the Statistical Inference Approach, and the Integer Programming Approach

Voice Conversion Based on Cross-Domain Features Using Variational Auto Encoders

An effective approach to non-parallel voice conversion (VC) is to utilize deep neural networks (DNNs), specifically variational auto encoders (VAEs), to model the latent structure of speech in an unsupervised manner. A previous study has confirmed the ef- fectiveness of VAE using the STRAIGHT spectra for VC. How- ever, VAE using other types of spectral features such as mel- cepstral coefficients (MCCs), which are related to human per- ception and have been widely used in VC, have not been prop- erly investigated. Instead of using one specific type of spectral feature, it is expected that VAE may benefit from using multi- ple types of spectral features simultaneously, thereby improving the capability of VAE for VC. To this end, we propose a novel VAE framework (called cross-domain VAE, CDVAE) for VC. Specifically, the proposed framework utilizes both STRAIGHT spectra and MCCs by explicitly regularizing multiple objectives in order to constrain the behavior of the learned encoder and de- coder. Experimental results demonstrate that the proposed CD- VAE framework outperforms the conventional VAE framework in terms of subjective tests.Comment: Accepted to ISCSLP 201