An autoregressive-moving average model in which all of the roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximation to the likelihood of the model in the ca...

Likelihood ratio criteria are developed for hypotheses concerning multivariate regression matrices when reduced rank is assumed or equivalently hypotheses concerning linear restrictions on regression matrices. In an econometric simultaneous equation model a single restriction may be called a ”structural equation.” A model of reduced rank in statistics is often termed a ”linear functional relati...

The experience of our self-help organisation shows that the reason patients with symptoms of magnesium (Mg) deficiency do not get Mg therapy is acceptance of an inappropriate lower limit of the reference values for serum Mg concentration. The commonly designated low limit of the normal range seems to have been selected from values obtained for symptomatic patients. It is below levels that exist...

The article is devoted to normality assumption in statistical data analysis. It gives a short historical review of the development of scientific views on the normal law and its applications. It also briefly covers normality tests and analyzes possible consequences of using the normality assumption incorrectly.

We introduce a new class of functions called almost gs-closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost gs-closed continuous surjections.

An ample study of the comparative powers of a number of omnibus multivariate normality tests is main object in this paper. Since testing for multivariate normality tests is considerably more challenging process than for testing of univariate one and therefore, study of testing for multivariate normality tests has its increasing demand. Through this paper, we have explored several techniques for...