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On the description and analysis of measurements of continuous quantities

Reinhard Viertl (2002)

Kybernetika

The measurement of continuous quantities is the basis for all mathematical and statistical analysis of phenomena in engineering and science.Therefore a suitable mathematical description of measurement results is basic for realistic analysis methods for such data. Since the result of a measurement of a continuous quantity is not a precise real number but more or less non- precise, it is necessary to use an appropriate mathematical concept to describe measurements. This is possible by the description...

On the distributions of R m n + ( j ) and ( D m n + , R m n + ( j ) )

Jagdish Saran, Kanwar Sen (1982)

Aplikace matematiky

The contents of the paper is concerned with the two-sample problem where F m ( x ) and G n ( x ) are two empirical distribution functions. The difference F m ( x ) - G n ( x ) changes only at an x i , i = 1 , 2 , ... , m + n , corresponding to one of the observations. Let R m n + ( j ) denote the subscript i for which F m ( x i ) - G n ( x i ) achieves its maximum value D m n + for the j th time ( j = 1 , 2 , ... ) . The paper deals with the probabilities for R m n + ( j ) and for the vector ( D m n + , R m n + ( j ) ) under H 0 : F = G , thus generalizing the results of Steck-Simmons (1973). These results have been derived by applying the random walk model.

On the distributivity equation for uni-nullnorms

Ya-Ming Wang, Hua-Wen Liu (2019)

Kybernetika

A uni-nullnorm is a special case of 2-uninorms obtained by letting a uninorm and a nullnorm share the same underlying t-conorm. This paper is mainly devoted to solving the distributivity equation between uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms and some binary operators, such as, continuous t-norms, continuous t-conorms, uninorms, and nullnorms. The new results differ from the previous ones about the distributivity in the class of 2-uninorms, which have not yet...

On the efficiency of procedures for estimation of parameters in ARIMA models.

Bala Chandra (1984)

Trabajos de Estadística e Investigación Operativa

The paper discusses the implementation of the Newton-Raphson iterative method of estimation of parameters in the autoregressive integrated moving average (ARIMA) models. The efficiency of this method has been compared with other well known methods of estimation.

On the equality of the ordinary least squares estimators and the best linear unbiased estimators in multivariate growth-curve models.

Gabriela Beganu (2007)

RACSAM

It is well known that there were proved several necessary and sufficient conditions for the ordinary least squares estimators (OLSE) to be the best linear unbiased estimators (BLUE) of the fixed effects in general linear models. The purpose of this article is to verify one of these conditions given by Zyskind [39, 40]: there exists a matrix Q such that ΩX = XQ, where X and Ω are the design matrix and the covariance matrix, respectively. It will be shown the accessibility of this condition in some...

On the Equivalence between Orthogonal Regression and Linear Model with Type-II Constraints

Sandra Donevska, Eva Fišerová, Karel Hron (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Orthogonal regression, also known as the total least squares method, regression with errors-in variables or as a calibration problem, analyzes linear relationship between variables. Comparing to the standard regression, both dependent and explanatory variables account for measurement errors. Through this paper we shortly discuss the orthogonal least squares, the least squares and the maximum likelihood methods for estimation of the orthogonal regression line. We also show that all mentioned approaches...

On the estimation in a class of diffusion-type processes. Aplication for diffusion branching processes.

Manuel Molina Fernández, Aurora Hermoso Carazo (1990)

Extracta Mathematicae

In this work a family of stochastic differential equations whose solutions are multidimensional diffusion-type (non necessarily markovian) processes is considered, and the estimation of a parametric vector θ which relates the coefficients is studied. The conditions for the existence of the likelihood function are proved and the estimator is obtained by continuously observing the process. An application for Diffusion Branching Processes is given. This problem has been studied in some special cases...

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