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Ramanujan-Fourier series and the conjecture D of Hardy and Littlewood

H. Gopalakrishna Gadiyar, Ramanathan Padma (2014)

Czechoslovak Mathematical Journal

We give a heuristic proof of a conjecture of Hardy and Littlewood concerning the density of prime pairs to which twin primes and Sophie Germain primes are special cases. The method uses the Ramanujan-Fourier series for a modified von Mangoldt function and the Wiener-Khintchine theorem for arithmetical functions. The failing of the heuristic proof is due to the lack of justification of interchange of certain limits. Experimental evidence using computer calculations is provided for the plausibility...

Random coefficients bifurcating autoregressive processes

Benoîte de Saporta, Anne Gégout-Petit, Laurence Marsalle (2014)

ESAIM: Probability and Statistics

This paper presents a new model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton−Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency, with a convergence rate, and asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new results in both these frameworks.

Rate of convergence for a class of RCA estimators

Pavel Vaněček (2006)

Kybernetika

This work deals with Random Coefficient Autoregressive models where the error process is a martingale difference sequence. A class of estimators of unknown parameter is employed. This class was originally proposed by Schick and it covers both least squares estimator and maximum likelihood estimator for instance. Asymptotic behavior of such estimators is explored, especially the rate of convergence to normal distribution is established.

Redescending M-estimators in regression analysis, cluster analysis and image analysis

Christine H. Müller (2004)

Discussiones Mathematicae Probability and Statistics

We give a review on the properties and applications of M-estimators with redescending score function. For regression analysis, some of these redescending M-estimators can attain the maximum breakdown point which is possible in this setup. Moreover, some of them are the solutions of the problem of maximizing the efficiency under bounded influence function when the regression coefficient and the scale parameter are estimated simultaneously. Hence redescending M-estimators satisfy several outlier robustness...

Regime-switching models of time series with cubic spline transition function in geodetic application

Tomáš Bognár, Jozef Komorník, Magda Komorníková (2004)

Kybernetika

A new class of Smooth Transition Autoregressive models, based on cubic spline type transition functions, has been introduced and subjected to comparison with models based on the traditional logistic transition functions. A very high degree of similarity between the two model classes has been demonstrated. The new class of models can be slightly preferable because of its more simple formal and geometrical structure that may enable users more convenient manipulation in statistical inference procedures....

Regresión espectral sesgada.

Fernando Tusell Palmer (1988)

Trabajos de Estadística

Se propone un método de regresión espectral adecuado cuando los regresores tienen potencia espectral despreciable sobre bandas de frecuencia estrechas. Se investiga la relación entre el método propuesto y los procedimientos de regresión sesgada habituales en el dominio del tiempo.

Relative Measurement and Its Generalization in Decision Making. Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors. The Analytic Hierarchy/Network Process.

Thomas L. Saaty (2008)

RACSAM

According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish measurements for intangible properties that have no scales of measurement. In that case the value...

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