On errors-in-variables estimation with unknown noise variance ratio

We propose an estimation method for an errors-in-variables model with unknown input and output noise variances. The main assumption that allows identifiability of the model is clustering of the data into two clusters that are distinct in a certain specified sense. We show an application of the proposed method for system identification

A googness of-fit-test for a multivariate errors-in-variables model

A multivariate errors-in-variables model AX ≈ B is considered, where the data matrices A and B are observed with errors, and a matrix parameter X is to be estimated. A goodness-of-fit test which is based on the moment estimator is constructed. The proposed test is asymptotically chi-squared under null hypothesis. The power of the test is discussed

Моделювання зіткнення літаків з використанням методики істотних вибірок

We introduce the model of movement of two conflicting aircrafts and state the problem, we apply the importance sampling technique and elaborate an algorithm of collision modeling based on normal distributions, a small simulation studyРассмотрена модель движения двух конфликтующих самолетов. Предложены методика важных выборок и алгоритм моделирования столкновения самолетов, основанный на нормальном распределенииРозглянуто модель руху двох конфліктуючих літаків. Запропоновано методику істотних вибірок і алгоритм моделювання зіткнення літаків, заснований на нормальному розподіл

Reselling of European option if the implied volatility varies as Cox-Ingersoll-Ross process

On Black and Scholes market Investor buys a European call option. At each moment of time till the maturity he is allowed to resell the option for the quoted market price. In Kukush et al. (2006) On reselling of European option, Theory Stoch. Process., 12(28), 75-87, a similar problem was investigated for another model of the market price. We propose a more realistic model based on Cox-Ingersoll-Ross process. Discrete approximation for this model is investigated, which is arbitrage–free. For this discrete model, a formula for penultimate optimal stopping domains is derived

Bounds for a sum of random variables under a mixture of normals

In two papers: Dhaene et al. (2002). Insurance: Mathematics and Economics 31, pp.3-33 and pp. 133-161, the approximation for sums of random variables (rv’s) was derived for the case where the distribution of the components is lognormal and known, but the stochastic dependence structure is unknown or too cumbersome to work with. In finance and actuarial science a lot of attention is paid to a regime switching model. In this paper we give the approximation for sums under a mixture of normals and consider approximate evaluation of provision under switching regime

Comparing the efficiency of estimates in concrete errors-in-variables models under unknown nuisance parameters

We consider a regression of y on x given by a pair of mean and variance functions with a parameter vector θ to be estimated that also appears in the distribution of the regressor variable x. The estimation of θ is based on an extended quasi score (QS) function. Of special interest is the case where the distribution of x depends only on a subvector α of θ, which may be considered a nuisance parameter. A major application of this model is the classical measurement error model, where the corrected score (CS) estimator is an alternative to the QS estimator. Under unknown nuisance parameters we derive conditions under which the QS estimator is strictly more аfficient than the CS estimator. We focus on the loglinear Poisson, the Gamma, and the logit model

On the characterization of premium principle with respect to pointwise comonotonicity

A premium principle is an economic decision rule used by the insurer in order to determine the amount of the net premium for each risk in his portfolio. In this paper we investigate the problem how to determine the premium principle to be used. In Goovaerts & Dhaene (1997), DTEW Research Report 9740, K.U.Leuven, we can see some desirable properties of a premium principle. We consider a premium principle for risks of any sign, and prove a representation of premium principle without some property which involves the distribution of a risk. Later we introduce this property as a corollary

Possible use of television broadcasting signals for wind meas- urements by the meteor radiolocation method -main theoretical as- pects and results of first experiments

Summary The possibility of using terrestrial television (TV) broadcast signals (TVBS) as sounding signals for mesosphere-lower thermosphere (MLT) wind measurements by the radio meteor method is investigated. Such approach allows to use external TV transmitters as sounding signal sources and consequently to reduce costs of measurements. It is shown that meteor trails in the area above the receiver should be selected to eliminate MLT wind measurement ambiguity. Results of experimental observations are presented. Validation of the results has been performed using datasets from the Thermosphere-IonosphereMesosphere Energetics and Dynamics (TIMED) satellite and a SKiYMET meteor radar (Collm Observatory, Germany). It is shown that the obtained experimental results and TIMED mean winds are correlated with a correlation coefficient of 0.58 (significance level 0.95 according to a t-test). The measurements show for the first time that terrestrial television broadcast signals can be used for MLT wind measurements and that the developed technique may be used for MLT wind monitoring on the base of the existing terrestrial TV broadcasting network. Zusammenfassung Es wird untersucht, inwieweit terrestrischer Fernsehsignale zur Sondierung des Windes in der Mesosphäre und unteren Thermosphäre genutzt werden können. Ein solcher Ansatz erlaubt es, externe Sender als Quelle zu verwenden und damit Kosten zu sparen. Es wird gezeigt, dass Meteorsignale im Raum über dem Empfänger genutzt werden können, welches die Uneindeutigkeit der Windsignale verringert. Ergebnisse eines Experiments werden gezeigt und anhand von TIMED-Satellitendaten und VHF-Radarmessungen validiert. Die Messungen zeigen zum ersten Mal die Möglichkeit einer Windmessung in der unteren Thermosphäre auf der Basis terrestrischer Fernsehsignale

On the Polynomial Measurement Error Model

This paper discusses point estimation of the coefficients of polynomial measurement error (errors-in-variables) models. This includes functional and structural models. The connection between these models and total least squares (TLS) is also examined. A compendium of existing as well as new results is presented