A polynomial structural regression model is studied, where the covariate is observed with a mixture of the classical and Berkson measurement errors. Both variances of the classical and Berkson errors, as well as some of their higher moments are assumed to be known. Without normality assumptions, consistent estimators of model parameters are constructed using the Corrected Score method, and conditions for their asymptotic normality are given. Under mild conditions, we found pairs of asymptotically independent estimators. A simulation study illustrates the results.

A criterion is proposed for testing the hypothesis about the nature of the error variance in the dependent variable in a linear model, which separates correctly and incorrectly specified models. In the former one, only the measurement errors determine the variance (i.e., the dependent variable is correctly explained by the independent ones, up to measurement errors), while the latter model lacks some independent covariates (or has a nonlinear structure). The proposed MEMV (Measurement Error Model Validity) test checks the validity of the model when both dependent and independent covariates are measured with errors. The criterion has an asymptotic character, but numerical simulations outlined approximate boundaries where estimates make sense. A practical example of the test’s implementation is discussed in detail – it shows the test’s ability to detect wrong specifications even in seemingly perfect models. Estimations of the errors due to the omission of the variables in the model are provided in the simulation study. The relation between measurement errors and model specification has not been studied earlier, and the proposed criterion may stimulate future research in this important area.

The low-rank approximation problem, that is the problem of approximating a given matrix with a matrix of lower rank, appears in many scientific fields. In some applications the given matrix is structured and the approximation is required to have the same structure. Examples of linear structures are Hankel, Toeplitz, and Sylvester. Currently, there are only a few results for nonlinearly structured low-rank approximation problems. The problem of Vandermonde structured low-rank approximation is considered. The high condition number of the Vandermonde matrix, in combination with the noise in the data, makes the problem challenging. A numerical method based on a bias correction procedure is proposed and its properties are demonstrated by simulation. The performance of the method is illustrated on numerical results.

A linear geostatistical model is considered. Properties of a universal kriging are studied when the locations of observations are measured with errors. Alternative prediction procedures are introduced and their least squares errors are analyzed.

This paper emphasizes the important role of assets valuation in assuring the transparency and stability of financial system as underlined by the international Basel Accord on banking supervision. One of the main aspect in this respect is necessity to take into account time factor influence that is especially important for secured lending operations, insurance processes, and in general for investment purposes where duration is essential. Existing approaches for accounting this factor in assets valuation processes are based on empirical analyses of historical data followed by forecasts for the future time period. In this respect two main streamline of approaches are formed: based on smoothing the cyclicity of value change over time or “through cycle” type and skirting of market value evolution trend or “under cycle” type, respectfully. In the paper, a new stochastic analytical model to consider time effect is proposed, which is based on the rational theory of warrant pricing developed by Samuelson. Analytical solution for estimation of proposed time factor Δ is presented. The influence of market value volatility, tendency of market future evolution and required level of certainty on this parameter is analyzed. General methodology of time effect assessment based on this “follow-the-cycle” type model is described. Actual problems of international relations. Issue 150. 2022 48 Testing of the model applicability was demonstrated using the available information data set for the residential apartments market evolution in 2019-2021 in Ukraine which is monitored by consulting-engineering group “Veritex”.

The current demographic pattern in Ukraine features the decreasing birth rate and the increasing mortality, resulting in ageing and decline of the population, which breaks the favourable demographic balance. At the Ukrainian territories affected by radioactive contamination because of the accident at the Chornobyl nuclear power plant, these processes differ from those on other territories. Given the considerable impact of emergency situations on the course of demographic processes, developing and testing prediction techniques specifically designed for those territories has essential importance. The purpose of this work is to forecast changes in demographic indicators (population number, birth rate, mortality,infant mortality and stillbirth) by spline functions, forthe areas with the heaviest radioactive contamination after the Chornobyl disaster, which are located in Zhytomyr region (Korosten, Luhyno, Narodychy, Ovruch and Olevsk), for 2020–2023, and the town of Korosten for 2021–2023.The data sources for the research were State Statistic Service of Ukraine for 1979–2020, and the Ministry of Health of Ukraine for the period of the COVID-19 pandemic. At the first phase, spline functions were used to forecast the abovementioned indicators in 2017–2020 by data for 1979–2016 for the town of Korosten. A comparison of the resulting forecast with the actual data led to the conclusion that that spline models of observations could be an effective tool for short-term forecasting of population number, birth rate and mortality. The most adequate prediction of population numbers could be achieved with cubic splines, whereas the best prediction of birth rate and mortality – with linear continuous splines. The forecasts of birth and mortality rates for 2017–2020 proved to be quite optimistic. However, in the pandemic conditions, a deviation of the predicted population numbers, birth rate and mortality was revealed: actual numbers for all the three indicators in 2020 were beyond the confidence region, which had not been the case in 2017–2019. The actual figures in 2020, found to be far worse than the predicted ones, may be caused by the impact of the COVID-19 pandemic in 2020, which is an unpredictable factor. The extra mortality caused by COVID-19 in 2020 was estimated for the town of Korosten. At the second phase, probable changes in the population number, birth rate and mortality were predicted for 2021–2023 in all the areas. The 95% confidence region and confidence intervals were built for the predictions. It was found that the last years’ trends in demographic indicators in radioactively contaminated territories would continue in a short-term perspective. It was shown that because annual numbers of infant mortality and stillbirthcould not be predicted due to their significant variations, averaging for 5-year periods should be used. A forecast of the average numbers was made for the 5 five-year periods where actual data were unknown. Also, it was emphasized that for the indicators predicted with linear continuous splines, actual numbers might turn to be far from the forecasted ones, because of the existence of extreme points, with growth suddenly changing for decline, and vice versa. Because such points cannot be predicted by extrapolation of observed trends, it is necessary to find other methods for their prediction. Further research will focus on other prediction methods, to achieve higher prediction accuracy,and on inclusion of economic indicators in the prediction models.

Thyroid doses from intake of radioiodine isotopes (131I, 132Te+132I, and 133I) and associated uncertainties were revised for the 13,204 Ukrainian-American cohort members exposed in childhood and adolescence to fallout from the Chornobyl nuclear power plant accident. The main changes related to the revision of the 131I thyroid activity measured in cohort members, the use of thyroid-mass values specific to the Ukrainian population, and the revision of the 131I ground deposition densities in Ukraine. Uncertainties in doses were assessed considering shared and unshared errors in the parameters of the dosimetry model. Using a Monte-Carlo simulation procedure, 1,000 individual stochastic thyroid doses were calculated for each cohort member. The arithmetic mean of thyroid doses from intake of 131I, 132Te+132I, and 133I for the entire cohort was 0.60 Gy (median = 0.22 Gy). For 9,474 subjects (71.6% of the total), the thyroid doses were less than 0.5 Gy. Thyroid doses for 42 cohort members (0.3% of the total) exceeded 10 Gy while the highest dose was 35 Gy. Intake of 131I contributed around 95% to internal thyroid exposure from radioiodine isotopes. The geometric standard deviation of individual stochastic thyroid doses varied among cohort members from 1.4 to 4.3 with an arithmetic mean of 1.6 and a median of 1.4. It was shown that the contribution of shared errors to the dose uncertainty was small. The revised thyroid doses resulted, in average, in around 40% decrease for cohort members from Zhytomyr Oblast and an increase of around 24% and 35% for the cohort members from Kyiv and Chernihiv Oblast, respectively. Arithmetic mean of TD20 doses for the cohort was around 8% less than that estimated in TD10, 0.60 Gy vs. 0.65 Gy, respectively; however, global median of TD20 doses somewhat increased compared to TD10: 0.22 Gy vs. 0.19 Gy, respectively. The difference between TD10 and TD20 was mainly due to a revision of the individual 131I thyroid activity measured in the cohort members.

We investigate the mixed fractional Brownian motion with trend of the form $$X_t = \theta t + \sigma W_t + \kappa B^H_t$$ , driven by a standard Brownian motion W and a fractional Brownian motion $$B^H$$ with Hurst parameter H. We develop and compare two approaches to estimation of four unknown parameters $$\theta $$ , $$\sigma $$ , $$\kappa $$ and H by discrete observations. The first algorithm is more traditional: we estimate $$\sigma $$ , $$\kappa $$ and H using the quadratic variations, while the estimator of $$\theta $$ is obtained as a discretization of a continuous-time estimator of maximum likelihood type. This approach has several limitations, in particular, it assumes that $$H<\frac{3}{4}$$ , moreover, some estimators have too low rate of convergence. Therefore, we propose a new method for simultaneous estimation of all four parameters, which is based on the ergodic theorem. Finally, we compare two approaches by Monte Carlo simulations.

The increased risk of thyroid cancer among individuals exposed during childhood and adolescence to Iodine-131 (131I) is the main statistically significant long-term effect of the Chornobyl accident. Several radiation epidemiological studies have been carried out or are currently in progress in Ukraine, to assess the risk of radiation-related health effects in exposed populations. About 150,000 measurements of 131I thyroid activity, so-called 'direct thyroid measurements', performed in May–June 1986 in the Ukrainian population served as the main sources of data used to estimate thyroid doses to the individuals of these studies. However, limitations in the direct thyroid measurements have been recently recognized including improper measurement geometry and unknown true values of calibration coefficients for unchecked thyroid detectors. In the present study, a comparative analysis of 131I thyroid activity measured by calibrated and unchecked devices in residents of the same neighboring settlements was conducted to evaluate the correct measurement geometry and calibration coefficients for measuring devices. As a result, revised values of 131I thyroid activity were obtained. On average, in Vinnytsia, Kyiv, Lviv and Chernihiv Oblasts and in the city of Kyiv, the revised values of the 131I thyroid activities were found to be 10–25% higher than previously reported, while in Zhytomyr Oblast, the values of the revised activities were found to be lower by about 50%. New sources of shared and unshared errors associated with estimates of 131I thyroid activity were identified. The revised estimates of thyroid activity are recommended to be used to develop an updated Thyroid Dosimetry system (TD20) for the entire population of Ukraine as well as to revise the thyroid doses for the individuals included in post-Chornobyl radiation epidemiological studies: the Ukrainian-American cohort of individuals exposed during childhood and adolescence, the Ukrainian in utero cohort and the Chornobyl Tissue Bank.

This paper describes the revision of the thyroid dosimetry system in Ukraine using new, recently available data on (i) revised 131I thyroid activities derived from direct thyroid measurements done in May and June 1986 in 146,425 individuals; (ii) revised estimates of 131I ground deposition density in each Ukrainian settlement; and (iii) estimates of age- and gender-specific thyroid masses for the Ukrainian population. The revised dosimetry system estimates the thyroid doses for the residents of the settlements divided into three levels depending on the availability of measurements of 131I thyroid activity among their residents. Thyroid doses due to 131I intake were estimated in this study for different age and gender groups of residents of 30,353 settlements in 24 oblasts of Ukraine, Autonomous Republic Krym, and cities of Kyiv and Sevastopol. Among them, dose estimates for 835 settlements were based on 131I thyroid activities measured in more than ten residents (the first level), for 690 settlements based on such measurements done in neighboring settlements (the second level), and for 28,828 settlements based on a purely empirical relationship between the thyroid doses due to 131I intake and the cumulative 131I ground deposition densities in settlements (the third level). The arithmetic mean of the thyroid doses due to 131I intake among 146,425 measured individuals was 0.23 Gy (median of 0.094 Gy); about 99.8% of them received doses less than 5 Gy. The highest oblast-average population-weighted thyroid doses were estimated for residents of Chernihiv (0.15 Gy for arithmetic mean and 0.060 Gy for geometric mean), Kyiv (0.13 and 0.051 Gy) and Zhytomyr (0.12 and 0.049 Gy) Oblasts followed by Rivne (0.10 and 0.039 Gy) and Cherkasy (0.088 and 0.032 Gy) Oblasts, and Kyiv City (0.076 and 0.031 Gy). The geometric mean of thyroid doses estimated in this study for the entire Ukraine essentially did not change in comparison with a previous estimate, 0.020 vs. 0.021 Gy, respectively. The ratio of geometric mean of oblast-specific thyroid doses estimated in the present study to previously calculated doses varied from 0.51 to 3.9. The highest increase in thyroid doses was found in areas remote from the Chornobyl nuclear power plant with a low level of radioactive contamination: by 3.9 times for Zakarpatska Oblast, 3.5 times for Luhansk Oblasts and 2.9 times for Ivano-Frankivsk Oblast. The developed thyroid dosimetry system is being used to revise the thyroid doses due to 131I intake for the individuals of post-Chornobyl radiation epidemiological studies: the Ukrainian-American cohort of individuals exposed during childhood and adolescence, the Ukrainian in utero cohort, and the Chornobyl Tissue Bank.

We consider the fractional Ornstein–Uhlenbeck process with an unknown drift parameter and known Hurst parameter H . We propose a new method to test the hypothesis of the sign of the parameter and prove the consistency of the test. Contrary to the previous works, our approach is applicable for all H ∈ (0, 1). We also study the estimators for drift parameter for continuous and discrete observations and prove their strong consistency for all H ∈ (0, 1).

Objective of research is to improve the electronic database of WBC measurements dated 1986 by inputting of newinformation from paper carriers, reconstruction of information gaps, verification and analysis of new entered data,revision of internal exposure doses that are based on results of WBC measurements dated 1986.MATERIALS AND METHODS:In 2013-2015 during a revision of databases (DB) of WBC measurements results dated1986-2014, it was discovered a great amount of paper carriers with information about WBC measurements, includ-ing the ones dated 1986, that were not inputted to the electronic DB. The paper carriers were systematized andordered by the following indicators: place of residence of a person and place of WBC measurement, institution andoperator that made the measurement, measurement device and date of measurement. For a comfortable inputtingof the information to the electronic DB, it was additionally created a form which exists as an option in existing program complex Silbody (Version 19.0.9). In the revised DB of WBC measurements dated 1986 internal exposure dosesfrom radio-cesium of Chornobyl origin were computed based on an ecological and dosimetric model for radio-cesiummigration in environment and a model for radio-cesium metabolism in human body. In the work, mathematical andstatistical methods of research were used.RESULTS:In 2019-2021 additionally 35,319 notes were inputted to the electronic DB of WBC measurement dated1986, and as a result its volume increased in 2.2 times. Mostly those are data on results concerning residents of Kyiv,Zhytomyr, Donetsk, Cherkasy, Odessa, Ivano-Frankivsk, and Rivne Oblasts. It was established the information onmeasurement devices and respectively on the minimal detected activity (MDA) for 27,119 notes (76.7 % of all newentered). Information is reconstructed about the body mass of all persons under investigation. Evaluation is madefor values of intake of incorporated radionuclides 137Cs and 134Cs for all new entered to DB. Quality of reconstructedinformation was analyzed. To group 1, «qualitative», it was classified 18,598 notes (53 % of all new entered), measurements in 1986 (including new entered). Dose not exceeding 1 mSv was obtained by 80 % of adults (older than20), as well as 73 % of persons younger than 20.CONCLUSION:To DB of WBC measurements, it was additionally inputted 35,319 notes on results of measurementsdated 1986. New entered information is verified and distributed by the quality groups. Individual exposure dosesevaluated based on those data can be used for further scientific research.

A linear structural regression model is studied, where the covariate is observed with a mixture of the classical and Berkson measurement errors. Both variances of the classical and Berkson errors are assumed known. Without normality assumptions, consistent estimators of model parameters are constructed and conditions for their asymptotic normality are given. The estimators are divided into two asymptotically independent groups.

A multivariate errors-in-variables (EIV) model with an intercept term, and a polynomial EIV model are considered. Focus is made on a structural homoskedastic case, where vectors of covariates are i.i.d. and measurement errors are i.i.d. as well. The covariates contaminated with errors are normally distributed and the corresponding classical errors are also assumed normal. In both models, it is shown that (inconsistent) ordinary least squares estimators of regression parameters yield an a.s. approximation to the best prediction of response given the values of observable covariates. Thus, not only in the linear EIV, but in the polynomial EIV models as well, consistent estimators of regression parameters are useless in the prediction problem, provided the size and covariance structure of observation errors for the predicted subject do not differ from those in the data used for the model fitting.

For an arbitrage-free market with a single underlying asset, we investigate conditions under which the consecutive price levels are comonotonic. Furthermore, for an arbitrage-free market with n assets we investigate the consequences of assuming comonotonicity of the vector containing the price levels of each asset at a single future date T. Although being of a theoretical nature, the results of this paper give insight in the reachability of the comonotonic upper bounds for Asian options and for basket options that can be found in Simon et al. (2000), Dhaene et al. (2002) [1], Hobson et al. (2005) and Chen et al. (2008).