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PL
Losowanie zrównoważone polega na takim doborze próby, aby szacunki sum zmiennych pomocniczych estymatorem Horvitza-Thompsona równały się rzeczywistym sumom tych zmiennych. Kalibracja natomiast polega na modyfikacji wyjściowych wag wynikających z planu losowania w taki sposób, aby zmodyfikowane wagi odtwarzały znane sumy zmiennych pomocniczych. Ideą obu metod jest odwzorowanie wartości globalnych zmiennych dodatkowych. Celem artykułu jest przedstawienie i porównanie obu technik traktowanych jako alternatywa do osiągnięcia tego samego celu. Więcej uwagi poświęcono losowaniu zrównoważonemu. Algorytm doboru próby zilustrowano za pomocą dwóch prostych przykładów. Porównanie losowania zrównoważonego z kalibracją wypada korzystniej dla tej drugiej metody, jednak najlepszym rozwiązaniem jest zastosowanie obu metod jednocześnie.
EN
A balanced sampling design is a design in which Horvitz-Thompson estimators of population totals for a set of auxiliary variables equal the known totals of these variables. On the other hand, calibration is a technique where the modification of design weights occurs in such a way that the new weights, when applied to auxiliary variables, reproduce, i.e. estimate without error, the known totals for these variables. The general idea behind balanced sampling and calibration is thus the same — both techniques tend to reproduce known totals of the auxiliary variables. The purpose of the paper is to describe and compare both techniques, considering them as alternatives in achieving the same goal. More attention was devoted to balanced sampling. The algorithm for selecting a sample was illustrated with two numerical examples. The comparison between balanced sampling and calibration, as alternatives, indicates calibration, but the best strategy is to use both methods simultaneously.
RU
Сбалансированная выборка заключается в такой выборке, чтобы оценки вспомогательных сумм величин оценкой Хорвица-Томсона были равны фактическим суммам этих величин. В то же время калибровка состит в модификации выходных весов являющихся результатом плана выборки так, чтобы модифицированные весы воссоздавали известные суммы вспомогательных величин. Идея обоих методов состоит в копировании значения глобальных дополнительных величин. Целью статьи является представление и сопоставление двух методов, которые считаются альтернативой для достижения той же цели. Больше внимание было уделено сбалансированной выборке. Алгоритм выборки представлен с помощью двух простых примеров. Сравнение сбалансированной выборки с калибровкой является выгодным для другого метода, но самым хорошим решением является одновременное использование обоих методов.
EN
The aim of this study was to verify the short-term impact of financial variables on the corporate reputation perceived by investors. In the study we applied an approach from the field of business valuation assuming that corporate reputation perceived by investors is reflected in the difference between the valuation of a company by investors and its book value. Using panel data methodology, we analysed impacts of selected financial variables, representing company’s profitability, stability and its level of risk, on these differences in valuations of selected companies listed on the Warsaw Stock Exchange. Particularly, we chose companies operating in Construction and IT sectors to represent different types of activities (industry vs. services), which impacts also the diversity in the structure of their financial statements. In the study we used multiple regression models and analysis of contingency tables (chi-squared tests of independence and Yule’s coefficient of colligation). Our data suggest that there is a lack of strong short-term relations between analysed financial variables and corporate reputation. Nevertheless, we found different determinants of corporate reputation in the Construction sector (stability and profitability as well as their changes) and in the IT sector (stability, changes in profitability and the level of financial risk).
EN
One of the main descriptive characteristics is the mode. For continuous variables it is not always easy to properly determine the mode. There are some estimates of the mode provided in literature, however, unlike the median or the arithmetic mean, for the mode there does not exist the estimator which would be commonly considered as the best one. Moreover, in many statistical textbooks and computer packages this problem seems to be ignored. In this paper authors consider seven different methods of estimation the mode presented in literature. The efficiency of the estimation procedures has been evaluated on the basis simulation experiments for the normal and lognormal distributions with different degrees of skewness. The evaluation criteria of those procedures involve not only the efficiency of estimation but also simplicity of computation, which is an important aspect of teaching statistics.
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