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The article deals with the special subclass of φ-mixing periodically correlated (PC) time series and the estimation of autocovariance through Fourier coefficients. The aim is to investigate whether the subsampling of the autocovariance estimator is consistent. It is shown that the consistency holds for frequencies λ=0 and λ=π. Theoretical reasoning is supplemented with a simulation study.
EN
In the current literature, many different stochastic extensions of the DEA framework can be found. Such generalized approaches enable one to model the uncertainty inherent to the form of the production possibility set and the value of the technical efficiency measure at any given point of the former. In the paper we provide a detailed discussion of some statistical model and the subsampling algorithm which are used in statistical inference. The methodology is then illustrated with an empirical example using the real-world data from the Polish energy sector.
EN
The phenomenon of nonresponse in sample surveys usually results in biased estimates of population characteristics. One of the means to deal with nonresponse is the subsampling technique. It relies on re-contacting some subset of nonrespondents by using more expensive and more efficient tools (e.g. direct interview) than those used in the first attempt to collect data. This allows to increase response rate and to obtain unbiased estimates of population characteristics. In this paper, the problem of establishing the sample and subsample sizes minimizing the expected cost of the survey, while achieving desired precision of multiple mean value estimates, is considered. An algorithm is proposed that allows to establish the optimum initial sample and subsample sizes for two-phase sampling strategy.
EN
The main objective of the paper is to investigate properties of business cycles in the Polish economy before and after the recent crisis. The essential issue addressed here is whether there is statistical evidence that the recent crisis has affected the properties of the business cycle fluctuations. In order to improve robustness of the results, we do not confine ourselves to any single inference method, but instead use different groups of statistical tools, including non-parametric methods based on subsampling and parametric Bayesian methods. We examine monthly series of industrial production (from January 1995 till December 2014), considering the properties of cycles in growth rates and in deviations from long-run trend. Empirical analysis is based on the sequence of expanding-window samples, with the shortest sample ending in December 2006. The main finding is that the two frequencies driving business cycle fluctuations in Poland correspond to cycles with periods of 2 and 3.5 years, and (perhaps surprisingly) the result holds both before and after the crisis. We, therefore, find no support for the claim that features (in particular frequencies) that characterize Polish business cycle fluctuations have changed after the recent crisis. The conclusion is unanimously supported by various statistical methods that are used in the paper, however, it is based on relatively short series of the data currently available.
EN
One of the most challenging issues regarding water quality control is the lack of adequate measurements and lack of data on many water quality constituents. Since water quality is highly variable during time and space, traditional grab sampling often misses extreme events and the result isn’t always a representative one. This paper evaluated the usefulness of turbidity measurement as a surrogate for the determination of the Total Phosphorus. Instead of in-situ sensors for real time turbidity measurements, another approach was taken during this investigation. The suitability of using turbidity as a surrogate for TP was investigated using prepared subsamples, each with different concentration of water quality constituents. Laboratory results, with the use of the linear regression techniques, enabled the development of the model that relates the total phosphorus to turbidity. The linear regression equation developed, TP = 0.3942TTU – 3.4279 shows that there is a very good prediction of the total phosphorus based on the turbidity measurement, with the correlation coefficient as good as R2 = 0.8782 and p-value less than 0.5. Even though the equation is site specific, and more investigation is needed, we conclude that it can be used in similar situations, when there is a lack of monitoring programs.
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