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EN
In this paper we present the problem of forecasting efficiency of the TAR models. Three methods of forecasting are considered to compare their accuracy: the Monte Carlo method, and the two versions the bootstrap technique. The basic models are two- or three- regimes stationary threshold autoregressive models with the endogenous or exogenus switching variable. The time series set consists of the weekly stock returns of the banking sector quoted at the Warsaw Stock Exchange.
PL
Celem artykułu jest porównanie metod prognozowania nieliniowych modeli progowych. Wykorzystane zostały dwie metody prognozowania: metoda bootstrap w dwóch wariantach oraz metoda Monte Carlo. Przedmiotem analizy są tygodniowe stopy zwrotu spółek sektora bankowego, notowanych na GPW w Warszawie. W konkluzji stwierdza się, że przewidywanie dokładnych wartości stóp zwrotu jest bardzo trudne, natomiast modele progowe dają bardzo dobre wyniki w zakresie przewidywania kierunków zmian w przyszłości.
EN
Bootstrap is one of the resampling statistical methods. This method was proposed by B. Efron. The main idea of bootstrap is to treat the original sample of values as a stand-in for the population and to resample with replacement from it repeatedly. Bootstrap allows estimation of the sampling distribution of almost any statistics using only very simple methods. This paper presents a modification of a resampling procedure based on bootstrap sampling. The proposal leads to sampling from population with density function f(x), where f(x) is estimated based on the kernel estimation. The properties of the method were analyzed in the median estimation in Monte Carlo study.The proposal could be useful for the parameters estimation in the case of a small sample. This method could be used in quality control procedures such as control charts or in the acceptance sampling.
EN
Nowadays, in many fields of science it is necessary to carry out miscellaneous analyses using classical statistical methods, which usually have correct assumptions. These assumptions in the research realities cannot always be met, which makes it impossible to carry out analyses and leads to incorrect conclusions and recommendations. The study of the production process largely consists in the use of tools of statistical quality control which are based on classical statistical methods. These methods result in some improvements in technological and economic results of the manufacturing process. One of the tools of statistical quality control is the design of experiments, whose important element is the estimation of response surface function. The aim of this paper is to present the bootstrap method of estimation of response surface function and its use for empirical data.
PL
W pracy przedstawiono wybrane metody bootstrapowe estymacji przedziałowej wartości oczekiwanej populacji o rozkładzie asymetrycznym. Rozważano standardową metodę bootstrapowa, metodę percentyli oraz metodę t-bootstrapową. Metody te można stosować przy estymacji wartości oczekiwanej zmiennej losowej o rozkładzie asymetrycznym, zarówno dla małych jak i dużych prób. Analiza własności bootstrapowych metod estymacji przedziałowej przeprowadzona została metodami Monte Carlo.
EN
In the paper we present some chosen bootstrap methods of interval estimation of the population expectation for asymmetric distribution. We consider the standard bootstrap method, percentile method and t-bootstrap method. These methods can be used to estimate the expected value of asymmetric distribution for, both, small and large sample sizes. The analysis of the properties of bootstrap methods of interval estimation is performed by means of a simulation experiment.
PL
Wprowadzone w 2011 i 2014 roku zmiany systemowe dotyczące dostosowania kształcenia do potrzeb rynku pracy wpłynęły na sytuację w szkolnictwie wyższym w kolejnych latach. W niniejszym artykule dokonano pomiaru efektywności polskich uczelni publicznych i prywatnych oraz oszacowano wpływ poszczególnych determinant na poziom efektywności uczelni. Do pomiaru efektywności wykorzystano model BCC należący do metody DEA. Natomiast do oszacowania wpływu zmiennych środowiskowych na poziom efektywności uczelni wykorzystano regresję uciętą. W badaniu przeanalizowano efektywność działalności dydaktycznej uczelni publicznych i prywatnych zarówno w zakresie liczebności, uwzględniając liczbę absolwentów, jak i jakości edukacji w kontekście rynku pracy, ujmując wartość zarobków absolwentów po ukończeniu edukacji akademickiej. Wyniki badania wskazują, że uczelnie publiczne były bardziej efektywne pod względem liczby absolwentów, ale mniej efektywne pod względem poziomu wynagrodzeń absolwentów. Odwrotnie było w przypadku uczelni prywatnych. Na poziom efektywności wpływały zarówno zmienne związane z samymi szkołami wyższymi, jak i sytuacją społeczno-ekonomiczną regionu, w którym funkcjonują szkoły.
EN
Changes introduced to Poland’s education system in 2011 and 2014 amid efforts to adjust it to the needs of the labour market had an effect on the country’s institutions of higher learning. This paper provides an analysis of the efficiency of public and private Polish universities and examines the impact of selected factors in the years that followed. To estimate this efficiency, a Banker, Charnes and Cooper (BCC) model of the Data Envelopment Analysis (DEA) method was used. To gauge the impact of environmental variables on the efficiency of universities, a truncated regression analysis was performed. The results of the study indicate that public universities were more efficient in terms of the number of graduates they produced but less efficient when considering the level of graduate salaries. The opposite was true for private institutions. The level of efficiency was affected by variables related to specific universities and the socio-economic situation of the region in which they operate. The study analyses the efficiency of educational activities of public and private universities, both in terms of the number of graduates and the quality of education and in the context of the labour market. The analysis also considers the level of graduate earnings.
EN
A class of approximately locally most powerful type tests based on ranks of residuals is suggested for testing the hypothesis that the regression coefficient is constant in a standard regression model against the alternatives that a random walk process generates the successive regression coefficients. We derive the asymptotic null distribution of such a rank test. This distribution can be described as a generalization of the asymptotic distribution of the Cramer-von Mises test statistic. However, this distribution is quite complex and involves eigen values and eigen functions of a known positive definite kernel, as well as the unknown density function of the error term. It is then natural to apply bootstrap procedures. Extending a result due to Shorack in [25], we have shown that the weighted empirical process of residuals can be bootstrapped, which solves the problem of finding the null distribution of a rank test statistic. A simulation study is reported in order to judge performance of the suggested test statistic and the bootstrap procedure.
EN
Typically survey data have responses with gaps, outliers and ties, and the distributions of the responses might be skewed. Usually, in small area estimation, predictive inference is done using a two-stage Bayesian model with normality at both levels (responses and area means). This is the Scott-Smith (S-S) model and it may not be robust against these features. Another model that can be used to provide a more robust structure is the two-stage Dirichlet process mixture (DPM) model, which has independent normal distributions on the responses and a single Dirichlet process on the area means. However, this model does not accommodate gaps, outliers and ties in the survey data directly. Because this DPM model has a normal distribution on the responses, it is unlikely to be realized in practice, and this is the problem we tackle in this paper. Therefore, we propose a two-stage non-parametric Bayesian model with several independent Dirichlet processes at the first stage that represents the data, thereby accommodating some of the difficulties with survey data and permitting a more robust predictive inference. This model has a Gaussian (normal) distribution on the area means, and so we call it the DPG model. Therefore, the DPM model and the DPG model are essentially the opposite of each other and they are both different from the S-S model. Among the three models, the DPG model gives us the best head-start to accommodate the features of the survey data. For Bayesian predictive inference, we need to integrate two data sets, one with the responses and other with area sizes. An application on body mass index, which is integrated with census data, and a simulation study are used to compare the three models (S-S, DPM, DPG); we show that the DPG model might be preferred.
EN
Objectives To explore the relationship between depressive symptoms, fatigue and psychological flexibility, as well as their interactions on depression in Chinese nurses. Material and Methods Using convenience sampling, a cross-sectional survey of 796 nurses in municipal hospitals of Zhengzhou, Henan Province, China, was conducted. The questionnaires of Work-related Acceptance and Action Questionnaire, Center for Epidemiological Studies Depression Scale and Fatigue Assessment Instrument were used. Hierarchical regression and bootstrap methods were used to examine the mediating effect of psychological flexibility between fatigue and depression. Results More than 51.8% of the nurses were at risk of depression and 62.3% were at risk of fatigue. There was a significantly positive and moderate correlation between depression and fatigue severity, situation specificity, and consequences (r = 0.43, r = 0.24 and r = 0.31, respectively, p < 0.01). Depression was negatively correlated with psychological flexibility (r = –0.28, p < 0.01). Psychological flexibility had a negative impact on depression with the explained variance increased by 4.2% (β = –0.211, p < 0.001). The bootstrap method showed that the mediating effect of psychological flexibility accounting for 8.5% and 12.3% on fatigue and depressive symptoms, respectively. Conclusions Psychological flexibility plays a partial mediating role between the fatigue severity, consequences of fatigue and depressive symptoms of nurses. Hospital managers should improve medical staff work acceptance to alleviate their depressive symptoms.
EN
A presence of a noise is typical for real-world data. In order to avoid its negative impact on methods of time series analysis, noise reduction procedures may be used. The achieved results of an application of such procedures in identification of chaos or nonlinearity seem to be encouraging. One of the noise reduction methods is the Schreiber method, which, as it has been shown, is able to effectively reduce a noise added to time series generated by deterministic systems with chaotic dynamics. However, while analyzing real-world data, a researcher usually cannot be sure if the generating system is deterministic. Therefore, there is a risk that a noise reduction method will be applied to random data. In this paper, it has been shown that in situations where there in no clear evidence that investigated data are generated by a deterministic system, the Schreiber noise reduction method may negatively affect identification of time series. In the simulation carried out in this paper, the BDS test, the mutual information measure and the Pearson autocorrelation coefficient were used. The research has shown that an application of the Schreiber method may introduce spurious nonlinear dependencies to investigated data. As a result, random series may be misidentified as nonlinear.
PL
Jednym ze sposobów ograniczenia negatywnego wpływu obecności szumu losowego na analizę rzeczywistych szeregów czasowych jest stosowanie metod redukcji szumu. Prezentowane w literaturze przedmiotu rezultaty zastosowania takich procedur w procesie identyfikacji nieliniowości i chaosu są zachęcające. Jedną z metod redukcji szumu jest metoda Schreibera, która, jak wykazano, prowadzi do efektywnej redukcji szumu losowego dodanego do danych wygenerowanych z systemów deterministycznych o dynamice chaotycznej. Jednakże w przypadku danych rzeczywistych, badacz zwykle pozbawiony jest wiedzy, czy system generujący rzeczywiście jest deterministyczny. Istnieje więc ryzyko, że redukcji szumu zostaną wówczas poddane dane losowe. W niniejszym artykule wykazano, iż w sytuacji, gdy brak jest wyraźnych podstaw do stwierdzenia, że badany szereg pochodzi z systemu deterministycznego, metodę Schreibera należy stosować z dużą ostrożnością. Z przeprowadzonych symulacji, w których wykorzystano test BDS, miarę informacji wzajemnej oraz współczynnik korelacji liniowej Pearsona wynika bowiem, że redukcja szumu może wprowadzić do analizowanych danych, zależności o charakterze nieliniowym. W efekcie szeregi losowe mogą zostać błędnie zidentyfikowane jako nieliniowe.
EN
The aim of this paper is to create a stable model of investment portfolio optimization through a high degree of diversification and reduction of sudden changes in the allocation with monitoring of the dynamics of the impact factor. In this sense, there is bootstrap application procedure, which, without an excessive number of constraints involved in the optimization process provides solutions based on uncertain information. Thus defined, the optimization method has been patented by Michaud (1999) entitled re-sampled efficiency. Accordingly, this paper offers a comparison of the performance block bootstrap optimization models and traditional Markowitz's model inside and outside of the sample by applying the most frequently traded stocks on the BSE. The results show a better performance out of the sample and the presence of a larger number of shares forming the portfolio through bootstrap methodology. However, only through the traditional optimization process could be attained optimum according to the required limits. Such effects can be observed by comparing the limits of efficiency obtained through these optimization models. However, optimization-based methods bootstrap finds its place in reducing errors of assessment resulting from the limited sample size.
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