Wyniki wyszukiwania - Biblioteka Nauki

1

On the estimation of the autocorrelation function

100%

Ortigueira M.

Discussiones Mathematicae Probability and Statistics

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2010

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tom 30

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nr 1

103-115

EN

The autocorrelation function has a very important role in several application areas involving stochastic processes. In fact, it assumes the theoretical base for Spectral analysis, ARMA (and generalizations) modeling, detection, etc. However and as it is well known, the results obtained with the more current estimates of the autocorrelation function (biased or not) are frequently bad, even when we have access to a large number of points. On the other hand, in some applications, we need to perform fast correlations. The usual estimators do not allow a fast computation, even with the FFT. These facts motivated the search for alternative ways of computing the autocorrelation function. 9 estimators will be presented and a comparison in face to the exact theoretical autocorrelation is done. As we will see, the best is the AR modified Burg estimate.

2

APPLICATION OF REGRESSION MODELS IN ANALYSIS OF THE ADVERTISEMENT'S IMPACT ON CONSUMER'S DECISION MAKING PROCESS

80%

Chrzanowska M. , Chudzian J.

Metody Ilościowe w Badaniach Ekonomicznych

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2014

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tom 15

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nr 2

64-73

EN

Consumer's behaviour in the market is a widely studied and analysed problem. Complexity of social, economic and psychological determinants that influence consumer's decision process is a reason for multilevel and multi-factor approaches to analyse this problem. Therefore the aim of this paper is to describe application of parametric regression model for the effectiveness of advertising. The study described is based on a survey covering 550 consumers of dairy product, all of age over 15 and living in one of the nine biggest Polish agglomerations. Built models were examined and verified statistically. Obtained results clearly show that the approach chosen to describe AIDA model is an appropriate method for analysing impact of advertisement on consumer's decision making process.

3

Gradient Boosting in Regression

80%

Gatnar E. , University of Economics in Katowice I. o. S.

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PL

Szeroko stosowane w praktyce metody nieparametryczne wykorzystujące tzw. drzewa regresyjne mają jedną istotną wadę. Otóż wykazują one niestabilność, która oznacza, że niewielka zmiana wartości cech obiektów w zbiorze uczącym może prowadzić do powstania zupełnie innego modelu. Oczywiście wpływa to negatywnie na ich trafność prognostyczną. Tę wadę można jednak wyeliminować, dokonując agregacji kilku indywidualnych modeli w jeden. Znane są trzy metody agregacji modeli i wszystkie opierają się na losowaniu ze zwracaniem obiektów ze zbioru uczącego do kolejnych prób uczących: agregacja bootstrapowa (boosting), losowanie adaptacyjne (bagging) oraz metoda hybrydowa, łącząca elementy obu poprzednich. W analizie regresji szczególnie warto zastosować gradientową, sekwencyjną, odmianę metody boosting. W istocie polega ona wykorzystaniu drzew regrcsyjnych w kolejnych krokach do modelowania reszt dla modelu uzyskanego w poprzednim kroku.

EN

The successful tree-based methodology has one serious disadvantage: lack of stability. That is, regression tree model depends on the training set and even small change in a predictor value could lead to a quite different model. In order to solve this problem single trees are combined into one model. There are three aggregation methods used in classification: bootstrap aggregation (bagging), adaptive resample and combine (boosting) and adaptive bagging (hybrid bagging-boosting procedure). In the field of regression a variant of boosting, i.e. gradient boosting, can be used. Friedman (1999) proved that boosting is equivalent to a stepwise function approximation in which in each step a regression tree models residuals from last step model.

4

On Some Composite Estimator of the Population Mean

80%

Gamrot W. , Department of Statistics U. o. E.

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EN

In this paper an estimator of the finite population mean in the unit nonresponse situation is proposed. It is constructed as a combination of the well-known regression estimator derived from the linear model and a reweighting-type estimator based on a logistic regression model. Combination weights depend on goodness of fit of respective models. Hence, the estimator for which the corresponding model better describes observed sample data dominates in the combination. Some Monte Carlo simulation results revealing its properties are presented.

PL

W artykule zaproponowano estymator złożony średniej w populacji skończonej przy brakach odpowiedzi. Jest on kombinacją estymatora regresyjnego opartego na modelu liniowym i estymatora wykorzystującego ważenie danych opartego na modelu logistycznym. Wagi kombinacji uzależniono od miar dobroci dopasowania tych modeli do danych. Przedstawiono wyniki symulacji wykonanych dla zbadania jego własności.

5

On mean squared error of Hierarchical Estimator

80%

Brodowski S.

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2011

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tom Vol. 20

83-99

EN

In this paper a new theorem about components of the mean squared error of Hierarchical Estimator is presented. Hierarchical Estimator is a machine learning meta-algorithm that attempts to build, in an incremental and hierarchical manner, a tree of relatively simple function estimators and combine their results to achieve better accuracy than any of the individual ones. The components of the error of a node of such a tree are: weighted mean of the error of the estimator in a node and the errors of children, a non-positive term that decreases below 0 if children responses on any example dier and a term representing relative quality of an internal weighting function, which can be conservatively kept at 0 if needed. Guidelines for achieving good results based on the theorem are brie y discussed.

6

Adaptive trimmed likelihood estimation in regression

80%

Bednarski T. , Clarke B. , Schubert D.

Discussiones Mathematicae Probability and Statistics

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2010

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tom 30

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nr 2

203-219

EN

In this paper we derive an asymptotic normality result for an adaptive trimmed likelihood estimator of regression starting from initial high breakdownpoint robust regression estimates. The approach leads to quickly and easily computed robust and efficient estimates for regression. A highlight of the method is that it tends automatically in one algorithm to expose the outliers and give least squares estimates with the outliers removed. The idea is to begin with a rapidly computed consistent robust estimator such as the least median of squares (LMS) or least trimmed squares (LTS) or for example the more recent MM estimators of Yohai. Such estimators are now standard in statistics computing packages, for example as in SPLUS or R. In addition to the asymptotics we provide data analyses supporting the new adaptive approach. This approach appears to work well on a number of data sets and is quicker than the related brute force adaptive regression approach described in Clarke (2000). This current approach builds on the work of Bednarski and Clarke (2002) which considered the asymptotics for the location estimator only.

7

Consistency of trigonometric and polynomial regression estimators

80%

Popiński W.

Applicationes Mathematicae

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1998-1999

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tom 25

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nr 1

73-83

EN

The problem of nonparametric regression function estimation is considered using the complete orthonormal system of trigonometric functions or Legendre polynomials $e_k$, k=0,1,..., for the observation model $y_i = f(x_i) + η_i $, i=1,...,n, where the $η_i$ are independent random variables with zero mean value and finite variance, and the observation points $x_i\in[a,b]$, i=1,...,n, form a random sample from a distribution with density $ϱ\in L^1[a,b]$. Sufficient and necessary conditions are obtained for consistency in the sense of the errors $\Vert f-\widehat f_N\Vert, \vert f(x)-\widehatf_N(x)\vert$, $x\in[a,b]$, and $E\Vert f-\widehatf_N\Vert^2$ of the projection estimator $\widehat f_N(x) = \sum_{k=0}^N\widehat{c}_ke_k(x)$ for $\widehat{c}_0,\widehat{c}_1,\ldots,\widehat{c}_N$ determined by the least squares method and $f\in L^2[a,b]$.

8

On least squares estimation of Fourier coefficients and of the regression function

80%

Popiński W.

Applicationes Mathematicae

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1993-1995

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tom 22

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nr 1

91-102

EN

The problem of nonparametric function fitting with the observation model $y_i = f(x_i) + η_i$, i=1,...,n, is considered, where $η_i$ are independent random variables with zero mean value and finite variance, and $x_i \in [a,b] \subset \R^1$, i=1,...,n, form a random sample from a distribution with density $ϱ \in L^1[a,b]$ and are independent of the errors $η_i$, i=1,...,n. The asymptotic properties of the estimator $\widehat{f}_{N(n)}(x) = \sum_{k=1}^{N(n)} \widehat{c}_ke_k(x)$ for $f \in L^2[a,b]$ and $\widehat{c}^{N(n)}=( \widehat{c}_1,..., \widehat{c}_{N(n)})^T$ obtained by the least squares method as well as the limits in probability of the estimators $\widehat{c}_k$, k=1,...,N, for fixed N, are studied in the case when the functions $e_k$, k=1,2,..., forming a complete orthonormal system in $L^2\[a,b\]$ are analytic.

9

Predicting Competitive Swimming Performance

80%

Wilk R. , Fidos- Czuba O. , Rutkowski Ł. , Kozłowski K. , Wiśniewski P. , Maszczyk A. , Stanula A. , Roczniok R.

Central European Journal of Sport Sciences and Medicine

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2015

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tom 9

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nr 1

105-112

EN

The aim of this study was to present the results of analyses conducted by means of complementary analytic tools in order to verify their efficacy and the hypothesis that Kohonen’s neural models may be applied in the classification process of swimmers. A group of 40 swimmers, aged 23 ±5 years took part in this research. For the purpose of verification of usefulness of Kohonen’s neural models, statistical analyses were carried out on the basis of results of the independent variables (physiological and physical profiles, specific tests in the water). In predicting the value of variables measured with the so called strong scale regression models, numerous variables were used. The construction of such models required strict determination of the endogenous variable (Y – results for swim distances of 200 m crawl), as well as the proper choice of variables in explaining the study’s phenomenon. The optimum choice of explanatory variables for the Kohonen’s networks was made on the grounds of regression analysis. During statistical analysis of the gathered material neural networks were used: Kohonen’s feature maps (data mining analysis). The obtained model has the form of a topological map, where certain areas can be separated, and the map constructed in this way can be used in the assessment of candidates for sports training.

10

Prediction of Exchange Rates With Autoregressive Model With Exponential Forgetting

70%

Kamil D. , Jana K. , Vojtěch S.

Littera Scripta

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2008

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tom 2

1-9

EN

The paper deals with a first-order autoregression model with parameter estimation with exponential forgetting, known and well established in the mathematical system theory. However, the use of exponential forgetting in econometry is not a standard. Under the assumption of slow timevariability of model parameters and model stationarity, this estimation method could however lead to significant improvement of the prediction quality. In this paper, we describe the Bayesian approach to such a modelling and parameter estimation. The use of the method is demonstrated on a one-step-ahead prediction of the EUR-USD exchange rate.

11

Methods for estimating vehicle queues at a marine terminal: a computational comparison

70%

Chen G. , Yang Z.-Z.

International Journal of Applied Mathematics and Computer Science

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2014

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tom 24

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nr 3

611-619

EN

A long queue of vehicles at the gate of a marine terminal is a common traffic phenomenon in a port-city, which sometimes causes problems in urban traffic. In order to be able to solve this issue, we firstly need accurate models to estimate such a vehicle queue length. In this paper, we compare the existing methods in a case study, and evaluate their advantages and disadvantages. Particularly, we develop a simulation-based regression model, using the micro traffic simulation software PARAMIC. In simulation, it is found that the queue transient process follows a natural logarithm curve. Then, based on these curves, we develop a queue length estimation model. In the numerical experiment, the proposed model exhibits better estimation accuracy than the other existing methods.

12

HPC strength prediction using Bayesian neural networks

60%

Słoński M.

|

2007

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tom Vol. 14, No. 2

345-352

EN

The objective of this paper is to investigate the efficiency of nonlinear Bayesian regression for modelling and predicting strength properties of high-performance concrete (HPC). A multilayer perceptron neural network (MLP) model is used. Two statistical approaches to learning and prediction for MLP based on the likelihood function maximization and Bayesian inference are applied and compared. Results of experimental data sets show that Bayesian approach for MLP offers some advantages over classical one.

13

Redescending M-estimators in regression analysis, cluster analysis and image analysis

60%

Müller C.

Discussiones Mathematicae Probability and Statistics

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2004

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tom 24

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nr 1

59-75

EN

We give a review on the properties and applications of M-estimators with redescending score function. For regression analysis, some of these redescending M-estimators can attain the maximum breakdown point which is possible in this setup. Moreover, some of them are the solutions of the problem of maximizing the efficiency under bounded influence function when the regression coefficient and the scale parameter are estimated simultaneously. Hence redescending M-estimators satisfy several outlier robustness properties. However, there is a problem in calculating the redescending M-estimators in regression. While in the location-scale case, for example, the Cauchy estimator has only one local extremum this is not the case in regression. In regression there are several local minima reflecting several substructures in the data. This is the reason that the redescending M-estimators can be used to detect substructures in data, i.e. they can be used in cluster analysis. If the starting point of the iteration to calculate the estimator is coming from the substructure then the closest minimum corresponds to this substructure. This property can be used to construct an edge and corner preserving smoother for noisy images so that there are applications in image analysis as well.

14

Ocena wpływu wybranych determinant na strukturę kapitału za pomocą regresji wielorakiej

60%

Szczęsna-Urbaniak A.

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2006

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tom Nr 48, t. 1

337-345

EN

The paper includes selected results of statistical research carried out on the base of data received from chosen chemical branch enterprises. Subjects of these researches were ratios, which describe capital structure factors, functions which show links between debt rate and analyzed factors as well as judgment of dependence between capital structure and selected ratios.

15

Philosophy in Times of Regression

60%

Veljak L.

Dialogue and Universalism

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2016

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nr 2

149-155

EN

In this paper the author tries to explore (or at least to indicate) the problem of the so-cial function of philosophy in the contemporary world. This world is characterized by universal modernization and in the last decades by globalization and unification, but at the same time also by controversies and contradictions which reveal tendencies of hu-man regression and degeneration. Philosophy must remain a study of general and fun-damental nature of a human-produced world. As such philosophy produces potentiali-ties of critical thinking, provides social investigations, and—at least in principle—gives people the power of an adequate understanding of our world, its fundamental character-istics and main tendencies. Thus philosophy is a ground for a reasonable social practice and adequate policies.

16

Charakterystyki wzorcowania przyrządów pomiarowych jako równania regresji z więzami

60%

Filipowski R. , Zawora J. , Sługocki G.

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2010

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tom nr 12

30-34

PL

Wynikiem wzorcowania przyrządu pomiarowego jest tabela lub wykres funkcji. Taka postać wyników skalowania może być niewystarczająca w celu wykonywania badań naukowych. Wygodniejsza byłaby postać funkcyjna wzorcowania przyrządu. Taką postacią analityczną może być funkcja regresji. Z definicji funkcja regresji nie przechodzi przez punkty pomiarowe. Aby funkcja regresji przechodziła na przykład przez pierwszy punkt wzorcowania przyrządu, należy zdefiniować funkcję regresji z pojedynczymi więzami. Do zdefiniowania funkcji regresji z pojedynczymi więzami zastosowano metodę Lagrange'a dla funkcji wielomianowej oraz zapis macierzowy układu równań normalnych. Stopień funkcji wielomianowej od 1. do 5. dobiera użytkownik programu w trybie interakcyjnym w autorskim programie regresyjnym.

EN

Result of measurement device calibration is presented mostly as a table or graph of a function. Results in this form could be insufficient for scientific research. More convenient could be function form of device calibration. Such an analytical form is regression function. According to definition regression function does not pass through measurement points. In order to obtaining regression function which passes through for example the first point of calibration it is necessary to define regression function with single constraints. For this purpose it was applied Lagrange method for multinomial function and matrix notation for system of normal equations. The order of multinomial function from 1 to 5 could be selected by user in special regression software.

17

Uwzględnienie niepewności danych w prognozach z wykorzystaniem regresji drugiego rodzaju

51%

Borawski M.

|

tom nr spec. (Tom 14)

9-15

EN

The data about the economic, phenomena are often loaded with the uncertainty, which, if it is possible to estimate, could be very precious information. Taken into account in the forecast results, could be an additional factor, telling about the likelihood of the prognosis. In the article the way of taking the data uncertainly into consideration on the example of second kind regression is shown.

18

Opracowanie wyników doświadczeń i metody numeryczne za pomocą MS Excela. Cz. 3. Korelacja i regresja danych dyskretnych (I)

51%

Ufnalski W.

|

2003

|

tom R. 8, nr 1

30-36

PL

Niniejszy artykuł jest kontynuacją cyklu, rozpoczętego w numerze 6/2001 naszego pisma, mającego na celu zaznajomienie Czytelników z obliczeniami i symulacjami "chemicznymi" za pomocą arkusza kalkulacyjnego MS Excel i zgodnie z przyjętymi założeniami dołączono do niego oprogramowanie i skoroszyty z przykładami; dalsze wyjaśnienia znajdzie czytelnik na końcu artykułu.

19

Applications of Kolmogorov Complexity and Universal Codes to Nonparametric Estimation of Characteristics of Time Series

51%

Ryabko B.

|

2008

|

tom Vol. 83, nr 1-2

177-196

EN

We consider finite-alphabet and real-valued time series and the following four problems: i) estimation of the (limiting) probability P(x0 1/4xs) for every s and each sequence x0 1/4xs of letters from the process alphabet (or estimation of the density p(x0, 1/4, xs) for real-valued time series), ii) the so-called on-line prediction, where the conditional probability P(xt+1| x1x2 1/4xt) (or the conditional density p(xt+1| x1x2 1/4xt)) should be estimated, where x1x21/4xt are given, iii) regression and iv) classification (or so-called problems with side information). We show that Kolmogorov complexity (KC) and universal codes (or universal data compressors), whose codeword length can be considered as an estimation of KC, can be used as a basis for constructing asymptotically optimal methods for the above problems. (By definition, a universal code can "compress" any sequence generated by a stationary and ergodic source asymptotically to the Shannon entropy of the source.)

20

Selected Issues of Transport Safety

51%

Seidl M. , Peterek K. , Kalupová B.

Logistics and Transport

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2017

|

tom 36

95-104

EN

This article is focused on two possibilities of perception of transport safety and transport systems. It describes basic characteristics and elements of road safety in the Czech Republic, and differences of safety in rail transport are also remembered. The article discusses traffic accidents as an indicator of road safety. The paper is created with examples of selection and processing of data transport systems, for road and rail transport of the Czech Republic.