Field-Induced Residual Dipolar Couplings (fiRDC) are a valuable source of long-range information ... more Field-Induced Residual Dipolar Couplings (fiRDC) are a valuable source of long-range information on structure of nucleic acids (NA) in solution. A web application (HERMES) was developed for structure-based prediction and analysis of the (fiRDCs) in NA. fiRDC prediction is based on input 3D model structure(s) of NA and a built-in library of nucleobase-specific magnetic susceptibility tensors and reference geometries. HERMES allows three basic applications: (i) the prediction of fiRDCs for a given structural model of NAs, (ii) the validation of experimental or modeled NA structures using experimentally derived fiRDCs, and (iii) assessment of the oligomeric state of the NA fragment and/or the identification of a molecular NA model that is consistent with experimentally derived fiRDC data. Additionally, the program's built-in routine for rigid body modeling allows the evaluation of relative orientation of domains within NA that is in agreement with experimental fiRDCs.
Ve dnech 11. až 13. zaři 2012 se v hotelu Podlesi ve Svratce uskutecnil workshop Financni matemat... more Ve dnech 11. až 13. zaři 2012 se v hotelu Podlesi ve Svratce uskutecnil workshop Financni matematika v praxi II. Sbornik přispěvků z tohoto zasedani prezentuje vybrane referaty, ktere během jednani zazněly. Ma za ukol seznamit připadne zajemce s tematy, kterými se zabývaji jednotliva pracovistě, jejichž clenove se workshopu zucastnili.
The kernel functions (kernels) can be used in many types of non-parametric methods - estimation o... more The kernel functions (kernels) can be used in many types of non-parametric methods - estimation of the density function of a random variable, estimation of the hazard function or the regression function. These methods belong to the most efficient non-parametric methods. Another non-parametric method uses so-called frames - overcompleted system of functions of some type. This paper compares the kernel smoothing and the frame smoothing with frames of a special kind - the kernel functions are used for their construction. Both the smoothing procedures are applied to environmental data. Obtained results will be presented graphically.
Cilem přispěvku je představit projekt objektově a maticově orientovane nadstavby jazyka C++. Po s... more Cilem přispěvku je představit projekt objektově a maticově orientovane nadstavby jazyka C++. Po strance syntakticke i funkcni je natolik kompatibilni s jadrem MATLABu, aby umožnila zcela nezavisle na něm: (i)snadný (mechanický) převod funkci zapsaných v jazyce MATLAB do prostředi C++, (ii) přimou implementaci numericky orientovaných algoritmů v C++ stejně pohodlně jako v jazyku MATLABu (zejmena bez potiži a rizik spojených s dynamickou alokaci paměti), (iii) modularni vytvařeni samostatných aplikaci ve formě spustitelných souborů EXE i DLL-knihoven. Vsechny funkce takto vytvořene v C++ lze přimo volat nejen z prostředi MATLABu (což napřiklad usnadni výrazně jejich laděni v C++), ale i z jakehokoliv programoveho systemu podporujiciho spolupraci s externimi DLL-knihovnami.
V přispěvku jsou uvedeny zakladni vlastnosti jadrových odhadů regresni funkce a je uveden algorit... more V přispěvku jsou uvedeny zakladni vlastnosti jadrových odhadů regresni funkce a je uveden algoritmus pro volbu parametrů vyhlazeni.
TIES is a nonprofit corporation organizing scientists with a common interest in quantitative meth... more TIES is a nonprofit corporation organizing scientists with a common interest in quantitative methods for environmental science and management. The objectives of the Society are to foster the development and use of statistical and other quantitative methods in the environmental sciences, environmental engineering, and environmental monitoring and protection. To this end, the Society promotes the participation of statisticians, mathematicians, scientists, and engineers in the solution of environmental problems and emphasizes the need for collaboration and for clear communication between individuals from different disciplines and between researchers and practitioners. The Society further promotes these objectives by conducting meetings and producing publications, and by encouraging a broad membership of statisticians, mathematicians, engineers, scientists, and others interested in furthering the role of statistical and mathematical techniques in service to the environment. This confere...
The kernel functions (kernels) can be used in many types of non-parametric methods - estimation o... more The kernel functions (kernels) can be used in many types of non-parametric methods - estimation of the density function of a random variable, estimation of the hazard function or the regression function. These methods belong to the most efficient non-parametric methods. Another non-parametric method uses so-called frames - overcomplete systems of functions of some type. This paper compares the kernel smoothing and the frame smoothing with frames of a special kind - the kernel functions are used for their construction. Both smoothing procedures are applied to simulated data. Obtained results will be presented graphically.
The most commonly used nonparametric estimate of a cumulative distribution function F is an empir... more The most commonly used nonparametric estimate of a cumulative distribution function F is an empirical distribution function F_n. But F_n is a step function even in case that F is continuous. The present paper aims to provide a smooth estimate of F. Kernel methods seem to be adequate for this purpose. There exist several methods how to choose a bandwidth. We propose a method of bandwidth selection based on a suitable estimate of Mean Integrated Square Error. We also focus on an estimate of a cumulative distribution function in case that random variables X_1,...,X_n are nonnegative. The aforementioned methods are not reliable near the point x=0. In order to avoid this problem we propose a~reflection method. A simulation study is conducted to compare the performance of the different methods of bandwidth choice. Theoretical results are applied to the data concerning the content of toxic material in the fish population in Lake Ontario.
The aim of this contribution is to compare several methods of estimating the area under the recie... more The aim of this contribution is to compare several methods of estimating the area under the reciever operating characteristic (ROC) curve for continous - scale diagnostic tests. The area under ROC curve is frequently used as a measure for the effectivness of diagnostic markers. Let AUC denote the area under this curve. Different estimates of the AUC are based on different approaches to estimating the ROC curve. In the present paper we investigate (i) parametric approach based on normal distribution or eliptically contoured distribution and (ii) nonparametric approach based on kernel smoothing.
Recently receiver operating characteristics ( ROC) curve has become a popular method for evalutin... more Recently receiver operating characteristics ( ROC) curve has become a popular method for evaluting the accuracy/performance of classification model.Aim of the paper is to compare different approches for estimating ROC curves.
This paper presents how a functional random variable can be expressed in the form of Fourier seri... more This paper presents how a functional random variable can be expressed in the form of Fourier series. This expansion can be used for the definition of components of the functional random variable and for the approximation of the random curves as the partial sum of the Fourier series. Thus we can estimate the distribution of the components, simulate the functional random variable with given components and compute some characteristics of the distribution of its norm.
Non-parametric estimates of survival and hazard function belongs to the basic instruments in surv... more Non-parametric estimates of survival and hazard function belongs to the basic instruments in survival analysis. In previous papers methods of kernel estimates involving growth models of cancer cells were designed by author's colleagues. To verify the quality of these the tests on the simulated data were suggested. During the test procedure some theoretical problems appeared. They concerned especially additional requests for distribution of simulated censoring data. The problems were largely resolved and estimation procedures were successfully tested on simulated data. This paper summarizes the achievements.
The paper is focused on kernel estimates of densities and distribution functions. But there is a ... more The paper is focused on kernel estimates of densities and distribution functions. But there is a serious difficulty with such estimates- a choice of a smoothing parameter and at the present paper an iterativ method is proposed. Theoretical results are applied to hydrological data.
The hazard function is a useful tool in survival analysis and reflects the instantaneous probabil... more The hazard function is a useful tool in survival analysis and reflects the instantaneous probability that an individual will die within the next time instant. In practice, the hazard function depends on covariates as an age and a gender. The most frequently used method to estimate a conditional hazard function is semiparametric model suggested by D. R. Cox. Assumptions of this model are too restrictive in many cases. In the present paper is proposed an estimator for conditional hazard function as the ratio of kernel estimators for the onditional density and survival function. We illustrate the utility of the proposed method through application to cancer data sets.
Nonparametric regression methods are often used to estimate an unknown function $m(x_1,\dots,x_p)... more Nonparametric regression methods are often used to estimate an unknown function $m(x_1,\dots,x_p)$ in a regression model $$Y=m(X_1,\dots,X_p)+\eps$$ for random variables $X_1,\dots,X_p,Y$ and error $\eps$. Additive model can be used for the function $m$ in the special form $$m(x_1,\dots,x_p)=m_1(x_1)+\dots m_p(x_p).$$ Application of kernel smoothing to additive models is shown in this contribution and some practical results, too.
ROC curves are important tool for comparing diagnostic tests. Nonparametric kernel estimation is ... more ROC curves are important tool for comparing diagnostic tests. Nonparametric kernel estimation is useful in the case when no information about the distribution of the data is available. Presented contribution is focused on the method of kernel estimate of ROC curve as a special type of cumulative distribution function. This approach can be applied for choice of smoothing parameter called bandwidth and also for evaluation of area under ROC curve (AUC) or partial AUC. Suggested method is compared with another methods and it is tested on simulated and real data.
Kernel density estimates attempt to reconstruct the probability density from the sample has come ... more Kernel density estimates attempt to reconstruct the probability density from the sample has come using the sample values and a few assumptions as possible. We focus on multivariate density estimates. A main attention is paid to a choice of a smoothing parameter. We extend an idea of an iterative method originally proposed for univariate densities to bivariate ones. The proposed method is compared with cross-validation methods in a simulation study.
Field-Induced Residual Dipolar Couplings (fiRDC) are a valuable source of long-range information ... more Field-Induced Residual Dipolar Couplings (fiRDC) are a valuable source of long-range information on structure of nucleic acids (NA) in solution. A web application (HERMES) was developed for structure-based prediction and analysis of the (fiRDCs) in NA. fiRDC prediction is based on input 3D model structure(s) of NA and a built-in library of nucleobase-specific magnetic susceptibility tensors and reference geometries. HERMES allows three basic applications: (i) the prediction of fiRDCs for a given structural model of NAs, (ii) the validation of experimental or modeled NA structures using experimentally derived fiRDCs, and (iii) assessment of the oligomeric state of the NA fragment and/or the identification of a molecular NA model that is consistent with experimentally derived fiRDC data. Additionally, the program's built-in routine for rigid body modeling allows the evaluation of relative orientation of domains within NA that is in agreement with experimental fiRDCs.
Ve dnech 11. až 13. zaři 2012 se v hotelu Podlesi ve Svratce uskutecnil workshop Financni matemat... more Ve dnech 11. až 13. zaři 2012 se v hotelu Podlesi ve Svratce uskutecnil workshop Financni matematika v praxi II. Sbornik přispěvků z tohoto zasedani prezentuje vybrane referaty, ktere během jednani zazněly. Ma za ukol seznamit připadne zajemce s tematy, kterými se zabývaji jednotliva pracovistě, jejichž clenove se workshopu zucastnili.
The kernel functions (kernels) can be used in many types of non-parametric methods - estimation o... more The kernel functions (kernels) can be used in many types of non-parametric methods - estimation of the density function of a random variable, estimation of the hazard function or the regression function. These methods belong to the most efficient non-parametric methods. Another non-parametric method uses so-called frames - overcompleted system of functions of some type. This paper compares the kernel smoothing and the frame smoothing with frames of a special kind - the kernel functions are used for their construction. Both the smoothing procedures are applied to environmental data. Obtained results will be presented graphically.
Cilem přispěvku je představit projekt objektově a maticově orientovane nadstavby jazyka C++. Po s... more Cilem přispěvku je představit projekt objektově a maticově orientovane nadstavby jazyka C++. Po strance syntakticke i funkcni je natolik kompatibilni s jadrem MATLABu, aby umožnila zcela nezavisle na něm: (i)snadný (mechanický) převod funkci zapsaných v jazyce MATLAB do prostředi C++, (ii) přimou implementaci numericky orientovaných algoritmů v C++ stejně pohodlně jako v jazyku MATLABu (zejmena bez potiži a rizik spojených s dynamickou alokaci paměti), (iii) modularni vytvařeni samostatných aplikaci ve formě spustitelných souborů EXE i DLL-knihoven. Vsechny funkce takto vytvořene v C++ lze přimo volat nejen z prostředi MATLABu (což napřiklad usnadni výrazně jejich laděni v C++), ale i z jakehokoliv programoveho systemu podporujiciho spolupraci s externimi DLL-knihovnami.
V přispěvku jsou uvedeny zakladni vlastnosti jadrových odhadů regresni funkce a je uveden algorit... more V přispěvku jsou uvedeny zakladni vlastnosti jadrových odhadů regresni funkce a je uveden algoritmus pro volbu parametrů vyhlazeni.
TIES is a nonprofit corporation organizing scientists with a common interest in quantitative meth... more TIES is a nonprofit corporation organizing scientists with a common interest in quantitative methods for environmental science and management. The objectives of the Society are to foster the development and use of statistical and other quantitative methods in the environmental sciences, environmental engineering, and environmental monitoring and protection. To this end, the Society promotes the participation of statisticians, mathematicians, scientists, and engineers in the solution of environmental problems and emphasizes the need for collaboration and for clear communication between individuals from different disciplines and between researchers and practitioners. The Society further promotes these objectives by conducting meetings and producing publications, and by encouraging a broad membership of statisticians, mathematicians, engineers, scientists, and others interested in furthering the role of statistical and mathematical techniques in service to the environment. This confere...
The kernel functions (kernels) can be used in many types of non-parametric methods - estimation o... more The kernel functions (kernels) can be used in many types of non-parametric methods - estimation of the density function of a random variable, estimation of the hazard function or the regression function. These methods belong to the most efficient non-parametric methods. Another non-parametric method uses so-called frames - overcomplete systems of functions of some type. This paper compares the kernel smoothing and the frame smoothing with frames of a special kind - the kernel functions are used for their construction. Both smoothing procedures are applied to simulated data. Obtained results will be presented graphically.
The most commonly used nonparametric estimate of a cumulative distribution function F is an empir... more The most commonly used nonparametric estimate of a cumulative distribution function F is an empirical distribution function F_n. But F_n is a step function even in case that F is continuous. The present paper aims to provide a smooth estimate of F. Kernel methods seem to be adequate for this purpose. There exist several methods how to choose a bandwidth. We propose a method of bandwidth selection based on a suitable estimate of Mean Integrated Square Error. We also focus on an estimate of a cumulative distribution function in case that random variables X_1,...,X_n are nonnegative. The aforementioned methods are not reliable near the point x=0. In order to avoid this problem we propose a~reflection method. A simulation study is conducted to compare the performance of the different methods of bandwidth choice. Theoretical results are applied to the data concerning the content of toxic material in the fish population in Lake Ontario.
The aim of this contribution is to compare several methods of estimating the area under the recie... more The aim of this contribution is to compare several methods of estimating the area under the reciever operating characteristic (ROC) curve for continous - scale diagnostic tests. The area under ROC curve is frequently used as a measure for the effectivness of diagnostic markers. Let AUC denote the area under this curve. Different estimates of the AUC are based on different approaches to estimating the ROC curve. In the present paper we investigate (i) parametric approach based on normal distribution or eliptically contoured distribution and (ii) nonparametric approach based on kernel smoothing.
Recently receiver operating characteristics ( ROC) curve has become a popular method for evalutin... more Recently receiver operating characteristics ( ROC) curve has become a popular method for evaluting the accuracy/performance of classification model.Aim of the paper is to compare different approches for estimating ROC curves.
This paper presents how a functional random variable can be expressed in the form of Fourier seri... more This paper presents how a functional random variable can be expressed in the form of Fourier series. This expansion can be used for the definition of components of the functional random variable and for the approximation of the random curves as the partial sum of the Fourier series. Thus we can estimate the distribution of the components, simulate the functional random variable with given components and compute some characteristics of the distribution of its norm.
Non-parametric estimates of survival and hazard function belongs to the basic instruments in surv... more Non-parametric estimates of survival and hazard function belongs to the basic instruments in survival analysis. In previous papers methods of kernel estimates involving growth models of cancer cells were designed by author's colleagues. To verify the quality of these the tests on the simulated data were suggested. During the test procedure some theoretical problems appeared. They concerned especially additional requests for distribution of simulated censoring data. The problems were largely resolved and estimation procedures were successfully tested on simulated data. This paper summarizes the achievements.
The paper is focused on kernel estimates of densities and distribution functions. But there is a ... more The paper is focused on kernel estimates of densities and distribution functions. But there is a serious difficulty with such estimates- a choice of a smoothing parameter and at the present paper an iterativ method is proposed. Theoretical results are applied to hydrological data.
The hazard function is a useful tool in survival analysis and reflects the instantaneous probabil... more The hazard function is a useful tool in survival analysis and reflects the instantaneous probability that an individual will die within the next time instant. In practice, the hazard function depends on covariates as an age and a gender. The most frequently used method to estimate a conditional hazard function is semiparametric model suggested by D. R. Cox. Assumptions of this model are too restrictive in many cases. In the present paper is proposed an estimator for conditional hazard function as the ratio of kernel estimators for the onditional density and survival function. We illustrate the utility of the proposed method through application to cancer data sets.
Nonparametric regression methods are often used to estimate an unknown function $m(x_1,\dots,x_p)... more Nonparametric regression methods are often used to estimate an unknown function $m(x_1,\dots,x_p)$ in a regression model $$Y=m(X_1,\dots,X_p)+\eps$$ for random variables $X_1,\dots,X_p,Y$ and error $\eps$. Additive model can be used for the function $m$ in the special form $$m(x_1,\dots,x_p)=m_1(x_1)+\dots m_p(x_p).$$ Application of kernel smoothing to additive models is shown in this contribution and some practical results, too.
ROC curves are important tool for comparing diagnostic tests. Nonparametric kernel estimation is ... more ROC curves are important tool for comparing diagnostic tests. Nonparametric kernel estimation is useful in the case when no information about the distribution of the data is available. Presented contribution is focused on the method of kernel estimate of ROC curve as a special type of cumulative distribution function. This approach can be applied for choice of smoothing parameter called bandwidth and also for evaluation of area under ROC curve (AUC) or partial AUC. Suggested method is compared with another methods and it is tested on simulated and real data.
Kernel density estimates attempt to reconstruct the probability density from the sample has come ... more Kernel density estimates attempt to reconstruct the probability density from the sample has come using the sample values and a few assumptions as possible. We focus on multivariate density estimates. A main attention is paid to a choice of a smoothing parameter. We extend an idea of an iterative method originally proposed for univariate densities to bivariate ones. The proposed method is compared with cross-validation methods in a simulation study.
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Papers by Jiří Zelinka