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We present a semiparametric statistical model for the probabilistic index which is defined as P (Y< Y*), where Y and Y* are independent random response variables associated with covariate patterns X and X*, respectively. In... more
We present a semiparametric statistical model for the probabilistic index which is defined as P (Y< Y*), where Y and Y* are independent random response variables associated with covariate patterns X and X*, respectively. In particular, we consider the model P (Y< Y*)= ...
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A general method is proposed for detecting differential genes in high density oligonucleotide microarrays. It is a unified approach in the sense that it integrates the three preprocessing steps and the statistical testing methods into one... more
A general method is proposed for detecting differential genes in high density oligonucleotide microarrays. It is a unified approach in the sense that it integrates the three preprocessing steps and the statistical testing methods into one semiparametric model. An important characteristic is that no stringent assumptions are imposed on the background correction and normalization steps. Instead of focusing on mean differences in gene expression, we formulate the model in terms of stochastic ordering. In particular, probabilities $P(Y_1 < Y_2 )$, with $Y_i$ the intensity of a gene in group $i$ ($i = 1, 2$), are modeled in terms of predictor variables. We present some theoretical results and spike-in studies are considered for comparing the performance of this new method with existing methods. Finally we apply the new method to a publicly available data set.
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ABSTRACT
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ABSTRACT A practical method is constructed in order to obtain the adiabatic invariant of a Hamiltonian H(p, q, τ) (τ = εt, ε ⪡ 1), where some parameters vary slowly in time. Using the action-angle variables (J, w) of the non-perturbed... more
ABSTRACT A practical method is constructed in order to obtain the adiabatic invariant of a Hamiltonian H(p, q, τ) (τ = εt, ε ⪡ 1), where some parameters vary slowly in time. Using the action-angle variables (J, w) of the non-perturbed system (ε = 0) two successive time-dependent canonical transformations are used. The first few terms of the adiabatic series are calculated explicitly as a function of the terms H0(J, τ) and H1(J, w, τ) of the transformed Hamiltonian.
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Starting from a smooth test for goodness of fit we develop a method to alter this test to a reweighted smooth test, which has greater power to a certain directional alternative. Whereas the original smooth test gives equal weight to the... more
Starting from a smooth test for goodness of fit we develop a method to alter this test to a reweighted smooth test, which has greater power to a certain directional alternative. Whereas the original smooth test gives equal weight to the different directions in the space of alternatives, the reweighted smooth test makes a distinction in importance of the directions. The advantage of this test, as opposed to directional tests, is that the smooth character is largely maintained. We discuss both nested and non nested directional alternatives.
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Regression diagnostics and lack-of-fit tests mainly focus on linear-linear regression models. When the design points are distributed on the circumference of a circle, difficulties arise as there is no natural starting point or origin.... more
Regression diagnostics and lack-of-fit tests mainly focus on linear-linear regression models. When the design points are distributed on the circumference of a circle, difficulties arise as there is no natural starting point or origin. Most classical lack-of-fit tests require an arbitrarily chosen origin, but different choices may result in different conclusions. We propose a graphical diagnostic tool and a closely related lack-of-fit test, which does not require a natural starting point. The method is based on regional residuals which are defined on arcs of the circle. The graphical method formally locates and visualizes subsets of poorly fitting observations on the circle. A data example from the food technology is used to point out the before-mentioned problems with conventional lack-of-fit tests and to illustrate the strength of the methodology based on regional residuals in detecting and localizing departures from the no-effect hypothesis. A small simulation study shows a good performance of the regional residual test in case of both global and local deviations from the null model. Finally, the ideas are extended to the case of more than one predictor variable.
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Research Interests: Mathematics, Computer Science, Econometrics, Statistics, Linear Model, and 12 moreRegression, Regression Analysis, Multiple Regression, Regression Model, Simulation Study, Linear Regression, Linear Regression Model, Computational Statistics and Data Analysis, Location Area, Graphical Method, Residual, and Diagnostic Tool
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Research Interests: Engineering, Bioinformatics, Computer Science, Nonparametric Statistics, Medicine, and 15 moreBiological Sciences, Bioconductor, Humans, qPCR, Mathematical Sciences, Rt, R package, Data, Neuroblastoma, microRNAs, Mathematics and Statistics, R, Science and Technology Studies, Analyzing, and real time polymerase chain reaction
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This paper describes a set of didactic tools for statistical teaching, implemented as JAVA applets. The tools allow to visualize a number of statistical concepts, and to experiment with them interactively.
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Research Interests: Engineering, Mathematics, Algorithms, Medicine, Gene expression, and 15 moreBiological Sciences, Extension, Humans, Computer Simulation, Mathematical Sciences, Data, Normalization, Neuroblastoma, microRNAs, Mathematics and Statistics, Analyzing, Gene expression profiling, Case Control Studies, Outlier, and MYCN
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Research Interests: Mathematics and Z
: The basic principles of acousto-optical diffraction in an isotropic medium are briefly reviewed. Focus is on the derivation of the Raman-Nath equations for the amplitudes of the diffracted light waves and on the physical meaning of the... more
: The basic principles of acousto-optical diffraction in an isotropic medium are briefly reviewed. Focus is on the derivation of the Raman-Nath equations for the amplitudes of the diffracted light waves and on the physical meaning of the various parameters occurring in this diffraction problem. Three distinct methods for the numerical integration of the truncated Raman-Nath system are outlined: Raman-Nath's elementary theory, Merten's perturbation method, and the N-th order approximation method. For each of these methods, the theoretical results are compared with experimental data. An eigenvalue method and an operational method (due to Heaviside-Jeffreys) are used to integrate the truncated Raman-Nath system in the case of normal incidence of the light. Both methods lead to closed form expressions for the intensities of the diffracted light beams, which are easily implemented on a computer. A comparison of the various approximation methods is presented. Fifteen figures illus...
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Promotors and transcription factors regulate gene expression in eukaryotes. Eukaryotic transcription factors are highly modular proteins that activate or inhibit the transcription of genes by binding simultaneously to a recognition... more
Promotors and transcription factors regulate gene expression in eukaryotes. Eukaryotic transcription factors are highly modular proteins that activate or inhibit the transcription of genes by binding simultaneously to a recognition sequence element on the DNA and to the transcription machine. Gibbs sampling is a stochastic process that looks for overrepresentation of those so-called motifs against a background model ([1].,[2],[3],[4]).This approach is used for finding the genomic binding sites for the transcription factors, mainly on sets of co-expressed genes and their corresponding promoter sequences