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Igor Volobouev

Publications and source records attributed to Igor Volobouev.

7 recordsLinked to original sources
arXiv2024

Asymmetric Errors

We present a procedure for handling asymmetric errors. Many results in particle physics are presented as values with different positive and negative errors, and there is no consistent procedure for handling them. We consider the difference between errors quoted using pdfs and using likelihoods, and the difference between the rms spread of a measurement and the 68\% central confidence region. We provide a comprehensive analysis of the possibilities, and software tools to enable their use.

stat.ME↗
arXiv2024

The Effective Number of Parameters in Kernel Density Estimation

The quest for a formula that satisfactorily measures the effective degrees of freedom in kernel density estimation (KDE) is a long standing problem with few solutions. Starting from the orthogonal polynomial sequence (OPS) expansion for the ratio of the empirical to the oracle density, we show how convolution with the kernel leads to a new OPS with respect to which one may express the resulting KDE. The expansion coefficients of the two OPS systems can then be related via a kernel sensitivity matrix, and this then naturally leads to a definition of effective parameters by taking the trace of a symmetrized positive semi-definite normalized version. The resulting effective degrees of freedom (EDoF) formula is an oracle-based quantity; the first ever proposed in the literature. Asymptotic properties of the empirical EDoF are worked out through influence functions. Numerical investigations confirm the theoretical insights.

stat.ME↗
arXiv2016

Improved Inference for the Signal Significance

We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all statistics follow a standard normal distribution in large samples, but substantial deviations can occur at low sample sizes. Approximations for respective $p$-values are derived to various orders of accuracy using the methodology of Edgeworth expansions. Adherence to normality is studied, and the magnitude of deviations is quantified according to resulting inflation or deflation. We find that approximations to third-order accuracy are generally sufficient to guarantee $p$-values with nominal false positive error rates in the five sigma range ($p$-value $= 2.87 \times 10^{-7}$) for the classic Wald, score, and likelihood ratio (LR) statistics at relatively low samples. Not only does LR have better adherence to normality, but it also consistently outperforms all other statistics in terms of false negative error rates. The reasons for this are shown to be connected with high-order cumulant behavior gleaned from fourth order Edgeworth expansions. Finally, a conservative procedure is suggested for making finite sample adjustments while accounting for the look elsewhere effect with the theory of random fields (a.k.a. the Gross-Vitells method).

physics.data-an↗
arXiv2015

Local Orthogonal Polynomial Expansion for Density Estimation

A Local Orthogonal Polynomial Expansion (LOrPE) of the empirical density function is proposed as a novel method to estimate the underlying density. The estimate is constructed by matching localized expectation values of orthogonal polynomials to the values observed in the sample. LOrPE is related to several existing methods, and generalizes straightforwardly to multivariate settings. By manner of construction, it is similar to Local Likelihood Density Estimation (LLDE). In the limit of small bandwidths, LOrPE functions as Kernel Density Estimation (KDE) with high-order (effective) kernels inherently free of boundary bias, a natural consequence of kernel reshaping to accommodate endpoints. Faster asymptotic convergence rates follow. In the limit of large bandwidths, LOrPE is equivalent to Orthogonal Series Density Estimation (OSDE) with Legendre polynomials. We compare the performance of LOrPE to KDE, LLDE, and OSDE, in a number of simulation studies. In terms of mean integrated squared error, the results suggest that with a proper balance of the two tuning parameters, bandwidth and degree, LOrPE generally outperforms these competitors when estimating densities with sharply truncated supports.

stat.AP↗
arXiv2015

On the Expectation-Maximization Unfolding with Smoothing

Error propagation formulae are derived for the expectation-maximization iterative unfolding algorithm regularized by a smoothing step. The effective number of parameters in the fit to the observed data is defined for unfolding procedures. Based upon this definition, the Akaike information criterion is proposed as a principle for choosing the smoothing parameters in an automatic, data-dependent manner. The performance and the frequentist coverage of the resulting method are investigated using simulated samples. A number of issues of general relevance to all unfolding techniques are discussed, including irreducible bias, uncertainty increase due to a data-dependent choice of regularization strength, and presentation of results.

physics.data-an↗
arXiv2011

Precision measurements of the top quark mass from the Tevatron in the pre-LHC era

The top quark is the heaviest of the six quarks of the Standard Model. Precise knowledge of its mass is important for imposing constraints on a number of physics processes, including interactions of the as yet unobserved Higgs boson. The Higgs boson is the only missing particle of the Standard Model, central to the electroweak symmetry breaking mechanism and generation of particle masses. In this Review, experimental measurements of the top quark mass accomplished at the Tevatron, a proton-antiproton collider located at the Fermi National Accelerator Laboratory, are described. Topologies of top quark events and methods used to separate signal events from background sources are discussed. Data analysis techniques used to extract information about the top mass value are reviewed. The combination of several most precise measurements performed with the two Tevatron particle detectors, CDF and \D0, yields a value of $\Mt = 173.2 \pm 0.9$ GeV/$c^2$.

hep-ex↗