Confidence intervals for the minimum of a function using extreme value statistics

Carvalho, Miguel de

doi:10.1504/ijmmno.2011.040793

Cited by 4 publications

(2 citation statements)

References 14 publications

(18 reference statements)

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“…In principle, several runs with different starting points should be tested to ensure that the global minimizer is reached. Also, formal statistical procedures can be performed to test wether the given minimizer is indeed the global minimizer; see, e.g., (de Carvalho 2011(de Carvalho , 2012Veall 1990). We found that a single run was enough to find what appeared to be the global optimum.…”

Section: Applications To Simulated and Real Datasetsmentioning

confidence: 95%

A flexible and tractable class of one-factor copulas

2015

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International audienceCopulas are a useful tool to model multivariate distributions. While there exist various families of bivariate copulas, the construction of flexible and yet tractable copulas suitable for high-dimensional applications is much more challenging. This is even more true if one is concerned with the analysis of extreme values. In this paper, we construct a class of one-factor copulas and a family of extreme-value copulas well suited for high-dimensional applications and exhibiting a good balance between tractability and flexibility. The inference for these copulas is performed by using a least-squares estimator based on dependence coefficients. The modeling capabilities of the copulas are illustrated on simulated and real datasets

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Section: Applications To Simulated and Real Datasetsmentioning

confidence: 95%

A flexible and tractable class of one-factor copulas

2015

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“…Turnbull and Ghosh [2014] provide a justification for the choice of A and B as the estimates for the bounds of the density. They also discuss an alternate way of estimating the boundaries using ideas presented in De Carvalho [2011], and suggest that the Carvalho method produces wider and more conservative boundary estimates.…”

Section: Estimation Of Densities With Unknown Supportmentioning

confidence: 99%

A Two-Step Geometric Framework For Density Modeling

Dasgupta¹,

Pati²,

Srivastava³

2019

STAT SINICA

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We introduce a novel two-step approach for estimating a probability density function (pdf) given its samples, with the second and important step coming from a geometric formulation. The procedure involves obtaining an initial estimate of the pdf and then transforming it via a warping function to reach the final estimate. The initial estimate is intended to be computationally fast, albeit suboptimal, but its warping creates a larger, flexible class of density functions, resulting in substantially improved estimation. The search for optimal warping is accomplished by mapping diffeomorphic functions to the tangent space of a Hilbert sphere, a vector space whose elements can be expressed using an orthogonal basis. Using a truncated basis expansion, we estimate the optimal warping under a (penalized) likelihood criterion and, thus, the optimal density estimate. This framework is introduced for univariate, unconditional pdf estimation and then extended to conditional pdf estimation. The approach avoids many of the computational pitfalls associated with classical conditional-density estimation methods, without losing on estimation performance. We derive asymptotic convergence rates of the density estimator and demonstrate this approach using both synthetic datasets and real data, the latter relating to the association of a toxic metabolite on preterm birth. Key words and phrases: conditional density; density estimation; warped density; Hilbert sphere; sieve estimation; tangent space; weighted likelihood maximization S Saoudi, A Hillion, and F Ghorbel. Non-parametric probability density function estimation on a bounded support: Applications to shape classification and speech coding. Applied Stochastic models and data analysis, 10(3):215-231, 1994. S Saoudi, F Ghorbel, and A Hillion. Some statistical properties of the kernel-diffeomorphism estimator. Applied stochastic models and data analysis, 13(1):39-58, 1997. Simon J Sheather and Michael C Jones. A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society. Series B (Methodological), pages 683-690, 1991. Anuj Srivastava and Eric P Klassen. Functional and shape data analysis. Springer, 2016. EG Tabak and Cristina V Turner. A family of nonparametric density estimation algorithms. Communications on Pure and Applied

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A generalization of the Solis–Wets method

Carvalho

2012

Journal of Statistical Planning and Inference

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a b s t r a c tIn this paper we focus on the application of global stochastic optimization methods to extremum estimators. We propose a general stochastic method-the master method -which includes several stochastic optimization algorithms as a particular case. The proposed method is sufficiently general to include the Solis-Wets method, the improving hit-and-run algorithm, and a stochastic version of the zigzag algorithm. A matrix formulation of the master method is presented and some specific results are given for the stochastic zigzag algorithm. Convergence of the proposed method is established under a mild set of conditions, and a simple regression model is used to illustrate the method.

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Confidence intervals for the minimum of a function using extreme value statistics

Cited by 4 publications

References 14 publications

A flexible and tractable class of one-factor copulas

A flexible and tractable class of one-factor copulas

A Two-Step Geometric Framework For Density Modeling

A generalization of the Solis–Wets method

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