Kernel Smoothing in Matlab

Horová, Ivanka; Koláček, Jan; Zelinka, Jiří

doi:10.1142/8468

Cited by 42 publications

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“…Let the density function bound second derivative , leading to Taylor expansion, where See Horová et al ( 2012 ) for details.…”

Section: The Semiparametric Methodsmentioning

confidence: 99%

“…There is no universally accepted approach to select the optimal kernel function that has little influence on the estimation results. We concentrate on the selection of the optimal bandwidth using cross-validation theory (Horová et al 2012 ). A bias estimation for the perturbed optimal bandwidth is derived.…”

Section: Literature Reviewmentioning

confidence: 99%

“…These are many choices of kernel functions, such as Gaussian kernel, exponential kernel, and Cauchy kernel. However, the Gaussian kernel, is commonly used in practice because it does not influence the asymptotic of the estimation as significant as the bandwidth used by Horová et al ( 2012 ).…”

Section: Literature Reviewmentioning

confidence: 99%

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Stressed portfolio optimization with semiparametric method

Han

Wang

2022

Financ Innov

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Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks, while the traditional mean–variance approach may fail to perform well. This study proposes an innovative semiparametric method consisting of two modeling components: the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution, respectively. We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction. Empirical studies include statistical estimation for the semiparametric method, risk measure minimization for optimal weights, and value measure maximization for the optimal scale to enlarge the investment. From the outputs of short-term and long-term data analysis, optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean–variance method.

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“…Let the density function bound second derivative , leading to Taylor expansion, where See Horová et al ( 2012 ) for details.…”

Section: The Semiparametric Methodsmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

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Stressed portfolio optimization with semiparametric method

Han

Wang

2022

Financ Innov

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“…If no additional information are available (this means that only the set of realizations is known), the way for solving this problem is to use the nonparametric density estimate and multivariate smoothing, which constitute a powerful statistical tool [25,89,106]. If no additional information are available (this means that only the set of realizations is known), the way for solving this problem is to use the nonparametric density estimate and multivariate smoothing, which constitute a powerful statistical tool [25,89,106].…”

Section: Multivariate Kernel Density Estimation Methods In Nonparametrmentioning

confidence: 99%

Uncertainty Quantification

Soize

2017

Interdisciplinary Applied Mathematics

124

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“…Therefore, we focused on methods of nonparametric estimations, especially of kernel estimates of the survival and hazard functions. These methods are simple to understand and possess good statistical properties of estimates (see [ 7 ]).…”

Section: Methodsmentioning

confidence: 99%

Survival of Patients with Primary Brain Tumors: Comparison of Two Statistical Approaches

et al. 2016

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PurposeWe reviewed the survival time for patients with primary brain tumors undergoing treatment with stereotactic radiation methods at the Masaryk Memorial Cancer Institute Brno. We also identified risk factors and characteristics, and described their influence on survival time.MethodsIn summarizing survival data, there are two functions of principal interest, namely, the survival function and the hazard function. In practice, both of them can depend on some characteristics. We focused on nonparametric methods, propose a method based on kernel smoothing, and compared our estimates with the results of the Cox regression model. The hazard function is conditional to age and gross tumor volume and visualized as a color-coded surface. A multivariate Cox model was also designed.ResultsThere were 88 patients with primary brain cancer, treated with stereotactic radiation. The median survival of our patient cohort was 47.8 months. The estimate of the hazard function has two peaks (about 10 months and about 40 months). The survival time of patients was significantly different for various diagnoses (p≪0.001), KI (p = 0.047) and stereotactic methods (p = 0.033). Patients with a greater GTV had higher risk of death. The suitable threshold for GTV is 20 cm3. Younger patients with a survival time of about 50 months had a higher risk of death. In the multivariate Cox regression model, the selected variables were age, GTV, sex, diagnosis, KI, location, and some of their interactions.ConclusionKernel methods give us the possibility to evaluate continuous risk variables and based on the results offer risk-prone patients a different treatment, and can be useful for verifying assumptions of the Cox model or for finding thresholds of continuous variables.

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Kernel Smoothing in Matlab

Cited by 42 publications

References 0 publications

Stressed portfolio optimization with semiparametric method

Stressed portfolio optimization with semiparametric method

Uncertainty Quantification

Survival of Patients with Primary Brain Tumors: Comparison of Two Statistical Approaches

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