Unknown Function Parameters Research Articles

Nonparametric inference on smoothed quantile regression process

This paper studies the global estimation in semiparametric quantile regression models. For estimating unknown functional parameters, an integrated quantile regression loss function with penalization is proposed. The first step is to obtain a vector-valued functional Bahadur representation of the resulting estimators, and then derive the asymptotic distribution of the proposed infinite-dimensional estimators. Furthermore, a resampling approach that generalizes the minimand perturbing technique is adopted to construct confidence intervals and to conduct hypothesis testing. Extensive simulation studies demonstrate the effectiveness of the proposed method, and applications to the real estate dataset and world happiness report data are provided.

Bayesian nonparametric estimation of hazard rate in monotone Aalen model

This text describes a method of estimating the hazard rate of survival data following monotone Aalen regression model. The proposed approach is based on techniques which were introduced by Arjas and Gasbarra [4]. The unknown functional parameters are assumed to be a priori piecewise constant on intervals of varying count and size. The estimates are obtained with the aid of the Gibbs sampler and its variants. The performance of the method is explored by simulations. The results indicate that the method is applicable on small sample size datasets.

Modèles linéaires généralisés fonctionnels avec dérivée

We consider the functional generalized linear model whose response function is a linear operator depending on an explanatory variable X belonging to a functional space. It has been studied, among others, by Cardot and Sarda [4]. In this paper, we consider the functional generalized linear model with derivative component, denoted MLGFD in the following, whose response function depends on a linear operator of X and on its derivative. We propose estimators for the unknown functional parameters and provide convergence rates.

Problems of structural and functional identification of biological tissues

The theoretical methods of identification of topological and functional parameters for biological tissues, such as myocardium, are considered. Among the unknown topological parameters are the dimension and connectivity of a network, and the unknown functional parameters include the electrical resistance of the cellular membrane and cytoplasm. Experimentally known data are the sizes of cells (length and diameter), the input resistance of tissue, and also the field of electrical potential formed by a "dot" current source (by an intracellular microelectrode).

Weighted approximations of tail copula processes with application to testing the bivariate extreme value condition

Consider n i.i.d. random vectors on ℝ2, with unknown, common distribution function F. Under a sharpening of the extreme value condition on F, we derive a weighted approximation of the corresponding tail copula process. Then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value distribution, one obtained from the tail copula process and the other obtained by first estimating the spectral measure which is then used as a building block for the limiting extreme value distribution. We derive the limiting distribution of the test statistic from the aforementioned weighted approximation. This limiting distribution contains unknown functional parameters. Therefore, we show that a version with estimated parameters converges weakly to the true limiting distribution. Based on this result, the finite sample properties of our testing procedure are investigated through a simulation study. A real data application is also presented.

Weighted Approximations of Tail Copula Processes with Application to Testing the Multivariate Extreme Value Condition

Consider n i.i.d. random vectors on R2, with unknown, common distribution function F. Under a sharpening of the extreme value condition on F, we derive a weighted approximation of the corresponding tail copula process. Then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value distribution, one obtained from the tail copula process and the other obtained by first estimating the spectral measure which is then used as a building block for the limiting extreme value distribution. We derive the limiting distribution of the test statistic from the aforementioned weighted approximation. This limiting distribution contains unknown functional parameters. Therefore, we show that a version with estimated parameters converges weakly to the true limiting distribution. Based on this result, the finite sample properties of our testing procedure are investigated through a simulation study. A real data application is also presented.

Identification of time-varying nonlinear systems using Chebyshev polynomials

This paper is devoted to an identification of time-varying nonlinear systems using Chebyshev polynomials of the first kind. For systems being linear relatively unknown functional parameters, a method of approximate determination of these parameters has been worked out. As the identification problems are ill-posed to solve the obtained redefinite system of linear algebraic equations, a regularization method is used.

Identification in nonlinear, distributed parameter water quality models

Systematic and efficient numerical algorithms are developed and applied to the identification of unknown functional parameters in nonlinear estuarine water quality models based on input‐output measurements. As an illustration of the methodology the longitudinal dispersion coefficient is identified from an intratidal, time‐varying, variable area, salinity intrusion model by using both simulated data and actual data from the Delaware River estuary. A comparison among three proposed algorithms through extensive simulation research shows that Marquardt's algorithm emerged as the most efficient one. Effects of noise content and the number of data measurement locations on parameter sensitivity are investigated. Actual monitored salinity data for 3 days in September 1965 are tested in the saline portion of the Delaware River estuary. The spatial variation of the longitudinal dispersion coefficient for this period is estimated. The results obtained indicate that the methodology is generally applicable and it represents a different and supplementary alternative to the methods based on analytical predictions and empirical correlations.