scholarly journals Asymptotic Properties for Weighted Averages of Longitudinal Dependent Data

2018 ◽  
Vol 7 (6) ◽  
pp. 100
Author(s):  
Brahima Soro ◽  
Ouagnina Hili ◽  
Youssouf Diagana
Keyword(s):  
Longitudinal Data ◽  
Covariance Function ◽  
Kernel Method ◽  
Asymptotic Properties ◽  
Dependent Data ◽  
Independent Data ◽  
Function Estimation ◽  
Mixing Conditions ◽  
Weighted Averages ◽  
Nonparametric Kernel

This paper presents a set of normality general results for kernel weighted averages. We extend existing literature for independent data (Yao, 2007) to stationary dependent longitudinal data. The asymptotic properties of proposed weighted averages are investigate under α-mixing conditions. These results are useful for covariance function estimation based on nonparametric kernel method.

scholarly journals Asymptotic Properties of Longitudinal Weighted Averages for Strongly Mixing Data

2017 ◽  
Vol 9 (2) ◽  
pp. 65
Author(s):  
Brahima Soro ◽  
Ouagnina Hili ◽  
Sophie Dabo- Niang
Keyword(s):  
Covariance Function ◽  
Asymptotic Properties ◽  
Random Variable ◽  
Weighted Averages ◽  
Strongly Mixing

We present general results of consistency and normality of a real-valued longitudinal random variable. We suppose that this random variable is some formed weighted averages of alpha-mixing data. The results can be applied to within-subject covariance function.

Asymptotic for LS estimators in the EV regression model for dependent errors

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4845-4856
Author(s):  
Konrad Furmańczyk
Keyword(s):  
Regression Model ◽  
Functional Dependence ◽  
Dependent Data ◽  
Errors In Variables ◽  
Mixing Conditions ◽  
Asymptotic Results ◽  
Dependence Measure ◽  
Wide Range ◽  
Ev Regression Model ◽  
Linear And Nonlinear

We study consistency and asymptotic normality of LS estimators in the EV (errors in variables) regression model under weak dependent errors that involve a wide range of linear and nonlinear time series. In our investigations we use a functional dependence measure of Wu [16]. Our results without mixing conditions complete the known asymptotic results for independent and dependent data obtained by Miao et al. [7]-[10].

scholarly journals A Generic Approach to Covariance Function Estimation Using ARMA-Models

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 591 ◽  
Author(s):  
Till Schubert ◽  
Johannes Korte ◽  
Jan Martin Brockmann ◽  
Wolf-Dieter Schuh
Keyword(s):  
Numerical Method ◽  
Covariance Function ◽  
Function Estimation ◽  
Arma Models ◽  
Linear System Of Equations ◽  
Covariance Functions ◽  
Analytical Functions ◽  
Covariance Modeling ◽  
Base Functions ◽  
Finite Sum

Covariance function modeling is an essential part of stochastic methodology. Many processes in geodetic applications have rather complex, often oscillating covariance functions, where it is difficult to find corresponding analytical functions for modeling. This paper aims to give the methodological foundations for an advanced covariance modeling and elaborates a set of generic base functions which can be used for flexible covariance modeling. In particular, we provide a straightforward procedure and guidelines for a generic approach to the fitting of oscillating covariance functions to an empirical sequence of covariances. The underlying methodology is developed based on the well known properties of autoregressive processes in time series. The surprising simplicity of the proposed covariance model is that it corresponds to a finite sum of covariance functions of second-order Gauss–Markov (SOGM) processes. Furthermore, the great benefit is that the method is automated to a great extent and directly results in the appropriate model. A manual decision for a set of components is not required. Notably, the numerical method can be easily extended to ARMA-processes, which results in the same linear system of equations. Although the underlying mathematical methodology is extensively complex, the results can be obtained from a simple and straightforward numerical method.

scholarly journals Fishery-dependent and -independent data lead to consistent estimations of essential habitats

2016 ◽  
Vol 73 (9) ◽  
pp. 2302-2310 ◽  
Author(s):  
Maria Grazia Pennino ◽  
David Conesa ◽  
Antonio López-Quílez ◽  
Facundo Muñoz ◽  
Angel Fernández ◽  
...  
Keyword(s):  
Spatial Patterns ◽  
Survey Design ◽  
Scientific Information ◽  
Marine Species ◽  
Dependent Data ◽  
Independent Data ◽  
Elasmobranch Species ◽  
Spatio Temporal ◽  
Definition Of ◽  
Spatial Locations

Abstract Species mapping is an essential tool for conservation programmes as it provides clear pictures of the distribution of marine resources. However, in fishery ecology, the amount of objective scientific information is limited and data may not always be directly comparable. Information about the distribution of marine species can be derived from two main sources: fishery-independent data (scientific surveys at sea) and fishery-dependent data (collection and sampling by observers in commercial vessels). The aim of this paper is to compare whether these two different sources produce similar, complementary, or different results. We compare them in the specific context of identifying the Essential Fish Habitats of three elasmobranch species (S. canicula, G. melastomus, and E. spinax). Similarity and prediction statistics are used to compare the two different spatial patterns obtained by applying the same Bayesian spatio-temporal modelling approach in the two sources. Results showed that the spatial patterns obtained are similar, although differences are present. In particular, models based on fishery-dependent data are better able to identify temporal relationships between the probability of presence of the species and seasonal environmental variables. In contrast, fishery-independent data better discriminate spatial locations where a species is present or absent. Besides the spatial and temporal differences of the two datasets, the consistency of habitat results highlights the inclusion in each dataset of most of the environmental envelope of each species, both in time and space. Consequently, sampling data should be adapted to each species to reasonably cover their environmental envelope, and a combination of datasets will likely provide a better habitat estimation than using each dataset independently. These findings can be useful in helping fishery managers improve definition of survey design and analyses.

scholarly journals Central Limit Theorems for Law-Invariant Coherent Risk Measures

2012 ◽  
Vol 49 (01) ◽  
pp. 1-21 ◽  
Author(s):  
Denis Belomestny ◽  
Volker Krätschmer
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Risk Measures ◽  
Risk Measure ◽  
Asymptotic Properties ◽  
Dependent Data ◽  
Distributed Data ◽  
Coherent Risk Measures ◽  
Coherent Risk ◽  
Weakly Dependent Data

In this paper we study the asymptotic properties of the canonical plugin estimates for law-invariant coherent risk measures. Under rather mild conditions not relying on the explicit representation of the risk measure under consideration, we first prove a central limit theorem for independent and identically distributed data, and then extend it to the case of weakly dependent data. Finally, a number of illustrating examples is presented.

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