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Afrika Statistika
Afrika Statistika
Katchekpele, Edoh; Gneyou, Kossi Essona; Diongue, Abdou Kâ
We study a Cumulative Sum (CUSUM)-type test to detect a change in the
unconditional variance of GARCH models. We show that, under the null hypothesis
(no change), the CUSUM test statistic converges to the supremum of a standard
Brownian bridge. Using Monte Carlo simulation, we demonstrate that the
asymptotic power of the test is almost the unity and compare the test result
with existing results in the literature. Finally, the test procedure is applied
to real-world situation namely the Standard and Poor (S&P) 500 stock market
returns (09/16/1980 to 01/31/2008) where we are able to detect a change in the
unconditional variance at a very early stage of...
Katchekpele, Edoh; Gneyou, Kossi Essona; Diongue, Abdou Kâ
We study a Cumulative Sum (CUSUM)-type test to detect a change in the
unconditional variance of GARCH models. We show that, under the null hypothesis
(no change), the CUSUM test statistic converges to the supremum of a standard
Brownian bridge. Using Monte Carlo simulation, we demonstrate that the
asymptotic power of the test is almost the unity and compare the test result
with existing results in the literature. Finally, the test procedure is applied
to real-world situation namely the Standard and Poor (S&P) 500 stock market
returns (09/16/1980 to 01/31/2008) where we are able to detect a change in the
unconditional variance at a very early stage of...
Ibrahim, Mahmud; Benyah, Francis
The study explores the optimal harvesting of renewable resources like fisheries.
The fish biomass dynamics is described by a nonlinear growth model that
maximizes the total net revenue whilst taking into consideration the sustainable
and effective utilization of the resource. In addition, stability dynamics of
the model is assessed through bifurcation analysis. Pontryagin's maximum
principle is used to derive the optimality system and characterize the optimal
control. A numeric iterative method employing the fourth order Runge-Kutta
scheme facilitates the solution of the optimality system. The simulation results
obtained are then discussed. The results show that the sum of the maximum
allowable harvest and the final biomass level must not...
Ibrahim, Mahmud; Benyah, Francis
The study explores the optimal harvesting of renewable resources like fisheries.
The fish biomass dynamics is described by a nonlinear growth model that
maximizes the total net revenue whilst taking into consideration the sustainable
and effective utilization of the resource. In addition, stability dynamics of
the model is assessed through bifurcation analysis. Pontryagin's maximum
principle is used to derive the optimality system and characterize the optimal
control. A numeric iterative method employing the fourth order Runge-Kutta
scheme facilitates the solution of the optimality system. The simulation results
obtained are then discussed. The results show that the sum of the maximum
allowable harvest and the final biomass level must not...
Ben Gherbal, Hanane; Mezerdi, Brahim
This paper is concerned with optimal control of systems driven by
stochastic differential equations (SDEs), with jump processes, where the control
variable appears in the drift and in the jump term. We study the relaxed
problem, in which admissible controls are measure-valued processes and the state
variable is governed by an SDE\ driven by a counting measure valued process
called relaxed Poisson measure such that the compensator is a product measure.
Under some conditions on the coefficients, we prove that every diffusion process
associated to a relaxed control is a limit of a sequence of diffusion processes
associated to strict controls. As a consequence, we show that the...
Ben Gherbal, Hanane; Mezerdi, Brahim
This paper is concerned with optimal control of systems driven by
stochastic differential equations (SDEs), with jump processes, where the control
variable appears in the drift and in the jump term. We study the relaxed
problem, in which admissible controls are measure-valued processes and the state
variable is governed by an SDE\ driven by a counting measure valued process
called relaxed Poisson measure such that the compensator is a product measure.
Under some conditions on the coefficients, we prove that every diffusion process
associated to a relaxed control is a limit of a sequence of diffusion processes
associated to strict controls. As a consequence, we show that the...
Prakash, Gyan
When some sample values at either or both the extremes might have been assorted,
a censoring scheme is much useful. Nevertheless, in some reliability
experiments, the number of items fell out the experiment cannot be prefixed
random in some situations. For such situations, a random removal scheme with
censoring scheme may offer a good result. Here, a random removal scheme with the
Progressive censoring plan is assumed for statistical inference, when fill out
items of the experiments cannot be prefixed. The analysis of the present
discussion has carried out with the help of a real data set for the Burr
Type-XII distribution.
Prakash, Gyan
When some sample values at either or both the extremes might have been assorted,
a censoring scheme is much useful. Nevertheless, in some reliability
experiments, the number of items fell out the experiment cannot be prefixed
random in some situations. For such situations, a random removal scheme with
censoring scheme may offer a good result. Here, a random removal scheme with the
Progressive censoring plan is assumed for statistical inference, when fill out
items of the experiments cannot be prefixed. The analysis of the present
discussion has carried out with the help of a real data set for the Burr
Type-XII distribution.
Anani, Lotsi; Wit, Ernst
Microarray technologies and related methods coupled with appropriate mathematical
and statistical models have made it possible to identify dynamic regulatory
networks by measuring time course expression levels of many genes
simultaneously. However one of the challenges is the high-dimensional nature of
such data coupled with the fact that these gene expression data are known not to
include various biological process. As genomic interactions are highly
structured, the aim was to derive a method for inferring a sparse dynamic
network in a high dimensional data setting. The paper assumes that the
observations are noisy measurements of gene expression in the form of mRNAs,
whose dynamics can be described by some...
Anani, Lotsi; Wit, Ernst
Microarray technologies and related methods coupled with appropriate mathematical
and statistical models have made it possible to identify dynamic regulatory
networks by measuring time course expression levels of many genes
simultaneously. However one of the challenges is the high-dimensional nature of
such data coupled with the fact that these gene expression data are known not to
include various biological process. As genomic interactions are highly
structured, the aim was to derive a method for inferring a sparse dynamic
network in a high dimensional data setting. The paper assumes that the
observations are noisy measurements of gene expression in the form of mRNAs,
whose dynamics can be described by some...
Cherfaoui, Mouloud; Boualem, Mohamed; Aïssani, Djamil; Adjabi, Smaïl
In this paper, we aim at highlighting the influence of the density pole on the
performances of its gamma-kernel estimator. To do this, we performed a
comparative study for the performances of the gamma-kernel estimators with those
provided by other bias effect correction techniques at the bounds, using the
simulation technique. In conclusion, the results obtained confirm those provided
in the literature and show that in some cases the normalization of the gamma
estimators can considerably improve local and global performances of the
gamma-kernel estimators.
Cherfaoui, Mouloud; Boualem, Mohamed; Aïssani, Djamil; Adjabi, Smaïl
In this paper, we aim at highlighting the influence of the density pole on the
performances of its gamma-kernel estimator. To do this, we performed a
comparative study for the performances of the gamma-kernel estimators with those
provided by other bias effect correction techniques at the bounds, using the
simulation technique. In conclusion, the results obtained confirm those provided
in the literature and show that in some cases the normalization of the gamma
estimators can considerably improve local and global performances of the
gamma-kernel estimators.
Tour, Madiha; Sayah, Abdallah; Yahia, Djebrane
Kernel distribution estimators are not consistent near the boundary of its
support. Several solutions to this problem have already been proposed. In this
paper, we propose a new kernel estimation of the cumulative distribution
function for heavy tailed distributions based on the method of the
transformation of the data set with a modification of the Champernowne
distribution and the generalized reflection method of boundary correction for
kernel distribution estimation. The asymptotic bias, variance and mean squared
error of the proposed estimator are given. Simulations are drawn to show that
the proposed method perform quite well when compared with other existing
methods.
Tour, Madiha; Sayah, Abdallah; Yahia, Djebrane
Kernel distribution estimators are not consistent near the boundary of its
support. Several solutions to this problem have already been proposed. In this
paper, we propose a new kernel estimation of the cumulative distribution
function for heavy tailed distributions based on the method of the
transformation of the data set with a modification of the Champernowne
distribution and the generalized reflection method of boundary correction for
kernel distribution estimation. The asymptotic bias, variance and mean squared
error of the proposed estimator are given. Simulations are drawn to show that
the proposed method perform quite well when compared with other existing
methods.