scholarly journals BARTLETT CORRECTION IN THE STABLE AR(1) MODEL WITH INTERCEPT AND TREND

2009 ◽  
Vol 25 (3) ◽  
pp. 857-872 ◽  
Author(s):  
Noud P.A. van Giersbergen
Keyword(s):  
Likelihood Ratio ◽  
Linear Trend ◽  
Likelihood Ratio Statistic ◽  
Stability Boundary ◽  
Small Samples ◽  
Bartlett Correction ◽  
Testing Hypotheses ◽  
Autoregressive Parameter ◽  
Simulation Results ◽  
The Stability

Bartlett corrections are derived for testing hypotheses about the autoregressive parameter ρ in the stable (a) AR(1) model, (b) AR(1) model with intercept, (c) AR(1) model with intercept and linear trend. The correction is found explicitly as a function of ρ. In the models with deterministic terms, the correction factor is asymmetric in ρ. Furthermore, the Bartlett correction is monotonically increasing in ρ and tends to infinity when ρ approaches the stability boundary of + 1. Simulation results indicate that the Bartlett corrections are useful in controlling the size of the likelihood ratio statistic in small samples, although these corrections are not the ultimate panacea.

scholarly journals On the Correction of the Asymptotic Distribution of the Likelihood Ratio Statistic If Nuisance Parameters Are Estimated Based on an External Source

2014 ◽  
Vol 10 (2) ◽  
Author(s):  
Marianne Jonker ◽  
Aad Van der Vaart
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Confidence Intervals ◽  
Likelihood Ratio ◽  
Statistical Models ◽  
Likelihood Ratio Statistic ◽  
External Source ◽  
Nuisance Parameters ◽  
Testing Hypotheses

AbstractIn practice, nuisance parameters in statistical models are often replaced by estimates based on an external source, for instance if estimates were published before or a second dataset is available. Next these estimates are assumed to be known when the parameter of interest is estimated, a hypothesis is tested or confidence intervals are constructed. By this assumption, the level of the test is, in general, higher than supposed and the coverage of the confidence interval is too low. In this article, we derive the asymptotic distribution of the likelihood ratio statistic if the nuisance parameters are estimated based on a dataset that is independent of the data used for estimating the parameter of interest. This distribution can be used for correctly testing hypotheses and constructing confidence intervals. Four theoretical and practical examples are given as illustration.

Nonlinear Dynamics of a Rigid Block on a Rigid Base

1996 ◽  
Vol 63 (1) ◽  
pp. 55-61 ◽  
Author(s):  
R. N. Iyengar ◽  
D. Roy
Keyword(s):  
Stability Boundary ◽  
Three Dimensional ◽  
Melnikov Function ◽  
Rigid Base ◽  
Rigid Block ◽  
Stable And Unstable Manifolds ◽  
Melnikov Functions ◽  
Unstable Manifolds ◽  
Simulation Results ◽  
The Stability

The planar rocking of a prismatic rectangular rigid block about either of its corners is considered. The problem of homoclinic intersections of the stable and unstable manifolds of the perturbed separatrix is addressed to and the corresponding Melnikov functions are derived. Inclusion of the vertical forcing in the Hamiltonian permits the construction of a three-dimensional separatrix. The corresponding modified Melnikov function of Wiggins for homoclinic intersections is derived. Further, the 1-period symmetric orbits are predicted analytically using the method of averaging and compared with the simulation results. The stability boundary for such orbits is also established.

scholarly journals Prediction and Stability Assessment of Soft Foundation Settlement of the Fishbone-Shaped Dike Near the Estuary of the Yangtze River Using Machine Learning Methods

2021 ◽  
Vol 13 (7) ◽  
pp. 3744
Author(s):  
Mingcheng Zhu ◽  
Shouqian Li ◽  
Xianglong Wei ◽  
Peng Wang
Keyword(s):  
Extreme Learning Machine ◽  
Prediction Models ◽  
Good Prediction ◽  
Foundation Settlement ◽  
Machine Method ◽  
Settlement Prediction ◽  
Soft Foundation ◽  
Simulation Results ◽  
Learning Machine ◽  
The Stability

Fishbone-shaped dikes are always built on the soft soil submerged in the water, and the soft foundation settlement plays a key role in the stability of these dikes. In this paper, a novel and simple approach was proposed to predict the soft foundation settlement of fishbone dikes by using the extreme learning machine. The extreme learning machine is a single-hidden-layer feedforward network with high regression and classification prediction accuracy. The data-driven settlement prediction models were built based on a small training sample size with a fast learning speed. The simulation results showed that the proposed methods had good prediction performances by facilitating comparisons of the measured data and the predicted data. Furthermore, the final settlement of the dike was predicted by using the models, and the stability of the soft foundation of the fishbone-shaped dikes was assessed based on the simulation results of the proposed model. The findings in this paper suggested that the extreme learning machine method could be an effective tool for the soft foundation settlement prediction and assessment of the fishbone-shaped dikes.

scholarly journals Latency-Optimal Computational Offloading Strategy for Sensitive Tasks in Smart Homes

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2347
Author(s):  
Yanyan Wang ◽  
Lin Wang ◽  
Ruijuan Zheng ◽  
Xuhui Zhao ◽  
Muhua Liu
Keyword(s):  
Queue Length ◽  
Optimization Problem ◽  
Time Slot ◽  
Smart Homes ◽  
Back Pressure ◽  
Smart Devices ◽  
Smart Device ◽  
Simulation Results ◽  
Computational Offloading ◽  
The Stability

In smart homes, the computational offloading technology of edge cloud computing (ECC) can effectively deal with the large amount of computation generated by smart devices. In this paper, we propose a computational offloading strategy for minimizing delay based on the back-pressure algorithm (BMDCO) to get the offloading decision and the number of tasks that can be offloaded. Specifically, we first construct a system with multiple local smart device task queues and multiple edge processor task queues. Then, we formulate an offloading strategy to minimize the queue length of tasks in each time slot by minimizing the Lyapunov drift optimization problem, so as to realize the stability of queues and improve the offloading performance. In addition, we give a theoretical analysis on the stability of the BMDCO algorithm by deducing the upper bound of all queues in this system. The simulation results show the stability of the proposed algorithm, and demonstrate that the BMDCO algorithm is superior to other alternatives. Compared with other algorithms, this algorithm can effectively reduce the computation delay.

The Application of Bayesian Statistics in Calculating Project Buffer

2011 ◽  
Vol 58-60 ◽  
pp. 1018-1024
Author(s):  
Feng Ye ◽  
Gui Chen Xu ◽  
Di Kang Zhu
Keyword(s):  
Bayesian Statistics ◽  
Statistical Approach ◽  
Implementation Process ◽  
Current Method ◽  
Practical Application ◽  
Great Flexibility ◽  
Crystal Ball ◽  
Simulation Results ◽  
The Stability

This paper reviews several current methods of calculating buffer on the basis of pointing out each merits and pitfalls and then introduces Bayesian statistical approach to CCS / BM domain to calculate the size of the project buffer, to overcome that the current method of the buffer calculation is too subjective and the defect on lacking of practical application. In Crystal Ball, we compare the simulation results of implementation process on the benchmark of C&PM, RESM and SM. The results show that the buffer using this method can ensure the stability of the project’s completion probability, and this method has great flexibility.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

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