Robust estimation in multiple linear regression model with non-Gaussian noise

Akkaya, Ayşen D.; Tiku, M. L.

doi:10.1016/j.automatica.2007.06.029

Cited by 36 publications

(18 citation statements)

References 22 publications

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“…In addition, a multivariate linear regression model was used to test the hypothesis that GVS had a significant effect on cursor position during tracking. As the traditional least squares regression may be sensitive to noisy and gross errors ( Akkaya and Tiku, 2008 ), we chose a robust regression method to analyze our data (“robustfit” function in MATLAB). This method is known to be robust to outliers utilizing an iteratively reweighted scheme to deweight the influences of outliers.…”

Section: Methodsmentioning

confidence: 99%

Multifaceted effects of noisy galvanic vestibular stimulation on manual tracking behavior in Parkinsonâ€™s disease

Lee

Kim

Svenkeson

et al. 2015

Front. Syst. Neurosci.

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Parkinson's disease (PD) is a neurodegenerative movement disorder that is characterized clinically by slowness of movement, rigidity, tremor, postural instability, and often cognitive impairments. Recent studies have demonstrated altered cortico-basal ganglia rhythms in PD, which raises the possibility of a role for non-invasive stimulation therapies such as noisy galvanic vestibular stimulation (GVS). We applied noisy GVS to 12 mild-moderately affected PD subjects (Hoehn and Yahr 1.5-2.5) off medication while they performed a sinusoidal visuomotor joystick tracking task, which alternated between 2 task conditions depending on whether the displayed cursor position underestimated the actual error by 30% ('Better') or overestimated by 200% ('Worse'). Either sham or subthreshold, noisy GVS (0.1-10 Hz, 1/f-type power spectrum) was applied in pseudorandom order. We used exploratory (linear discriminant analysis with bootstrapping) and confirmatory (robust multivariate linear regression) methods to determine if the presence of GVS significantly affected our ability to predict cursor position based on target variables. Variables related to displayed error were robustly seen to discriminate GVS in all subjects particularly in the Worse condition. If we considered higher frequency components of the cursor trajectory as "noise," the signal-tonoise ratio of cursor trajectory was significantly increased during the GVS stimulation. The results suggest that noisy GVS influenced motor performance of the PD subjects, and we speculate that they were elicited through a combination of mechanisms: enhanced cingulate activity resulting in modulation of frontal midline theta rhythms, improved signal processing in neuromotor system via stochastic facilitation and/or enhanced "vigor" known to be deficient in PD subjects. Further work is required to determine if GVS has a selective effect on corrective submovements that could not be detected by the current analyses.

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Section: Methodsmentioning

confidence: 99%

Multifaceted effects of noisy galvanic vestibular stimulation on manual tracking behavior in Parkinsonâ€™s disease

Lee

Kim

Svenkeson

et al. 2015

Front. Syst. Neurosci.

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show abstract

“…Applying the following corollary of [21, Lemma 1 and Remark 8], 1 we then obtain GAS of the origin. The different proof technique and, in particular, the use of Lemma 1 has the consequence that for our discrete-time result we do not establish GES but only GAS of the origin.…”

Section: Stabilitymentioning

confidence: 99%

“…Most of the results rely on the idea of setting the Kalman filter so as to make it robust to outliers (see, among others, [9,22,8]). In [1] statistical tests are proposed that are less sensitive to abnormal noises. Identification based on an l 1 criterion is addressed in [16,27].…”

Section: Introductionmentioning

confidence: 99%

Stubborn state observers for linear time-invariant systems

Alessandri

Zaccarian

2018

Automatica

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For the purpose of estimating the state of a linear time-invariant system with measurements subject to outliers, we propose an observer with a saturated output injection in such a way to mitigate the effect of abnormal and isolated measurement noise on the error dynamics. Stability conditions in both the continuous-time and the discrete-time cases are derived, which ensure global exponential stability to the origin for the error dynamics. Such conditions can be expressed in terms of linear matrix inequalities, allowing for a viable design by using convex optimization. The effectiveness of the approach is illustrated by means of simulations in comparison with the Luenberger observer.

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“…To handle these contaminated measurements, some initial research has conducted for SE or filtering, see Akkaya and Tiku (2008), Alessamdri and Zaccarian (2018) and Gandhi and Mili (2010). For example, in Akkaya and Tiku (2008), a modified maximum likelihood estimator has been designed which is robust to the possible outliers, and a new prewhitening method has been applied to the filtering issue for discrete linear system in Gandhi and Mili (2010). Recently, in Alessamdri and Zaccarian (2018), by utilizing a saturated output, a novel observer has been constructed for SEIs.…”

Section: Introductionmentioning

confidence: 99%

Outlier-resistant l₂-l_∞ state estimation for discrete-time memristive neural networks with time-delays

Zhao

Liu

et al. 2021

Systems Science & Control Engineering

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Robust estimation in multiple linear regression model with non-Gaussian noise

Cited by 36 publications

References 22 publications

Multifaceted effects of noisy galvanic vestibular stimulation on manual tracking behavior in Parkinsonâ€™s disease

Multifaceted effects of noisy galvanic vestibular stimulation on manual tracking behavior in Parkinsonâ€™s disease

Stubborn state observers for linear time-invariant systems

Outlier-resistant l₂-l_∞ state estimation for discrete-time memristive neural networks with time-delays

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Robust estimation in multiple linear regression model with non-Gaussian noise

Cited by 36 publications

References 22 publications

Multifaceted effects of noisy galvanic vestibular stimulation on manual tracking behavior in Parkinsonâ€™s disease

Multifaceted effects of noisy galvanic vestibular stimulation on manual tracking behavior in Parkinsonâ€™s disease

Stubborn state observers for linear time-invariant systems

Outlier-resistant l2-l∞ state estimation for discrete-time memristive neural networks with time-delays

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Outlier-resistant l₂-l_∞ state estimation for discrete-time memristive neural networks with time-delays