EDA on the asymptotic normality of the standardized sequential stopping times, Part-I: Parametric models

2018 ◽  
Vol 37 (3) ◽  
pp. 342-374 ◽  
Author(s):  
Nitis Mukhopadhyay ◽  
Chen Zhang
Keyword(s):  
Asymptotic Normality ◽  
Parametric Models ◽  
Stopping Times

Monitoring shifts in mean: Asymptotic normality of stopping times

Test ◽  
2007 ◽  
Vol 17 (3) ◽  
pp. 515-530 ◽  
Author(s):  
Alexander Aue ◽  
Lajos Horváth ◽  
Piotr Kokoszka ◽  
Josef Steinebach
Keyword(s):  
Asymptotic Normality ◽  
Stopping Times

scholarly journals Asymptotic Normality of Sequential Stopping Times with Applications: Confidence Intervals for an Exponential Mean

2020 ◽  
Vol 72 (1) ◽  
pp. 17-34
Author(s):  
Nitis Mukhopadhyay
Keyword(s):  
Asymptotic Normality ◽  
Confidence Intervals ◽  
Stopping Times ◽  
Sample Mean ◽  
Variable Formula ◽  
Asymptotic Normal Distribution ◽  
The Mean ◽  
Asymptotic Normal ◽  
Better Than

In sequential methodologies, finally accrued data customarily look like [Formula: see text] where [Formula: see text] is the total number of observations collected through termination. Under mild regulatory conditions, a standardized version of [Formula: see text] follows an asymptotic normal distribution (Ghosh–Mukhopadhyay theorem) which we highlight with a number of illustrations from the recent literature for completeness. Then, we emphasize the role of such asymptotic normality results along with second-order approximations for stopping times in the construction of sequential fixed-width confidence intervals for the mean in an exponential distribution. Two kinds of confidence intervals are developed: (a) one centred at the randomly stopped sample mean [Formula: see text] and (b) the two other centred at appropriate constructs using the stopping variable [Formula: see text] alone. Ample comparisons among all three proposed methodologies are summarized via simulations. We emphasize our finding that the two fixed-width confidence intervals centred at appropriate constructs using the stopping variable [Formula: see text] alone perform as well or better than the customary one centred at the randomly stopped sample mean.

scholarly journals Estimation of stopping times for stopped self-similar random processes

2021 ◽  
Author(s):  
Viktor Schulmann
Keyword(s):  
Brownian Motion ◽  
Convergence Rate ◽  
Asymptotic Normality ◽  
Mellin Transform ◽  
Random Processes ◽  
Random Time ◽  
Stopping Times ◽  
Bessel Processes ◽  
One Dimensional ◽  
Self Similar

AbstractLet $$X=(X_t)_{t\ge 0}$$ X = ( X t ) t ≥ 0 be a known process and T an unknown random time independent of X. Our goal is to derive the distribution of T based on an iid sample of $$X_T$$ X T . Belomestny and Schoenmakers (Stoch Process Appl 126(7):2092–2122, 2015) propose a solution based the Mellin transform in case where X is a Brownian motion. Applying their technique we construct a non-parametric estimator for the density of T for a self-similar one-dimensional process X. We calculate the minimax convergence rate of our estimator in some examples with a particular focus on Bessel processes where we also show asymptotic normality.

Asymptotic normality of processes with a branching structure

1998 ◽  
Vol 14 (4) ◽  
pp. 833-848
Author(s):  
Malcolm P. Quine ◽  
Władysław Szczotka
Keyword(s):  
Asymptotic Normality

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

Structural-parametric model of an electroelastic actuator for nanomechanics

2020 ◽  
pp. 3-11
Author(s):  
S.M. Afonin
Keyword(s):  
Transfer Function ◽  
Piezoelectric Actuator ◽  
Transfer Functions ◽  
Piezoelectric Effect ◽  
Parametric Model ◽  
Elastic Compliance ◽  
Parametric Models ◽  
Piezo Actuator ◽  
Structural Scheme ◽  
Model Transfer

Structural-parametric models, structural schemes are constructed and the transfer functions of electro-elastic actuators for nanomechanics are determined. The transfer functions of the piezoelectric actuator with the generalized piezoelectric effect are obtained. The changes in the elastic compliance and rigidity of the piezoactuator are determined taking into account the type of control. Keywords electro-elastic actuator, piezo actuator, structural-parametric model, transfer function, parametric structural scheme

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