The Asymptotic Behavior of the Limit Distribution of the Kolmogorov–Smirnov Statistic in the Case of a Composite Hypothesis for the Class of Projecting Estimates of an Unknown Parameter

1988 ◽  
Vol 32 (2) ◽  
pp. 380-383
Author(s):  
A. A. Makarov
Keyword(s):  
Asymptotic Behavior ◽  
Limit Distribution ◽  
Unknown Parameter ◽  
Composite Hypothesis ◽  
Kolmogorov Smirnov ◽  
Smirnov Statistic

An absorption probability for the Ornstein-Uhlenbeck process

1975 ◽  
Vol 12 (3) ◽  
pp. 595-599 ◽  
Author(s):  
John P. Dirkse
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Closed Form ◽  
Asymptotic Expression ◽  
Uhlenbeck Process ◽  
Absorption Probability ◽  
Optional Stopping ◽  
Ornstein Uhlenbeck Process ◽  
Kolmogorov Smirnov ◽  
Smirnov Statistic

An asymptotic expression for an absorption probability for the Ornstein-Uhlenbeck process is presented along with an application of the result to a problem in optional stopping. The relation of this result to the asymptotic behavior of a weighted Kolmogorov-Smirnov statistic is also discussed. Sweet and Hardin (1970) derive an exact solution (not in closed form) for this same problem.

An absorption probability for the Ornstein-Uhlenbeck process

1975 ◽  
Vol 12 (03) ◽  
pp. 595-599
Author(s):  
John P. Dirkse
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Closed Form ◽  
Asymptotic Expression ◽  
Uhlenbeck Process ◽  
Absorption Probability ◽  
Optional Stopping ◽  
Ornstein Uhlenbeck Process ◽  
Kolmogorov Smirnov ◽  
Smirnov Statistic

An asymptotic expression for an absorption probability for the Ornstein-Uhlenbeck process is presented along with an application of the result to a problem in optional stopping. The relation of this result to the asymptotic behavior of a weighted Kolmogorov-Smirnov statistic is also discussed. Sweet and Hardin (1970) derive an exact solution (not in closed form) for this same problem.

The distinction machine: Physics journals from the perspective of the Kolmogorov–Smirnov statistic

2019 ◽  
Vol 13 (4) ◽  
pp. 100982
Author(s):  
Yurij L. Katchanov ◽  
Yulia V. Markova ◽  
Natalia A. Shmatko
Keyword(s):  
Kolmogorov Smirnov ◽  
Physics Journals ◽  
Smirnov Statistic

Predicting Aircraft Detectability

1979 ◽  
Vol 21 (3) ◽  
pp. 277-291 ◽  
Author(s):  
Akerman Alexander ◽  
Robert E. Kinzly
Keyword(s):  
Field Tests ◽  
Contrast Threshold ◽  
Large Set ◽  
Threshold Data ◽  
Detection Probabilities ◽  
Model Predictions ◽  
Kolmogorov Smirnov ◽  
Aircraft Detection ◽  
Parameter Estimation Techniques ◽  
Smirnov Statistic

A visual search model, VIDEM, has been formulated for predicting the detectability of a single, unknown target in an unstructured surround. The intended application is aircraft detection. The model consists of four components: a liminal contrast threshold, a frequency-of-seeing curve, a soft shell search representation, and discrete cumulation of single glimpse detection probabilities. The formulation was developed by registering five existing models against three controlled search experiments. The five models used represent all appropriate laboratory threshold data, including those of Blackwell, Lamar, Sloan, and Taylor. The search experiments included a large set of aircraft field tests, with precise photometric target measurements correlated to the detection events. The model registrations were done using nonlinear parameter estimation techniques and by comparing model predictions to actual event cumulatives with the Kolmogorov-Smirnov statistic. The resultant VIDEM model is a derivative of Sloan's data, cast into the popular visual lobe equations of Lamar.

Kolmogorov-Smirnov statistic and its application in library design

2000 ◽  
Vol 18 (4-5) ◽  
pp. 368-382 ◽  
Author(s):  
Dmitrii N Rassokhin ◽  
Dimitris K Agrafiotis
Keyword(s):  
Library Design ◽  
Kolmogorov Smirnov ◽  
Smirnov Statistic

Central limit theorem for the solution to the heat equation with moving time

2016 ◽  
Vol 19 (01) ◽  
pp. 1650005 ◽  
Author(s):  
Junfeng Liu ◽  
Ciprian A. Tudor
Keyword(s):  
Asymptotic Behavior ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Heat Equation ◽  
White Noise ◽  
Limit Distribution ◽  
Malliavin Calculus ◽  
Time Variable ◽  
Time Space ◽  
Quadratic Variations

We consider the solution to the stochastic heat equation driven by the time-space white noise and study the asymptotic behavior of its spatial quadratic variations with “moving time”, meaning that the time variable is not fixed and its values are allowed to be very big or very small. We investigate the limit distribution of these variations via Malliavin calculus.

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