scholarly journals Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices

2006 ◽  
Vol 34 (1) ◽  
pp. 80-121 ◽  
Author(s):  
Hock Peng Chan ◽  
Tze Leung Lai
Keyword(s):  
Random Fields ◽  
Random Variables ◽  
Gaussian Random Fields ◽  
Moderate Deviation ◽  
Boundary Crossing ◽  
Sums Of Random Variables ◽  
Multidimensional Indices ◽  
Crossing Probabilities

scholarly journals On the Density Functions of Integrals of Gaussian Random Fields

2013 ◽  
Vol 45 (02) ◽  
pp. 398-424 ◽  
Author(s):  
Jingchen Liu ◽  
Gongjun Xu
Keyword(s):  
Closed Form ◽  
Random Fields ◽  
Random Variables ◽  
Gaussian Random Fields ◽  
Density Functions ◽  
Exponential Functions ◽  
Asymptotic Bounds

In the paper we consider the density functions of random variables that can be written as integrals of exponential functions of Gaussian random fields. In particular, we provide closed-form asymptotic bounds for the density functions and, under smoothness conditions, we derive exact tail approximations of the density functions.

Boundary-crossing probabilities of some random fields related to likelihood ratio tests for epidemic alternatives

1993 ◽  
Vol 30 (01) ◽  
pp. 52-65
Author(s):  
Qiwei Yao
Keyword(s):  
Likelihood Ratio ◽  
Random Fields ◽  
Mean Value ◽  
Likelihood Ratio Tests ◽  
Boundary Crossing ◽  
Square Wave ◽  
Monte Carlo Experiments ◽  
Wave Drift ◽  
Significance Levels ◽  
Crossing Probabilities

We consider the likelihood ratio tests to detect an epidemic alternative in the following two cases of normal observations: (1) the alternative specifies a square wave drift in the mean value of an i.i.d. sequence; (2) the alternative permits a square wave drift in the intercept of a simple linear regression model. To develop the approximations for the significance levels leads us to consider boundary-crossing problems of some two-dimensional discrete-time Gaussian fields. By the method which was proposed originally by Woodroofe (1976) and adapted to study maxima of some random fields by Siegmund (1988), some large deviations for the conditional non-linear boundary-crossing probabilities are developed. Some results of Monte Carlo experiments confirm the accuracy of these approximations.

scholarly journals On the Density Functions of Integrals of Gaussian Random Fields

2013 ◽  
Vol 45 (2) ◽  
pp. 398-424 ◽  
Author(s):  
Jingchen Liu ◽  
Gongjun Xu
Keyword(s):  
Closed Form ◽  
Random Fields ◽  
Random Variables ◽  
Gaussian Random Fields ◽  
Density Functions ◽  
Exponential Functions ◽  
Asymptotic Bounds

In the paper we consider the density functions of random variables that can be written as integrals of exponential functions of Gaussian random fields. In particular, we provide closed-form asymptotic bounds for the density functions and, under smoothness conditions, we derive exact tail approximations of the density functions.

Boundary-crossing probabilities of some random fields related to likelihood ratio tests for epidemic alternatives

1993 ◽  
Vol 30 (1) ◽  
pp. 52-65 ◽  
Author(s):  
Qiwei Yao
Keyword(s):  
Likelihood Ratio ◽  
Random Fields ◽  
Mean Value ◽  
Likelihood Ratio Tests ◽  
Boundary Crossing ◽  
Square Wave ◽  
Monte Carlo Experiments ◽  
Wave Drift ◽  
Significance Levels ◽  
Crossing Probabilities

We consider the likelihood ratio tests to detect an epidemic alternative in the following two cases of normal observations: (1) the alternative specifies a square wave drift in the mean value of an i.i.d. sequence; (2) the alternative permits a square wave drift in the intercept of a simple linear regression model. To develop the approximations for the significance levels leads us to consider boundary-crossing problems of some two-dimensional discrete-time Gaussian fields. By the method which was proposed originally by Woodroofe (1976) and adapted to study maxima of some random fields by Siegmund (1988), some large deviations for the conditional non-linear boundary-crossing probabilities are developed. Some results of Monte Carlo experiments confirm the accuracy of these approximations.

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