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.

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.

Gradation of the significance level of trends in precipitation over China

2018 ◽  
Vol 49 (6) ◽  
pp. 1890-1901 ◽  
Author(s):  
Ping Xie ◽  
Yuxi Zhao ◽  
Yan-Fang Sang ◽  
Haiting Gu ◽  
Ziyi Wu ◽  
...  
Keyword(s):  
Correlation Coefficient ◽  
Global Climate ◽  
Kendall Test ◽  
Mean Value ◽  
Annual Precipitation ◽  
Significance Level ◽  
Monte Carlo Experiments ◽  
Dispersion Degree ◽  
Significance Levels ◽  
The Relationship

Abstract How to accurately detect and estimate the significance level of trends in hydroclimate time series is a challenge. Building on correlation analysis, we propose an approach for evaluating and grading the significance level of trend in a series, and apply it to evaluate the changes in annual precipitation in China. The approach involved first formulating the relationship between the correlation coefficient and trend's slope. Four correlation coefficient thresholds are then determined by considering the influence of significance levels and data length, and the significance of trends is graded as five levels: no, weak, moderate, strong and dramatic. A larger correlation coefficient reflects a larger slope of trend and its higher significance level. Results of Monte-Carlo experiments indicated that the correlation coefficient-based approach not only reflects the magnitude of a trend, but also considers the influence of dispersion degree and mean value of the original series. Compared with the Mann–Kendall test used commonly, the proposed approach gave more accurate and specific gradation of the significance level of trends in annual precipitation over China. We find that the precipitation trends over China are not uniform, and the effects of global climate change on precipitation are not strong and limited to some regions.

Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes

1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Partial Ordering ◽  
Boundary Crossing ◽  
Conditional Probabilities ◽  
Life Distribution ◽  
Life Distributions ◽  
Bounded Below ◽  
Crossing Probabilities

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

scholarly journals Quasi-likelihood ratio tests for cointegration, cobreaking, and cotrending

2019 ◽  
Vol 38 (8) ◽  
pp. 881-898
Author(s):  
Josep Lluís Carrion-i-Silvestre ◽  
Dukpa Kim
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Tests
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