scholarly journals Large Deviations in Testing Squared Radial Ornstein-Uhleneck Model

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Shoujiang Zhao ◽  
Qiaojing Liu
Keyword(s):  
Large Deviations ◽  
Hypothesis Testing ◽  
Likelihood Ratio ◽  
Large Deviation ◽  
Decay Rates ◽  
Moderate Deviations ◽  
Large Deviation Principles ◽  
Log Likelihood ◽  
Log Likelihood Ratio ◽  
Error Probabilities

We study the large deviations and moderate deviations of hypothesis testing for squared radial Ornstein-Uhleneck model. Large deviation principles for the log-likelihood ratio are obtained, by which we give negative regions in testing squared radial Ornstein-Uhleneck model and get the decay rates of the error probabilities.

Cramér-type moderate deviations for the likelihood ratio process of Ornstein–Uhlenbeck process with shift

2020 ◽  
Vol 21 (02) ◽  
pp. 2150027
Author(s):  
Hui Jiang ◽  
Hui Liu
Keyword(s):  
Likelihood Ratio ◽  
Decay Rates ◽  
Moderate Deviations ◽  
Uhlenbeck Process ◽  
Testing Problem ◽  
Analysis Techniques ◽  
Log Likelihood ◽  
Ornstein Uhlenbeck Process ◽  
Deviation Inequalities ◽  
Error Probabilities

For the Ornstein–Uhlenbeck process in stationary and explosive cases, this paper studies Cramér-type moderate deviations for the log-likelihood ratio process. As an application, we give the negative regions of drift testing problem, and also obtain the decay rates of the error probabilities. The main methods of this paper consist of mod-[Formula: see text] convergence approach, deviation inequalities for multiple Wiener–Itô integrals and asymptotic analysis techniques.

scholarly journals Large-Deviation Results for Discriminant Statistics of Gaussian Locally Stationary Processes

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Junichi Hirukawa
Keyword(s):  
Likelihood Ratio ◽  
Quadratic Forms ◽  
Large Deviation ◽  
Stationary Processes ◽  
Deviation Rate ◽  
Log Likelihood ◽  
Log Likelihood Ratio ◽  
Rate Functions ◽  
Locally Stationary Processes ◽  
Mean Function

This paper discusses the large-deviation principle of discriminant statistics for Gaussian locally stationary processes. First, large-deviation theorems for quadratic forms and the log-likelihood ratio for a Gaussian locally stationary process with a mean function are proved. Their asymptotics are described by the large deviation rate functions. Second, we consider the situations where processes are misspecified to be stationary. In these misspecified cases, we formally make the log-likelihood ratio discriminant statistics and derive the large deviation theorems of them. Since they are complicated, they are evaluated and illustrated by numerical examples. We realize the misspecification of the process to be stationary seriously affecting our discrimination.

scholarly journals A Corpus-Based Study on the Use of the Logical Connector ‘Thus’ in the Academic Writing of Turkish EFL Learners

2017 ◽  
Vol 10 (2) ◽  
pp. 64
Author(s):  
Serpil Ucar ◽  
Ceyhun Yukselir
Keyword(s):  
Likelihood Ratio ◽  
Academic Writing ◽  
Native Speakers ◽  
American English ◽  
Advanced Learners ◽  
Efl Learners ◽  
Log Likelihood ◽  
Log Likelihood Ratio ◽  
Effect Relation ◽  
Academic Genre

This research was conducted to investigate how frequently Turkish advanced learners of English use the logical connector ‘thus’ in their academic prose and to investigate whether it was overused, underused or misused semantically in comparison to English native speakers. The data were collected from three corpora; Corpus of Contemporary American English and 20 scientific articles of native speakers as control corpora, and 20 scientific articles of Turkish advanced EFL learners. The raw frequencies, frequencies per million words, frequencies per text and log-likelihood ratio were measured so as to compare varieties across the three corpora. The findings revealed that Turkish learners of English showed underuse in the use of the connector ‘thus’ in their academic prose compared to native speakers. Additionally, they did not demonstrate misuse in the use of the connector ‘thus’. Nevertheless, non-native learners of English tended to use this connector in a resultative role (cause-effect relation) more frequently whereas native speakers used it in appositional and summative roles more as well as its resultative role. Furthermore, the most frequent occurrences of ‘thus’ have been in academic genre.

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