• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.911-918
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• 2013

This study deals with the small sample likelihood based inference for the ratio of two normal variances. The small sample likelihood inference is an approximation method. The signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic, which converge to standard normal distribution, are proposed for the normal variance ratio. Through the simulation study, the coverage probabilities of confidence interval and power of the exact, the signed log-likelihood and the modified signed log-likelihood ratio statistic will be compared. A real data example will be provided.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1173-1181
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• 2008

In this paper, when the parameter of interest is the shape parameter in Pareto distribution, we develop likelihood based inference for this parameter. Specially, we develop signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic for the shape parameter. It is well-known that as sample size grows, the modified signed log-likelihood ratio statistic converges to standard normal distribution faster than the signed log-likelihood ratio statistic. But the computation of the modified signed log-likelihood statistic is hard or even impossible when the sufficient statistics and the ancillary statistics are not clear. In this case, one can consider an approximation to the modified signed log-likelihood statistic. Specially, when the parameter of interest is informationally orthogonal to the nuisance parameters, we propose the approximate modified signed log-likelihood statistic. Through simulation, we investigate the performances of the proposed statistics with the signed log-likelihood statistic.

• Journal of the Korean Data and Information Science Society
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• v.23 no.1
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• pp.89-98
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• 2012

In this paper, the ratio of parameters in two independent Maxwell distributions is parameter of interest. We proposed test statistics, which converge to standard normal distribution, based on likelihood function. The exact distribution for testing the ratio is hard to obtain. We proposed the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic for testing the ratio. Through simulation, we show that the modified signed log-likelihood ratio statistic converges faster than signed log-likelihood ratio statistic to standard normal distribution. We compare two statistics in terms of type I error and power. We give an example using real data.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.655-666
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• 2008

Small sample likelihood based inference for the shape parameter of the inverse Gaussian distribution is the purpose of this paper. When shape parameter is of interest, the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic are derived. Hsieh (1990) gave a statistical inference for the shape parameter based on an exact method. Throughout simulation, we will compare the statistical properties of the proposed statistics to the statistic given by Hsieh (1990) in term of confidence interval and power of test. We also discuss a real data example.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.963-972
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• 2006

This paper focuses on the likelihood based confidence intervals for two inverse gaussian distributions when the parameter of interest is common scale parameter. Confidence intervals based on signed loglikelihood ratio statistic and modified signed loglikelihood ratio statistics will be compared in small sample through an illustrative simulation study.

• MALSORI
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• no.60
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• pp.165-180
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• 2006

In this paper, we present several confidence measures (CM) for speech recognition systems to evaluate the reliability of recognition results. We propose heuristic CMs such as mean log-likelihood score, N-best word log-likelihood ratio, likelihood sequence fluctuation and likelihood ratio testing(LRT)-based CMs using several types of anti-models. Furthermore, we propose new algorithms to add weighting terms on phone-level log-likelihood ratio to merge word-level log-likelihood ratios. These weighting terms are computed from the distance between acoustic models and knowledge-based phoneme classifications. LRT-based CMs show better performance than heuristic CMs excessively, and LRT-based CMs using phonetic information show that the relative reduction in equal error rate ranges between $8{\sim}13%$ compared to the baseline LRT-based CMs. We use the support vector machine to fuse several CMs and improve the performance of utterance verification. From our experiments, we know that selection of CMs with low correlation is more effective than CMs with high correlation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.4
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• pp.767-783
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• 2013

This paper aims at designing a selective demodulation scheme based on Log-likelihood Ratio threshold (SDLT) instead of the conventional adaptive demodulation (ADM) scheme, by using rateless codes. The major difference is that the Log-likelihood ratio (LLR) threshold is identified as a key factor to control the demodulation rate, while the ADM uses decision region set (DRS) to adjust the bit rate. In the 16-QAM SDLT scheme, we deduce the decision regions over an additive white Gaussian channel, corresponding to the variation of LLR threshold and channel states. We also derived the equations to calculate demodulation rate and bit error rate (BER), which could be proven by simulation results. We present an adaptation strategy for SDLT, and compare it with ADM and adaptive modulation (AM). The simulation results show that our scheme not only significantly outperforms the ADM in terms of BER, but also achieves a performance as good as the AM scheme. Moreover, the proposed scheme can support much more rate patterns over a wide range of channel states.

• Smart Structures and Systems
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• v.12 no.2
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• pp.181-207
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• 2013

In this paper, a statistical reference-free real-time damage detection methodology is proposed for detecting joint and member damage of truss bridge structures. For the statistical damage sensitive index (DSI), wavelet packet decomposition (WPD) in conjunction with the log likelihood ratio was suggested. A sensitivity test for selecting a wavelet packet that is most sensitive to damage level was conducted and determination of the level of decomposition was also described. Advantages of the proposed method for applications to real-time health monitoring systems were demonstrated by using the log likelihood ratios instead of likelihood ratios. A laboratory truss bridge structure instrumented with accelerometers and a shaker was used for experimental verification tests of the proposed methodology. The statistical reference-free real-time damage detection algorithm was successfully implemented and verified by detecting three damage types frequently observed in truss bridge structures - such as loss of bolts, loosening of bolts at multiple locations, sectional loss of members - without reference signals from pristine structure. The DSI based on WPD and the log likelihood ratio showed consistent and reliable results under different damage scenarios.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.519-527
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• 2004

Relationship between the partial likelihood ratio statistics for logisitic models and the partial goodness-of-fit statistics for corresponding log-linear models is discussed. This paper shows how definitions of suppression in logistic model can be adapted for log-linear model and how they are related to confounding in terms of collapsibility for categorical data. Several $2{times}2{times}2$ contingency tables are illustrated.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.2C
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• pp.117-122
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• 2006

In this paper, we present a simple and general soft bit decision expression for a Gray coded PAM signal over additive white Gaussian noise(AWGN) channel with the log likelihood ratio(LLR). In order to reduce the complexity of the LLR calculation, we make the bitwise LLR expression simple by replacing the mathematical max functions of the conventional Max-Log-MAP expression with simple arithmetic functions associated with some deterministic parameters, such as a received value and distance between symbols on a signal space. Taking the implementation issues, like the area of silicon, the power consumption, the timing latency, and so on, into consideration, we submit that the proposed method is a promising alternative way to conventional methods for reconfigurable systems.