ASYMPTOTIC DISTRIBUTION OF LIKELIHOOD RATIO STATISTIC FOR TESTING SPHERICTY IN GROWTH CURVE MODELS

In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose to the null hypothesis. These expansions are given in series form of beta distributions.

NONNULL DISTRIBUTION OF THE LIKELIHOOD RATIO CRITERION FOR TESTING THE EQUALITY OF DIAGONAL BLOCKS WITH BLOCKWISE INDEPENDENCE

In this paper, the nonnull moments and the distributions of the likelihood ratio criterion for testing the equality of diagonal blocks with blockwise independence under certain alternatives have derived.

Modified likelihood ratio test for homogeneity in normal mixtures with two samples

This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ratio test is X^2（1）.

Generalized Likelihood Ratio Tests for Varying-Coefficient Models with Censored Data

In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.

Profile Likelihood Tests for Common Risk Ratios in Meta-Analysis Studies

It is well-known that the power of Cochran’s Q test to assess the presence of heterogeneity among treatment effects in a clinical meta-analysis is low due to the small number of studies combined. Two modified tests (PL1, PL2) were proposed by replacing the profile maximum likelihood estimator (PMLE) into the variance formula of logarithm of risk ratio in the standard chi-square test statistic for testing the null common risk ratios across all k studies (i = 1, L, k). The simply naive test (SIM) as another comparative candidate has considerably arisen. The performance of tests in terms of type I error rate under the null hypothesis and power of test under the random effects hypothesis was done via a simulation plan with various combinations of significance levels, numbers of studies, sample sizes in treatment and control arms, and true risk ratios as effect sizes of interest. The results indicated that for moderate to large study sizes (k?≥ 16)?in combination with moderate to large sample sizes?(?≥ 50), three tests (PL1, PL2, and Q) could control type I error rates in almost all situations. Two proposed tests (PL1, PL2) performed best with the highest power when?k?≥ 16?and moderate sample sizes (= 50,100);this finding was very useful to make a recommendation to use them in practical situations. Meanwhile, the standard Q test performed best when?k?≥ 16 and large sample sizes (≥ 500). Moreover, no tests were reasonable for small sample sizes (≤ 10), regardless of study size k. The simply naive test (SIM) is recommended to be adopted with high performance when k = 4 in combination with (≥ 500).

Analysis of the stress ratio of anisotropic rocks in uniaxial tests

The effect of structural discontinuities on the progressive failure process of anisotropic rocks should be paid particular attention.The crack damage stress σ_(cd),also considered as the yield strength,and the relationship between σ_(cd) and the uniaxial peak strength σ_(ucs) of anisotropic rocks for different orientations 8 of the isotropy planes with respect to the loading directions were investigated theoretically and experimentally.A theoretical relation of σ_(cd)/σ_(ucs) with the function of the shape parameter m was established.Additionally,uniaxial compression tests of shale samples were conducted for several inclinations θ.The test result of σ_(cd)/σ_(ucs) was close to the theoretical value for a given orientation.Furthermore,both experimental results and theoretical solutions of σ_(cd)/σ_(ucs) were independent of the inclination θ while σ_(cd) andσ_(ucs) were strongly affected by θ.The strength ratio σ_(cd)/σ_(ucs) may therefore be an intrinsic property of anisotropic rocks and could be used to predict the failure of rock samples.

Voice activity detection based on deep belief networks using likelihood ratio

A novel technique is proposed to improve the performance of voice activity detection(VAD) by using deep belief networks(DBN) with a likelihood ratio(LR). The likelihood ratio is derived from the speech and noise spectral components that are assumed to follow the Gaussian probability density function(PDF). The proposed algorithm employs DBN learning in order to classify voice activity by using the input signal to calculate the likelihood ratio. Experiments show that the proposed algorithm yields improved results in various noise environments, compared to the conventional VAD algorithms. Furthermore, the DBN based algorithm decreases the detection probability of error with [0.7, 2.6] compared to the support vector machine based algorithm.

Fall cone tests considering water content, cone penetration index, and plasticity angle of fine-grained soils

This paper analyzed the consistency of some parameters of soils in the literature and experimental results from fall cone test and its application to soil plasticity classification.Over 500 data from both literatures and experiments using fall cone and Casagrande methods were compiled to assess the relationships among specified water content,cone penetration index ebT,and plasticity angle eaT of finegrained soils.The results indicate that no unique correlation exists among b,liquid limit of the fall cone test(LLc)and a.The water content at 1 mm cone penetration eC0T correlates well with b,plasticity ratio eRpT(i.e.the ratio of plastic limit to liquid limit),and a.Finally,the potential of using the btan a diagram to classify soil plasticity was also discussed.

Research on Dynamic and Static Test Methods for Evaluating the Poisson's Ratio of Orien ted Strand Board

In this article,dynamic method and static method of testing Poisson's ratio of OSB(Oriented Strand Board)were proposed.Through modal and static numerical analyses,the position where the transverse stress is equal to zero was determined.The binary linear regression method was applied to express the gluing position of the strain gauge as a relational express ion that depended on the length-width ratio and width-thickness ratio of the canti-lever plate.Then the longitudinal and transverse Poisson's ratios of OSB were mea sured by the given dynamic and static methods.In addition,the test results of OSB Poisson's ratio were analyzed with the probability distribution of random variables.The results showed that using the proposed dynamic method and static method,the test results for longitudinal and transverse Poisson's ratios of OSB were quite consistent,despite the gluing position of the strain gauges being different.And these OSB Poisson's ratios were accorded with that obtained by the axial tensile method and the four-point bending method.OSB longitudinal and transverse Poisson's ratios followed Weibull distribution.

THE ASYMPTOTIC DISTRIBUTIONS OF EMPIRICAL LIKELIHOOD RATIO STATISTICS IN THE PRESENCE OF MEASUREMENT ERROR

Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying accuracies are obtained. Statistical inference should be based on the pooled samples. In this article, the authors also assumes that all the imperfect instruments are unbiased. They consider the problem of combining this information to make statistical tests for parameters more relevant. They define the empirical likelihood ratio functions and obtain their asymptotic distributions in the presence of measurement error.

A Note on Approximation of Likelihood Ratio Statistic in Exploratory Factor Analysis

In normal theory exploratory factor analysis, likelihood ratio (LR) statistic plays an important role in evaluating the goodness-of-fit of the model. In this paper, we derive an approximation of the LR statistic. The approximation is then used to show explicitly that the expectation of the LR statistic agrees with the degrees of freedom of the asymptotic chi-square distribution.

Likelihood Ratio and Strong Limit Theorems for the Discrete Random Variable

This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a class of strong deviation theorems which represented by inequalities between random variables and their expectation are obtained. As a result, we obtain some strong deviation theorems for Poisson distribution and binomial distribution.

Sequential Probability Ratio Test of Correlation Coefficient Using Fuzzy Hypothesis Testing

One of the important fields in statistics is testing hypothesis of correlation coefficient. The extension of the idea of testing correlation to fuzzy hypothesis is of great interesting. In this study, we examined the use of fuzzy hypothesis testing approach for the Sequential Probability Ratio Test (SPRT) of correlation coefficient. Use of fuzzy hypothesis testing for correlation coefficient with SPRT is illustrated by an example.

Revisit the Two Sample t-Test with a Known Ratio of Variances

Inference for the difference of two independent normal means has been widely studied in staitstical literature. In this paper, we consider the case that the variances are unknown but with a known relationship between them. This situation arises frequently in practice, for example, when two instruments report averaged responses of the same object based on a different number of replicates, the ratio of the variances of the response is then known, and is the ratio of the number of replicates going into each response. A likelihood based method is proposed. Simulation results show that the proposed method is very accurate even when the sample sizes are small. Moreover, the proposed method can be extended to the case that the ratio of the variances is unknown.

A Tiling Lemma and Its Application to the Ratio Test for Convergence of Series

We prove that any collection which tiles the positive integers must contain one of two types of sub-collections. We then use this result to prove a variation of the Ratio Test for convergence of series. This version of the Ratio Test shows the convergence of certain series for which the Root Test (which is known to be more powerful than the conventional Ratio Test) fails. This version of the Ratio Test is also used to prove a version of the Banach Contraction Principle for self-maps of a complete metric space.

Test for Homogeneity of Odds Ratios Using <i>U</i>-Statistics

There are a few statistics testing the homogeneity of odds ratios across strata. Asymptotic statistics lose their power in the “sparse-data” setting. Both asymptotic statistics and exact tests have low power when the sample sizes are small. We created a set of U statistics and compared them with some existing statistics in testing homogeneity of OR at different data settings. We evaluated their performance in terms of the empirical size and power via Monto Carlo simulations. Our results showed that two of the U-statistics under our study had higher power for testing homogeneity of odds ratios for 2 by 2 contingency tables. The application of the tests was illustrated in two real examples.

Maximum likelihood channel estimation algorithm combines logarithm likelihood ratio decoding in the coal mine application

The environment of the wireless communication system in the coal mine has unique characteristics： great noise, strong multiple path interference, and the wireless communication of orthogonal frequency division multiplexing （OFDM） in underground coal mine is sensitive to the frequency selection of multiple path fading channel, whose decoding is separated from the traditional channel estimation algorithm. In order to increase its accuracy and reliability, a new iterating channel estimation algorithm combining the logarithm likelihood ratio （LLR） decode iterate based on the maximum likelihood estimation （ML） is proposed in this paper, which estimates iteration channel in combination with LLR decode. Without estimating the channel noise power, it exchanges the information between the ML channel estimation and the LLR decode using the feedback information of LLR decode. The decoding speed is very quick, and the satisfied result will be obtained by iterating in some time. The simulation results of the shortwave broadband channel in the coal mine show that the error rate of the system is basically convergent after the iteration in two times.

A new two-part test based on density ratio model for zero-inflated continuous distributions

In this paper,we consider testing the hypothesis concerning the means of two independent semicontinuous distributions whose observations are zero-inflated,characterized by a sizable number of zeros and positive observations from a continuous distribution.The continuous parts of the two semicontinuous distributions are assumed to follow a density ratio model.A new two-part test is developed for this kind of data.The proposed test takes the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution.The test is proved to follow a 2 distribution with two degrees of freedom.Simulation studies show that the proposed test controls the type I error rates at the desired level,and is competitive to,and most of the time more powerful than two popular tests.A real data example from a dietary intervention study is used to illustrate the usefulness of the proposed test.

Log Likelihood Ratio-Based Relaying for Distributed Turbo Codes

A distributed turbo codes（ DTC） scheme with log likelihood ratio（ LLR）-based threshold at the relay for a two-hop relay networks is proposed. Different from traditional DTC schemes,the retransmission scheme at the relay,where imperfect decoding occurs,is considered in the proposed scheme. By employing a LLR-based threshold at the relay in the proposed scheme,the reliability of decoder-LLRs can be measured. As a result,only reliable symbols will be forwarded to the destination and a maximum ratio combiner（ MRC） is used to combine signals received from both the source and the relay. In order to obtain the optimal threshold at the relay,an equivalent model of decoderLLRs is investigated,so as to derive the expression of the bit error probability（ BEP） of the proposed scheme under binary phase shift keying（ BPSK） modulation. Simulation results demonstrate that the proposed scheme can effectively mitigate error propagation at the relay and also outperforms other existing methods.

Incorporating Uncertain Costs within a Series of Sequential Probability Ratio Tests

We consider an extension to Sequential Probability Ratio Tests for when we have uncertain costs, but also opportunity to learn about these in an adaptive manner. In doing so we demonstrate the effects that allowing uncertainty has on observation cost, and the costs associated with Type I and Type II error. The value of information relating to modelled uncertainties is derived and the case of statistical dependence between the parameter affecting decision outcome and the parameter affecting unknown cost is also examined. Numerical examples of the derived theory are provided, along with a simulation comparing this adaptive learning framework to the classical one.