经济学视角下的大学生考试作弊行为分析

考试作弊不仅损害了考试结果的公正性,还助长了社会的不诚信之风。从经济学博弈论的角度对大学生考试作弊与监考者之间进行收益-成本分析;通过调查分析表明,任课教师在上课认真程度和考试的难易上都与作弊相关;同时还与监考老师的考场严厉程度相关;与大学生专业偏好相关。最后,针对考试内容和方法、监考老师的职责以及专业导论或职业规划教育等方面提出防止大学生考试作弊的一些建议。     

On Nonsmooth Estimating Functions via Jackknife Empirical Likelihood

In many applications, the parameters of interest are estimated by solving non‐smooth estimating functions with U‐statistic structure. Because the asymptotic covariances matrix of the estimator generally involves the underlying density function, resampling methods are often used to bypass the difficulty of non‐parametric density estimation. Despite its simplicity, the resultant‐covariance matrix estimator depends on the nature of resampling, and the method can be time‐consuming when the number of replications is large. Furthermore, the inferences are based on the normal approximation that may not be accurate for practical sample sizes. In this paper, we propose a jackknife empirical likelihood‐based inferential procedure for non‐smooth estimating functions. Standard chi‐square distributions are used to calculate the p‐value and to construct confidence intervals. Extensive simulation studies and two real examples are provided to illustrate its practical utilities.     

Distribution-free comparison of hazard rates of two distributions under progressive type-II censoring

Some distribution-free tests have been discussed in the literature with regard to the comparison of hazard rates of two distributions when the available samples are complete. We generalize here Kochar's [S.C. Kochar, A new distribution-free test for the equality of two failure rates, Biometrika 68 (1981), pp. 423–426] test statistic to the case when one available sample is progressively Type-II censored, and then derive its exact null distribution and examine its power properties by means of a Monte Carlo simulation study.     

Fitting DNA sequences through log-linear modelling with linear constraints

For some discrete state series, such as DNA sequences, it can often be postulated that its probabilistic behaviour is given by a Markov chain. For making the decision on whether or not an uncharacterized piece of DNA is part of the coding region of a gene, under the Markovian assumption, there are two statistical tools that are essential to be considered: the hypothesis testing of the order in a Markov chain and the estimators of transition probabilities. In order to improve the traditional statistical procedures for both of them when stationarity assumption can be considered, a new version for understanding the homogeneity hypothesis is proposed so that log-linear modelling is applied for conditional independence jointly with homogeneity restrictions on the expected means of transition counts in the sequence. In addition we can consider a variety of test-statistics and estimators by using φ-divergence measures. As special case of them the well-known likelihood ratio test-statistics and maximum-likelihood estimators are obtained.     

Nonparametric regression estimation of conditional tails: the random covariate case

We present families of nonparametric estimators for the conditional tail index of a Pareto-type distribution in the presence of random covariates. These families are constructed from locally weighted sums of power transformations of excesses over a high threshold. The asymptotic properties of the proposed estimators are derived under some assumptions on the conditional response distribution, the weight function and the density function of the covariates. We also introduce bias-corrected versions of the estimators for the conditional tail index, and propose in this context a consistent estimator for the second-order tail parameter. The finite sample performance of some specific examples from our classes of estimators is illustrated with a small simulation experiment.     

On the real representation of quaternion random variables

For the first time, the matrix-variate quaternion normal and quaternion Wishart distributions are derived from first principles, that is, from their real counterparts, exposing the relations between their respective densities and characteristic functions. Applications of this theory in hypothesis testing are presented, and the density function of Wilks’ statistic is derived for quaternion Wishart matrices.     

Multivariate testing and model-checking for generalized order statistics with applications

The exponential family structure of the joint distribution of generalized order statistics is utilized to establish multivariate tests on the model parameters. For simple and composite null hypotheses, the likelihood ratio test (LR test), Wald's test, and Rao's score test are derived and turn out to have simple representations. The asymptotic distribution of the corresponding test statistics under the null hypothesis is stated, and, in case of a simple null hypothesis, asymptotic optimality of the LR test is addressed. Applications of the tests are presented; in particular, we discuss their use in reliability, and to decide whether a Poisson process is homogeneous. Finally, a power study is performed to measure and compare the quality of the tests for both, simple and composite null hypotheses.     

A Note on the Upper Bound to Variance of the Sample Extreme from a Finite Population

We construct a new upper bound for the variance of the sample minimum and maximum in the case of a simple random sample drawn without replacement. The bound is optimal in the form provided. Similar bounds are shown for the other order statistics.     

Smooth tests of goodness of fit for regular distributions

Smooth tests of goodness of fit based on orthonormal functions for location-scale families were introducedin Rayner and Best (1986).This paper extends this class of tests from location -scale families to ‘regular’ families. The extension preserves the desirable properties of the class, such as weak optimality, accessible components and convenient distribution theory