中国旅游业发展与经济增长的统计分析

文章从总量、相关及回归、弹性和贡献率四个方面探讨了中国旅游业发展与经济增长的关系,得出了中国旅游业发展与经济增长存在双向关系。特别是依据中国1991~2005年相关统计数据,定量研究了经济增长对旅游业发展的弹性和旅游业对经济增长的贡献率,论证了经济增长促进旅游业的发展,旅游业的发展反过来又推动了经济增长,而且这种推动作用越来越明显。文章最后在统计分析的基础上提出了相关政策建议供相关部门决策参考。     

Optimal design of accelerated degradation tests based on Wiener process models

Optimal accelerated degradation test (ADT) plans are developed assuming that the constant-stress loading method is employed and the degradation characteristic follows a Wiener process. Unlike the previous works on planning ADTs based on stochastic process models, this article determines the test stress levels and the proportion of test units allocated to each stress level such that the asymptotic variance of the maximum-likelihood estimator of the qth quantile of the lifetime distribution at the use condition is minimized. In addition, compromise plans are also developed for checking the validity of the relationship between the model parameters and the stress variable. Finally, using an example, sensitivity analysis procedures are presented for evaluating the robustness of optimal and compromise plans against the uncertainty in the pre-estimated parameter value, and the importance of optimally determining test stress levels and the proportion of units allocated to each stress level are illustrated.     

Statistical considerations for crowdsourced perceptual ratings of human speech productions

Crowdsourcing has become a major tool for scholarly research since its introduction to the academic sphere in 2008. However, unlike in traditional laboratory settings, it is nearly impossible to control the conditions under which workers on crowdsourcing platforms complete tasks. In the study of communication disorders, crowdsourcing has provided a novel solution to the collection of perceptual ratings of human speech production. Such ratings allow researchers to gauge whether a treatment yields meaningful change in how human listeners' perceive disordered speech. This paper will explore some statistical considerations of crowdsourced data with specific focus on collecting perceptual ratings of human speech productions. Random effects models are applied to crowdsourced perceptual ratings collected in both a continuous and binary fashion. A simulation study is conducted to test the reliability of the proposed models under differing numbers of workers and tasks. Finally, this methodology is applied to a data set from the study of communication disorders.     

A test for zero point triserial correlation coefficient and its relationship with tests for homogeneity of means with ordered alternatives

The point triserial correlation coefficient is defined and, under appropriate order restrictions, an exact test that this correlation coefficient equals zero is developed. The power function of that test is derived and partially tabulated. The general problem of testing for homogeneity of means under ordered alternatives is discussed. The available procedures for performing such tests are considered, are seen to provide alternative approaches to the test developed herein, and are compared with that test. An exact test for the equality of dependent point triserial correlation coefficients is described through application of a procedure suggested by Wolfe ‘1976’     

An overview of tests for exponentiality

Developments since 1960 in goodness-of-fit tests for the one and two parameter exponential models using both complete and censored samples are reviewed. Special attention is given to both the omnibus or general alternative and to specialized alter-natives such as the class of distributions with increasing failure rates. The use of transformations in developing tests is also discussed.     

Assessing and communicating heterogeneity of treatment effects for patient subpopulations: Panel discussion on considerations in design and analysis

Clinical trials are primarily conducted to understand the average effects treatments have on patients. However, patients are heterogeneous in the severity of the condition and in ways that affect what treatment effect they can expect. It is therefore important to understand and characterize how treatment effects vary. The design and analysis of clinical studies play critical roles in evaluating and characterizing heterogeneous treatment effects. This panel discussed considerations in design and analysis under the recognition that there are heterogeneous treatment effects across subgroups of patients. Panel members discussed many questions including: What is a good estimate of the treatment effect in me, a 65-year-old, bald, Caucasian-American, male patient? What magnitude of heterogeneity of treatment effects (HTE) is sufficiently large to merit attention? What role can prior evidence about HTE play in confirmatory trial design and analysis? Is there anything described in the 21st Century Cures Act that would benefit from greater attention to HTE? An example of a Bayesian approach addressing multiplicity when testing for treatment effects in subgroups will be provided. We can do more or better at understanding heterogeneous treatment effects and providing the best information on heterogeneous treatment effects.     

Parameter estimation and design considerations in prospective applications of the � chart

The effects of parameter estimation on the in-control performance of the Shewhart X¯ chart are studied in prospective (phase 2 or stage 2) applications via a thorough examination of the attained false alarm rate (AFAR), the conditional false alarm rate (CFAR), the conditional and the unconditional run-length distributions, some run-length characteristics such as the ARL, the conditional ARL (CARL), some selected percentiles including the median, and cumulative run-length probabilities. The examination involves both numerical evaluations and graphical displays. The effects of parameter estimation need to be accounted for in designing the chart. To this end, as an application of the exact formulations, chart constants are provided for a specified in-control average run-length of 370 and 500 for a number of subgroups and subgroup sizes. These will be useful in the implementation of the X¯ chart in practice.     

Statistical tests for the comparison of two samples: The general alternative

It is common to test the null hypothesis that two samples were drawn from identical distributions; and the Smirnov (sometimes called Kolmogorov–Smirnov) test is conventionally applied. We present simulation results to compare the performance of this test with three recently introduced alternatives. We consider both continuous and discrete data. We show that the alternative methods preserve type I error at the nominal level as well as the Smirnov test but offer superior power. We argue for the routine replacement of the Smirnov test with the modified Baumgartner test according to Murakami (2006) Murakami, H. (2006). A k-sample rank test based on a modified Baumgartner statistic and its power comparison. Journal of the Japanese Society of Computational Statistics 19:1–13.[Crossref] , [Google Scholar], or with the test proposed by Zhang (2006) Zhang, J. (2006). Powerful two-sample tests based on the likelihood ratio. Technometrics 48:95–103.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar].     

Testing hypotheses about medical test accuracy: considerations for design and inference

Developing new medical tests and identifying single biomarkers or panels of biomarkers with superior accuracy over existing classifiers promotes lifelong health of individuals and populations. Before a medical test can be routinely used in clinical practice, its accuracy within diseased and non-diseased populations must be rigorously evaluated. We introduce a method for sample size determination for studies designed to test hypotheses about medical test or biomarker sensitivity and specificity. We show how a sample size can be determined to guard against making type I and/or type II errors by calculating Bayes factors from multiple data sets simulated under null and/or alternative models. The approach can be implemented across a variety of study designs, including investigations into one test or two conditionally independent or dependent tests. We focus on a general setting that involves non-identifiable models for data when true disease status is unavailable due to the nonexistence of or undesirable side effects from a perfectly accurate (i.e. ‘gold standard’) test; special cases of the general method apply to identifiable models with or without gold-standard data. Calculation of Bayes factors is performed by incorporating prior information for model parameters (e.g. sensitivity, specificity, and disease prevalence) and augmenting the observed test-outcome data with unobserved latent data on disease status to facilitate Gibbs sampling from posterior distributions. We illustrate our methods using a thorough simulation study and an application to toxoplasmosis.     

An alternative procedure for performing a power analysis of Mantel's test

This study proposes a simple way to perform a power analysis of Mantel's test applied to squared Euclidean distance matrices. The general statistical aspects of the simple Mantel's test are reviewed. The Monte Carlo method is used to generate bivariate Gaussian variables in order to create squared Euclidean distance matrices. The power of the parametric correlation t-test applied to raw data is also evaluated and compared with that of Mantel's test. The standard procedure for calculating punctual power levels is used for validation. The proposed procedure allows one to draw the power curve by running the test only once, dispensing with the time demanding standard procedure of Monte Carlo simulations. Unlike the standard procedure, it does not depend on a knowledge of the distribution of the raw data. The simulated power function has all the properties of the power analysis theory and is in agreement with the results of the standard procedure.     

Statistical inference for a class of life distributions

Life distributions with hazard rate functions of the form r(t) = Ag(t) + Bh(t) are considered. It is assumed that g(t) and h(t) are known and are independent of the unknown parameters A and B. The maximum likelihood estimators are studied for complete and censored samples. The estimation problem is reduced to a solution of one equation with one unknown parameter and it is observed that the solution is unique. The estimation procedure under the assumption of aging is also described. Some comments about the asymptotic variance-covariance matrix are given, and tests of hypo-theses are described for some cases.     

Statistical Analysis of Linear Degradation and Failure Time Data with Multiple Failure Modes

The paper considers linear degradation and failure time models with multiple failure modes. Dependence of traumatic failure intensities on the degradation level are included into the models. Estimators of traumatic event cumulative intensities, and of various reliability characteristics are proposed. Prediction of residual reliability characteristics given a degradation value at a given moment is discussed. Non-parametric, semiparametric and parametric estimation methods are given. Theorems on simultaneous asymptotic distribution of random functions characterising degradation and intensities of traumatic events are proposed. Asymptotic properties of unconditional and residual reliability characteristics estimators are given. Real tire wear and failure time data are analysed.     

Statistical considerations for assessing precision of heterogeneous duplicate measurements: An application to pharmaceutical bioanalysis

Duplicate analysis is a strategy commonly used to assess precision of bioanalytical methods. In some cases, duplicate analysis may rely on pooling data generated across organizations. Despite being generated under comparable conditions, organizations may produce duplicate measurements with different precision. Thus, these pooled data consist of a heterogeneous collection of duplicate measurements. Precision estimates are often expressed as relative difference indexes (RDI), such as relative percentage difference (RPD). Empirical evidence indicates that the frequency distribution of RDI values from heterogeneous data exhibits sharper peaks and heavier tails than normal distributions. Therefore, traditional normal-based models may yield faulty or unreliable estimates of precision from heterogeneous duplicate data. In this paper, we survey application of the mixture models that satisfactorily represent the distribution of RDI values from heterogeneous duplicate data. A simulation study was conducted to compare the performance of the different models in providing reliable estimates and inferences of percentile calculated from RDI values. These models are readily accessible to practitioners for study implementation through the use of modern statistical software. The utility of mixture models are explained in detail using a numerical example.     

Statistical inference for start-up demonstration tests with rejection of units upon observing d failures

In this paper, we consider the statistical inference for the success probability in the case of start-up demonstration tests in which rejection of units is possible when a pre-fixed number of failures is observed before the required number of consecutive successes are achieved for acceptance of the unit. Since the expected value of the stopping time is not a monotone function of the unknown parameter, the method of moments is not useful in this situation. Therefore, we discuss two estimation methods for the success probability: (1) the maximum likelihood estimation (MLE) via the expectation-maximization (EM) algorithm and (2) Bayesian estimation with a beta prior. We examine the small-sample properties of the MLE and Bayesian estimator. Finally, we present an example to illustrate the method of inference discussed here.     

Omnibus tests of multinormality based on skewness and kurtosis

Measures of univariate skewness and kurtosis have long been used as a test of univariate normality, several omnibus test procedures based on a combination of the measures having been proposed, see Pearson, D’Agestino and Bowman (1977) and Mardia (1979). Mardia (1970) proposed measures of multivariate skewness and kurtosis, and constructed a test of multinormality based on these measures. we obtain the correlation between these measures and propose several omnibus tests using the two measures. The performances of these tests are compared by means of a Monte Carlo study.     

Parametric bootstrap and approximate tests for two Poisson variates

The parametric bootstrap tests and the asymptotic or approximate tests for detecting difference of two Poisson means are compared. The test statistics used are the Wald statistics with and without log-transformation, the Cox F statistic and the likelihood ratio statistic. It is found that the type I error rate of an asymptotic/approximate test may deviate too much from the nominal significance level α under some situations. It is recommended that we should use the parametric bootstrap tests, under which the four test statistics are similarly powerful and their type I error rates are all close to α. We apply the tests to breast cancer data and injurious motor vehicle crash data.     

Local power of panel unit root tests allowing for structural breaks

The asymptotic local power of least squares–based fixed-T panel unit root tests allowing for a structural break in their individual effects and/or incidental trends of the AR(1) panel data model is studied. Limiting distributions of these tests are derived under a sequence of local alternatives, and analytic expressions show how their means and variances are functions of the break date and the time dimension of the panel. The considered tests have nontrivial local power in a N^?1/2 neighborhood of unity when the panel data model includes individual intercepts. For panel data models with incidental trends, the power of the tests becomes trivial in this neighborhood. However, this problem does not always appear if the tests allow for serial correlation in the error term and completely vanishes in the presence of cross-section correlation. These results show that fixed-T tests have very different theoretical properties than their large-T counterparts. Monte Carlo experiments demonstrate the usefulness of the asymptotic theory in small samples.     

A family of tests for exponentiality against IFR alternatives

In this paper we consider the problem of testing exponentiality against IFR alternatives. A measure of deviation from exponentiality is developed and a class of test statistics are constructed on the basis of this measure. It is shown that the test statistic is an L-statistic. The asymptotic as well as the exact distributions of the test statistics are obtained and the test statistics are proved to be consistent. The Pitman efficiency has also been studied.     

Local information and the design of sequential hypothesis tests

Various results on sequential hypotheses testing are reviewed. Optimal stopping rules are related to a local measure of statistical information. In some cases, local information can be approximated by L-numbers discovered by Lorden, and simple rules based on these approximations are asymptotically optimal to better order than the cost for a single observation.