Goodness-of-fit tests for multi-dimensional copulas:Expanding application to historical drought data

The question of how to choose a copula model that best fits a given dataset is a predominant limitation of the copula approach, and the present study aims to investigate the techniques of goodness-of-fit tests for multi-dimensional copulas. A goodness-of-fit test based on Rosenblatt＇s transformation was mathematically expanded from two dimensions to three dimensions and procedures of a bootstrap version of the test were provided. Through stochastic copula simulation, an empirical application of historical drought data at the Lintong Gauge Station shows that the goodness-of-fit tests perform well, revealing that both trivariate Gaussian and Student t copulas are acceptable for modeling the dependence structures of the observed drought duration, severity, and peak. The goodness-of-fit tests for multi-dimensional copulas can provide further support and help a lot in the potential applications of a wider range of copulas to describe the associations of correlated hydrological variables. However, for the application of copulas with the number of dimensions larger than three, more complicated computational efforts as well as exploration and parameterization of corresponding copulas are required.

Asymptomatic Distribution of Goodness-of-Fit Tests in Logistic Regression Model

The logistic regression model has been become commonly used to study the association between a binary response variable;it is widespread application rests on its easy application and interpretation. The subject of assessment of goodness-of-fit in logistic regression model has attracted the attention of many scientists and researchers. Goodness-of-fit tests are methods to determine the suitability of the fitted model. Many of methods proposed and discussed for assessing goodness-of fit in logistic regression model, however, the asymptotic distribution of goodness-of-fit statistics are less examine, it is need more investigated. This work, will focus on assessing the behavior of asymptotic distribution of goodness-of-fit tests, also make comparison between global goodness-of-fit tests, and evaluate it by simulation.

Asymptotic Results for Goodness-of-Fit Tests Using a Class of Generalized Spacing Methods with Estimated Parameters

A class of pseudo distances is used to derive test statistics using transformed data or spacings for testing goodness-of-fit for parametric models. These statistics can be considered as density based statistics and expressible as simple functions of spacings. It is known that when the null hypothesis is simple, the statistics follow asymptotic normal distributions without unknown parameters. In this paper we emphasize results for the null composite hypothesis: the parameters can be estimated by a generalized spacing method (GSP) first which is equivalent to minimize a pseudo distance from the class which is considered;subsequently the estimated parameters are used to replace the parameters in the pseudo distance used for estimation;goodness-of-fit statistics for the composite hypothesis can be constructed and shown to have again an asymptotic normal distribution without unknown parameters. Since these statistics are related to a discrepancy measure, these tests can be shown to be consistent in general. Furthermore, due to the simplicity of these statistics and they come a no extra cost after fitting the model, they can be considered as alternative statistics to chi-square statistics which require a choice of intervals and statistics based on empirical distribution (EDF) using the original data with a complicated null distribution which might depend on the parametric family being considered and also might depend on the vector of true parameters but EDF tests might be more powerful against some specific models which are specified by the alternative hypothesis.

Goodness-of-Fit Test for Non-Stationary and Strongly Dependent Samples

In this article we improve a goodness-of-fit test, of the Kolmogorov-Smirnov type, for equally distributed- but not stationary-strongly dependent data. The test is based on the asymptotic behavior of the empirical process, which is much more complex than in the classical case. Applications to simulated data and discussion of the obtained results are provided. This is, to the best of our knowledge, the first result providing a general goodness of fit test for non-weakly dependent data.

Life-Cycle Bearing Capacity for Pre-Stressed T-beams Based on Full-Scale Destructive Test

To investigate the evolution of load-bearing characteristics of pre-stressed beams throughout their service life and to provide a basis for accurately assessing the actual working state of damaged pre-stressed concrete T-beams,destructive tests were conducted on full-scale pre-stressed concrete beams.Based on the measurement and ana-lysis of beam deflection,strain,and crack development under various loading levels during the research tests,combined with the verification coefficient indicators specified in the codes,the verification coefficients of bridges at different stages of damage can be examined.The results indicate that the T-beams experience complete,incom-plete linear,and non-linear stages during the destructive test process.In the complete linear elastic stage,both the deflection and bottom strain verification coefficients comply with the specifications,indicating a good structural load-bearing capacity no longer adheres to the code’s requirements.In the non-linear stage,both coefficients exhi-bit a sharp increase,resulting in a further decrease in the structure’s load-bearing capacity.According to the pro-visions of the current code,the beam can be in the incomplete linear stage when both values fall within the code’s specified range.The strain verification coefficient sourced from the compression zone at the bottom of theflange is not recommended for assessing the bridge’s load-bearing capacity.

Large-scale shaking table test on unlined tunnel in fault zone under threedimensional earthquake

A fault is a geological structure characterized by significant displacement of rock masses along a fault plane within the Earth's crust.The Yunnan Tabaiyi Tunnel intersects multiple fault zones,making tunnel construction in fault-prone areas particularly vulnerable to the effects of fault activity due to the complexities of the surrounding geological environment.To investigate the dynamic response characteristics of tunnel structures under varying surrounding rock conditions,a three-dimensional large-scale shaking table physical model test was conducted.This study also aimed to explore the damage mechanisms associated with the Tabaiyi Tunnel under seismic loading.The results demonstrate that poor quality surrounding rock enhances the seismic response of the tunnel.This effect is primarily attributed to the distribution characteristics of acceleration,dynamic strain,and dynamic soil pressure.A comparison between unidirectional and multi-directional(including vertical)seismic motions reveals that vertical seismic motion has a more significant impact on specific tunnel locations.Specifically,the maximum tensile stress is observed at the arch shoulder,with values ranging from 60 to 100 k Pa.Moreover,NPR(Non-Prestressed Reinforced)anchor cables exhibit a substantial constant resistance effect under low-amplitude seismic waves.However,when the input earthquake amplitude reaches 0.8g,local sliding occurs at the arch shoulder region of the NPR anchor cable.These findings underscore the importance of focusing on seismic mitigation measures in fault zones and reinforcing critical areas,such as the arch shoulders,in practical engineering applications.

Model tests and numerical analysis of emergency treatment of cohesionless soil landslide with quick-setting polyurethane

Shotcrete is one of the common solutions for shallow sliding.It works by forming a protective layer with high strength and cementing the loose soil particles on the slope surface to prevent shallow sliding.However,the solidification time of conventional cement paste is long when shotcrete is used to treat cohesionless soil landslide.The idea of reinforcing slope with polyurethane solidified soil(i.e.,mixture of polyurethane and sand)was proposed.Model tests and finite element analysis were carried out to study the effectiveness of the proposed new method on the emergency treatment of cohesionless soil landslide.Surcharge loading on the crest of the slope was applied step by step until landslide was triggered so as to test and compare the stability and bearing capacity of slope models with different conditions.The simulated slope displacements were relatively close to the measured results,and the simulated slope deformation characteristics were in good agreement with the observed phenomena,which verifies the accuracy of the numerical method.Under the condition of surcharge loading on the crest of the slope,the unreinforced slope slid when the surcharge loading exceeded 30 k Pa,which presented a failure mode of local instability and collapse at the shallow layer of slope top.The reinforced slope remained stable even when the surcharge loading reached 48 k Pa.The displacement of the reinforced slope was reduced by more than 95%.Overall,this study verifies the effectiveness of polyurethane in the emergency treatment of cohesionless soil landslide and should have broad application prospects in the field of geological disasters concerning the safety of people's live.

GOODNESS-OF-FIT TEST WITH GENETIC BACKGROUND

The chi-square test is a well-known goodness-of-fit test. It is available for arbitrary alternative hypothesis, particularly for a very general alternative. However, when the alternative is a “one-sided” hypothesis, which usually appears in genetic linkage analysis, the chi-square test does not use the information offered by the one-sided hypothesis.Therefore, it is possible that an appropriate one-sided test, which uses the information,will be better than the chi-square test. This paper gives such an efficient one-sided test.Monte Carlo simulation results show that it is more powerful than the chi-square test, and its power has been increased by 30 percent as compared with that of the chi-square test in most situations.

Empirical Likelihood Ratio-Based Goodness-of-Fit Test for the Laplace Distribution

The Laplace distribution can be compared against the normal distribution.The Laplace distribution has an unusual,symmetric shape with a sharp peak and tailsthat are longer than the tails of a normal distribution.It has recently become quitepopular in modeling financial variables(Brownian Laplace motion)like stock returnsbecause of the greater tails.The Laplace distribution is very extensively reviewed in themonograph(Kotz et al.in the laplace distribution and generalizations-a revisit withapplications to communications,economics,engineering,and finance.Birkhauser,Boston,2001).In this article,we propose a density-based empirical likelihood ratio(DBELR)goodness-of-fit test statistic for the Laplace distribution.The test statisticis constructed based on the approach proposed by Vexler and Gurevich(Comput StatData Anal 54:531-545,2010).In order to compute the test statistic,parameters of theLaplace distribution are estimated by the maximum likelihood method.Critical valuesand power values of the proposed test are obtained by Monte Carlo simulations.Also,power comparisons of the proposed test with some known competing tests are carriedout.Finally,two illustrative examples are presented and analyzed.

AquiferTest软件在抽水试验中的应用

通过现场原位抽水试验确定的水文地质参数的精度和准确性会直接影响基坑降水工程的准确性和可靠性。结合在某场地进行的潜水非稳定流抽水试验,在数据处理过程中,传统人工配线法效率、精度低,运用AquiferTest软件计算了潜水含水层渗透系数,采用Neuman法、Boulton法、仿泰斯公式法计算,提高计算结果精度,并对计算结果进行分析优化得到最终结果,符合实际水文地质条件。

Empirical likelihood inference and goodness-of-fit test for logistic regression model under two-phase case-control sampling

Due tocost effectiveness and hIgh efidengy.two-phase Qse control sampling has been wldely used In epldemlology studles.We dewelop a seml-parametric empinial lkellood approach to two-phase ase-control data under the logst regresslon model.we show that the maxmum empintal lklhoo estimaton has an aymptotically nomal dstibutlon,n,and the empincal lke-lthood ratlo fllws an aymptotcallycentral chi-square dstibution We find that the maxdmum empintial lkellhood estimator Is equal to Breslow and Holubkow(1997175 madimum lkelhood estimator.Evenso,the lmting dstribution of the lkelhood ratio,helhlodratlo based interval,and test are all new.Futhemmiore,we construct new Kolmogorov-smimnov type godnes-F-fit tests to test the vlldation of the undertying lglstic rgressonmodelLour simulation results and a real pplcaion show that the lola based Interval and test hawe certain mentsowver the wald-type counterparts and that the proposed godness-f-f test Is vald.

A viable method for goodness-of-fit test in maximum likelihood fit

A test statistic is proposed to perform the goodness-of-fit test in the unbinned maximum likelihood fit. Without using a detailed expression of the efficiency function, the test statistic is found to be strongly correlated with the maximum likelihood function if the efficiency function varies smoothly. We point out that the correlation coefficient can be estimated by the Monte Carlo technique. With the established method, two examples are given to illustrate the performance of the test statistic.

The empirical likelihood goodness-of-fit test for regression model

Goodness-of-fit test for regression modes has received much attention in literature. In this paper, empirical likelihood (EL) goodness-of-fit tests for regression models including classical parametric and autoregressive (AR) time series models are proposed. Unlike the existing locally smoothing and globally smoothing methodologies, the new method has the advantage that the tests are self-scale invariant and that the asymptotic null distribution is chi-squared. Simulations are carried out to illustrate the methodology.

Empirical Likelihood Based Goodness-of-fit Testing for Generalized Linear Mixed Models

In this paper, we propose a bias-corrected empirical likelihood （BCEL） ratio to construct a goodness- of-fit test for generalized linear mixed models. BCEL test maintains the advantage of empirical likelihood that is self scale invariant and then does not involve estimating limiting variance of the test statistic to avoid deteri- orating power of test. Furthermore, the bias correction makes the limit to be a process in which every variable is standard chi-squared. This simple structure of the process enables us to construct a Monte Carlo test proce- dure to approximate the null distribution. Thus, it overcomes a problem we encounter when classical empirical likelihood test is used, as it is asymptotically a functional of Gaussian process plus a normal shift function. The complicated covariance function makes it difficult to employ any approximation for the null distribution. The test is omnibus and power study shows that the test can detect local alternatives approaching the null at parametric rate. Simulations are carried out for illustration and for a comparison with existing method.

Goodness-of-fit tests for vector autoregressive models in time series

The paper proposes and studies some diagnostic tools for checking the goodness-of-fit of general parametric vector autoregressive models in time series. The resulted tests are asymptotically chi-squared under the null hypothesis and can detect the alternatives converging to the null at a parametric rate. The tests involve weight functions,which provides us with the flexibility to choose scores for enhancing power performance,especially under directional alternatives. When the alternatives are not directional,we construct asymptotically distribution-free maximin tests for a large class of alternatives. A possibility to construct score-based omnibus tests is discussed when the alternative is saturated. The power performance is also investigated. In addition,when the sample size is small,a nonparametric Monte Carlo test approach for dependent data is proposed to improve the performance of the tests. The algorithm is easy to implement. Simulation studies and real applications are carried out for illustration.

GOODNESS-OF-FIT TEST ON TWO SAMPLES

In this paper, a new statistics for testing two samples coming from the same population is derived from a simple linear model with an artificial parameter. Its limit distribution is a chi-squared distribution with 2 degrees of freedom under null hypothesis and the limit distribution is a noncentral chi-squared distribution with 2 degrees of freedom under certain sequence of alternative hypothesis. Finally, we make power comparison with other tests on two samples, especially, with Smirnov statistics.

THE GOODNESS-OF-FIT TEST BY USING MULTIVARIATE RANDOM WEIGHTING METHOD

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昆明烟区土壤线虫数量与环境因子的Mantel Test分析

为进一步明确昆明烟区影响线虫的环境因素,于2022年采集云南昆明烟区8个县(市、区)64个乡镇的320个植烟土壤样品,调查与测定样品采集地的海拔、土壤线虫数量以及土壤理化性质(pH值及有机质、水解性氮、速效钾和有效磷含量),并探讨土壤线虫数量与植烟土壤环境因子之间的潜在关系。结果表明,昆明烟区土壤线虫数量一定程度上受到海拔及土壤理化性质的影响,海拔与有机质、水解性氮和速效钾呈显著正相关,pH值与有效磷呈极显著负相关,相关系数为-0.850;土壤线虫数量与土壤有效磷呈正相关,与海拔、pH值、有机质、水解性氮、速效钾呈负相关,其中与海拔、有机质和水解性氮的相关系数较大,分别为-0.751、-0.651和-0.568。通过Mantel test分析确定海拔、有机质和水解性氮含量是影响昆明烟区土壤线虫数量的重要因子。本结果可为有效防治土壤线虫提供科学依据。

A Modified Chi-Squared Goodness-of-Fit Test

In goodness-of-fit tests, Pearson＇s chi-squared test is one of most widely used tools of formal statistical analysis. However, Pearson＇s chi-squared test depends on the partition of the sample space. Different constructions of the partition of the sample space may lead to different conclusions. Based on an equiprobable partition of sample space, a modified chi^quared test is proposed. A method for constructing the modified chi-squared test is proposed. As an application, the proposed test is used to test whether vectorial data come from an uniformity distribution defined on the hypersphere. Some simulation studies show that the modified chisquared test against different alternative is robust.

Failure characterization of fully grouted rock bolts under triaxial testing

Confining stresses serve as a pivotal determinant in shaping the behavior of grouted rock bolts.Nonetheless,prior investigations have oversimplified the three-dimensional stress state,primarily assuming hydrostatic stress conditions.Under these conditions,it is assumed that the intermediate principal stress(σ_(2))equals the minimum principal stress(σ_(3)).This assumption overlooks the potential variations in magnitudes of in situ stress conditions along all three directions near an underground opening where a rock bolt is installed.In this study,a series of push tests was meticulously conducted under triaxial conditions.These tests involved applying non-uniform confining stresses(σ_(2)≠σ_(3))to cubic specimens,aiming to unveil the previously overlooked influence of intermediate principal stresses on the strength properties of rock bolts.The results show that as the confining stresses increase from zero to higher levels,the pre-failure behavior changes from linear to nonlinear forms,resulting in an increase in initial stiffness from 2.08 kN/mm to 32.51 kN/mm.The load-displacement curves further illuminate distinct post-failure behavior at elevated levels of confining stresses,characterized by enhanced stiffness.Notably,the peak load capacity ranged from 27.9 kN to 46.5 kN as confining stresses advanced from σ_(2)=σ_(3)=0 to σ_(2)=20 MPa and σ_(3)=10 MPa.Additionally,the outcomes highlight an influence of confining stress on the lateral deformation of samples.Lower levels of confinement prompt overall dilation in lateral deformation,while higher confinements maintain a state of shrinkage.Furthermore,diverse failure modes have been identified,intricately tied to the arrangement of confining stresses.Lower confinements tend to induce a splitting mode of failure,whereas higher loads bring about a shift towards a pure interfacial shear-off and shear-crushed failure mechanism.