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.

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.

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.

Unbound^(28)O,the heaviest oxygen isotope observed:a cutting-edge probe for testing nuclear models

The beyond-dripline oxygen isotopes^(27,28)O were recently observed at RIKEN,and were found to be unbound decaying into^(24)O by emitting neutrons.The unbound feature of the heaviest oxygen isotope,^(28)O,provides an excellent test for stateof-the-art nuclear models.The atomic nucleus is a self-organized quantum manybody system comprising specific numbers of protons Z and neutrons N.

Electrochemical biosensors for point-of-care testing

Point-of-care testing(POCT)is the practice of diagnosing and monitoring diseases where the patient is located,as opposed to traditional treatment conducted solely in a medical laboratory or other clinical setting.POCT has been less common in the recent past due to a lack of portable medical devices capable of facilitating effective medical testing.However,recent growth has occurred in this field due to advances in diagnostic technologies,device miniaturization,and progress in wearable electronics.Among these developments,electrochemical sensors have attracted interest in the POCT field due to their high sensitivity,compact size,and affordability.They are used in various applications,from disease diagnosis to health status monitoring.In this paper we explore recent advancements in electrochemical sensors,the methods of fabricating them,and the various types of sensing mechanisms that can be used.Furthermore,we delve into methods for immobilizing specific biorecognition elements,including enzymes,antibodies,and aptamers,onto electrode surfaces and how these sensors are used in real-world POCT settings.

Aquifer Test求群孔抽水试验水文地质参数

在水文地质条件复杂的地区,往往采用大型的群孔抽水试验充分揭露含水层特征,获取水文地质参数。用Aquifer Test软件求解水文地质参数,则方便实用、简捷高效,可快速输出拟合图形和求参结果。Aquifer Test提供了丰富的求参方案,求参必须结合当地当时的水文地质条件实际情况考虑,选择适合的方案和时空数据求取水文地质参数。

Micromechanical testing and property upscaling of planetary rocks:A critical review

Knowledge of the mechanical behavior of planetary rocks is indispensable for space explorations.The scarcity of pristine samples and the irregular shapes of planetary meteorites make it difficult to obtain representative samples for conventional macroscale rock mechanics experiments(macro-RMEs).This critical review discusses recent advances in microscale RMEs(micro-RMEs)techniques and the upscaling methods for extracting mechanical parameters.Methods of mineralogical and microstructural analyses,along with non-destructive mechanical techniques,have provided new opportunities for studying planetary rocks with unprecedented precision and capabilities.First,we summarize several mainstream methods for obtaining the mineralogy and microstructure of planetary rocks.Then,nondestructive micromechanical testing methods,nanoindentation and atomic force microscopy(AFM),are detailed reviewed,illustrating the principles,advantages,influencing factors,and available testing results from literature.Subsequently,several feasible upscaling methods that bridge the micro-measurements of meteorite pieces to the strength of the intact body are introduced.Finally,the potential applications of planetary rock mechanics research to guiding the design and execution of space missions are environed,ranging from sample return missions and planetary defense to extraterrestrial construction.These discussions are expected to broaden the understanding of the microscale mechanical properties of planetary rocks and their significant role in deep space exploration.