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 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.

Deriving CDF of Kolmogorov-Smirnov Test Statistic

In this review article, we revisit derivation of the cumulative density function (CDF) of the test statistic of the one-sample Kolmogorov-Smirnov test. Even though several such proofs already exist, they often leave out essential details necessary for proper understanding of the individual steps. Our goal is filling in these gaps, to make our presentation accessible to advanced undergraduates. We also propose a simple formula capable of approximating the exact distribution to a sufficient accuracy for any practical sample size.

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.

Kolmogorov-Smirnov APF Test for Inhomogeneous Poisson Processes with Shift Parameter

In this article, we study the Kolmogorov-Smirnov type goodness-of-fit test for the inhomogeneous Poisson process with the unknown translation parameter as multidimensional parameter. The basic hypothesis and the alternative are composite and carry to the intensity measure of inhomogeneous Poisson process and the intensity function is regular. For this model of shift parameter, we propose test which is asymptotically partially distribution free and consistent. We show that under null hypothesis the limit distribution of this statistic does not depend on unknown parameter.

我国上市公司资本结构与行业关系的实证分析

本文利用One-SampleKolmogorov-SmirnovTest对我国上市公司资本结构与行业关系进行了实证分析,结果发现:我国上市公司资产负债率近似服从正态分布,不同行业各总体的方差无显著性差异,不同行业上市公司资本结构存在显著性差异且在1999-2002年中都保持了相当的稳定性,波动较小。

Spatial and temporal variability of daily precipitation in Haihe River basin, 1958-2007

The seasonal variability and spatial distribution of precipitation are the main cause of flood and drought events. The study of spatial distribution and temporal trend of precipitation in river basins has been paid more and more attention. However, in China, the precipitation data are measured by weather stations （WS） of China Meteorological Administration and hydrological rain gauges （RG） of national and local hydrology bureau. The WS data usually have long record with fewer stations, while the RG data usually have short record with more stations. The consistency and correlation of these two data sets have not been well understood. In this paper, the precipitation data from 30 weather stations for 1958-2007 and 248 rain gauges for 1995-2004 in the Haihe River basin are examined and compared using linear regression, 5-year moving average, Mann-Kendall trend analysis, Kolmogorov-Smirnov test, Z test and F test methods. The results show that the annual precipitation from both WS and RG records are normally distributed with minor difference in the mean value and variance. It is statistically feasible to extend the precipitation of RG by WS data sets. Using the extended precipitation data, the detailed spatial distribution of the annual and seasonal precipitation amounts as well as their temporal trends are calculated and mapped. The various distribution maps produced in the study show that for the whole basin the precipitation of 1958-2007 has been decreasing except for spring season. The decline trend is significant in summer, and this trend is stronger after the 1980s. The annual and seasonal precipitation amounts and changing trends are different in different regions and seasons. The precipitation is decreasing from south to north, from coastal zone to inland area.

Gearbox Deterioration Detection under Steady State,Variable Load, and Variable Speed Conditions

Multiple dominant gear meshing frequencies are present in the vibration signals collected from gearboxes and the conventional spiky features that represent initial gear fault conditions are usually difficult to detect. In order to solve this problem, we propose a new gearbox deterioration detection technique based on autoregressive modeling and hypothesis testing in this paper. A stationary autoregressive model was built by using a normal vibration signal from each shaft. The established autoregressive model was then applied to process fault signals from each shaft of a two-stage gearbox. What this paper investigated is a combined technique which unites a time-varying autoregressive model and a two sample Kolmogorov-Smimov goodness-of-fit test, to detect the deterioration of gearing system with simultaneously variable shaft speed and variable load. The time-varying autoregressive model residuals representing both healthy and faulty gear conditions were compared with the original healthy time-synchronous average signals. Compared with the traditional kurtosis statistic, this technique for gearbox deterioration detection has shown significant advantages in highlighting the presence of incipient gear fault in all different speed shafts involved in the meshing motion under variable conditions.

A Review of the Logistic Regression Model with Emphasis on Medical Research

This study explored and reviewed the logistic regression (LR) model, a multivariable method for modeling the relationship between multiple independent variables and a categorical dependent variable, with emphasis on medical research. Thirty seven research articles published between 2000 and 2018 which employed logistic regression as the main statistical tool as well as six text books on logistic regression were reviewed. Logistic regression concepts such as odds, odds ratio, logit transformation, logistic curve, assumption, selecting dependent and independent variables, model fitting, reporting and interpreting were presented. Upon perusing the literature, considerable deficiencies were found in both the use and reporting of LR. For many studies, the ratio of the number of outcome events to predictor variables (events per variable) was sufficiently small to call into question the accuracy of the regression model. Also, most studies did not report on validation analysis, regression diagnostics or goodness-of-fit measures;measures which authenticate the robustness of the LR model. Here, we demonstrate a good example of the application of the LR model using data obtained on a cohort of pregnant women and the factors that influence their decision to opt for caesarean delivery or vaginal birth. It is recommended that researchers should be more rigorous and pay greater attention to guidelines concerning the use and reporting of LR models.

Parameter Estimations for Some Modifications of the Weibull Distribution

Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.

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

ＴＨＥＧＯＯＤＮＥＳＳ－ＯＦ－ＦＩＴＴＥＳＴＢＹＵＳＩＮＧＭＵＬＴＩＶＡＲＩＡＴＥＲＡＮＤＯＭＷＥＩＧＨＴＩＮＧ ＭＥＴＨＯＤＴＨＥＧＯＯＤＮＥＳＳ－ＯＦ－ＦＩＴＴＥＳＴＢＹＵＳＩＮＧＭＵＬＴＩＶＡＲＩＡＴＥＲＡＮＤＯＭＷＥＩＧＨＴＩＮＧＭＥＴＨＯＤ...

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.

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.

Discrete Circular Distributions with Applications to Shared Orthologs of Paired Circular Genomes

For structural comparisons of paired prokaryotic genomes,an important topic in synthetic and evolutionary biology,the locations of shared orthologous genes(henceforth orthologs)are observed as binned data.This and other data,e.g.,wind directions recorded at monitoring sites and intensive care unit arrival times on the 24-hour clock,are counted in binned circular arcs,thus modeling them by discrete circular distributions(DCDs)is required.We propose a novel method to construct a DCD from a base continuous circular distribution(CCD).The probability mass function is defined to take the normalized values of the probability density function at some pre-fixed equidistant points on the circle.Five families of constructed DCDs which have normalizing constants in closed form are presented.Simulation studies show that DCDs outperform the corresponding CCDs in modeling grouped(discrete)circular data,and minimum chi-square estimation outperforms maximum likelihood estimation for parameters.We apply the constructed DCDs,invariant wrapped Poisson and wrapped discrete skew Laplace to compare the structures of paired bacterial genomes.Specifically,discrete four-parameter wrapped Cauchy(nonnegative trigonometric sums)distribution models multi-modal shared orthologs in Clostridium(Sulfolobus)better than the others considered,in terms of AIC and Freedman’s goodness-of-fit test.The result that different DCDs fit the shared orthologs is consistent with the fact they belong to two kingdoms.Nevertheless,these prokaryotes have a common favored site around 70°on the unit circle;this finding is important for building synthetic prokaryotic genomes in synthetic biology.These DCDs can also be applied to other binned circular data.

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.

RAYLEIGH-DISTRIBUTION BASED MINIMUM ERROR THRESHOLDING FOR SAR IMAGES

This paper presents a minimum error thresholding (MET) algorithm under the hypothesis that the gray level histogram of SAR image fits to a mixture model of shifted Rayleigh distribution. This algorithm is applied to real SAR images and compared with traditional Otsu algorithm and other MET algorithms based on various models of histogram. The hypothesis of using Rayleigh distribution model is confirmed by Kolmogorov-Smirnov testing and the comparison results obtained show that the proposed new algorithm has good performance in thresholding SAR images.

An analysis of tourist’s perceptions toward tourism development:Study of cold desert destination,India

Tourism impacts on society are complex and mixed.However,they are vital to diverse societies,clusters,and individuals dependent upon their morals,attitudes,and resources existing for tourism development.Increasing tourism also brings many problems.Hence,tourist experience is fundamental for destination image and devel-opment.This research examines tourist perceptions and attitudes toward tourism impacts in Chitkul,Kalpa,and Nako in Kinnaur.Random sampling has been used to measure tourist responses on a range of indicators related to tourism development.Likert scale responses were analyzed using factor analysis,ANOVA,Mann-Whitney U-test,Kolmogorov test,and descriptive statistics.The results confirmed that tourists do not perceive any type of pollu-tion or societal barriers.They observed that natural magnetism and the socio-cultural milieu of the destination is what attracts tourists.However,tourists are not satisfied with‘networking services’,‘organization efforts’,‘sup-plementary conveniences’,and‘carriage concerns’at selected destinations in Kinnaur.Moreover,Chitkul emerged as the top tourist destination in Kinnaur.Since the destination would emerge as a hub of tourist activities shortly considering the congestion and exploitation of nearby tourist destinations at Kulu-Manali-Rohtang in Beas Valley.Hence,the assessment of tourist perceptions can be used as an indicator of tourism destination competitiveness and can assist in developing appropriate tourism policies and infrastructure upgrades.

Pseudodistance Methods Using Simultaneously Sample Observations and Nearest Neighbour Distance Observations for Continuous Multivariate Models

Using the fact that a multivariate random sample of n observations also generates n nearest neighbour distance (NND) univariate observations and from these NND observations, a set of n auxiliary observations can be obtained and with these auxiliary observations when combined with the original multivariate observations of the random sample, a class of pseudodistance?Dh?is allowed to be used and inference methods can be developed using this class of pseudodistances. The Dh?estimators obtained from this class can achieve high efficiencies and have robustness properties. Model testing also can be handled in a unified way by means of goodness-of-fit tests statistics derived from this class which have an asymptotic normal distribution. These properties make the developed inference methods relatively simple to implement and appear to be suitable for analyzing multivariate data which are often encountered in applications.