Accurate Critical Values Research Articles

Ratio Test for Mean Changes in Time Series with Heavy-Tailed AR(p) Noise Based on Multiple Sampling Methods

This paper discusses the problem of the mean changes in time series with heavy-tailed AR(p) noise. Firstly, it proposes a modified ratio-type test statistic, and the results show that under the null hypothesis of no mean change, the asymptotic distribution of the modified statistic is a functional of Lévy processes and the consistency under the alternative hypothesis is obtained. However, a heavy-tailed index exists in the asymptotic distribution and is difficult to estimate. This paper uses bootstrap sampling, jackknife sampling, and subsampling to approximate the distribution under the null hypothesis, and obtain more accurate critical values and empirical power. In addition, some results from a small simulation study and a practical example give an idea of the finite sample behavior of the proposed statistic.

Mechanism of Mechanical Analysis on Torsional Buckling of U-Shaped Bellows in FLNG Cryogenic Hoses

Floating liquefied natural gas (FLNG) cryogenic hoses can be employed for the transmission of liquefied natural gas (LNG). Usually, U-shaped metal bellows can be applied as the inner lining of FLNG cryogenic hoses. In installation, positioning and other working conditions, torsion is one of the main loads, and torsional buckling instability is a major failure mode of U-shaped metal bellows of FLNG cryogenic hoses. In the current research, the buckling instability of bellows under torsional loads has been investigated in detail, the mechanical mechanism of deformation in torsional buckling mode of bellows has been analyzed and the influence of the structural design parameters on the stability performance has been summarized. It was seen that the axis of the bellows was presented as a spiral line shape during the torsional buckling stage. At the same time, the torsional buckling properties of toroid and spiral bellows were analyzed. The obtained results showed that the torsional buckling stability of the spiral bellows was weaker than that of the toroid bellows and increase of the spiral angle of the spiral bellows intensified this trend. In addition, the post-buckling analysis of U-shaped bellows under torsional loads was carried out by means of experiments and finite element simulation. It was shown that the results obtained from finite element (FE) analysis in this research presented a relatively accurate critical torque value and a consistent buckling instability mode, compared with the experimental results. On this basis, the effects of common defects such as thickness thinning on the torsional stability of bellows were investigated. Considering the geometric defect of thickness thinning, the error of FE analysis was reduced further, and it was found that the defect could significantly decrease the stability of the bellows. The above analysis results could provide a reference for structural design and post-buckling analysis of bellows.

Subsampling ratio tests for structural changes in time series with heavy-tailed AR(p) errors

In this article, we consider that issues related to the mean and trend of heavy-tailed AR(p) series are possibly subject to change at most once at some unknown point in time. Under the inspiration of Shao (J. Time Ser. Anal., 2011, 32, 598–606), two ratio statistics are constructed to test whether unknown changes have occurred. It is shown that asymptotic distributions of these test statistics under the no-change null hypothesis are functional for Lévy processes and their consistencies are given under the alternative. To avoid the nuisance parameter, we provide a subsampling method that returns more accurate critical values for these tests. The validity of the subsampling algorithm is proved. A simulation study shows the subsampling-based ratio tests achieve the correct empirical sizes and comparable empirical powers in large samples. Finally, two practical applications using real data set are presented.

A note on statistical tests for homogeneities in multivariate extreme value models for block maxima

AbstractMathematical theory suggests to model annual or seasonal maxima by the generalized extreme value distribution. In environmental applications like hydrology, record lengths are typically small, whence respective parameter estimators typically exhibit a large variance. The variance may be decreased by pooling observations from different sites or variables, but this requires to check the validity of the inherent homogeneity assumption. The present paper provides an overview of (partly new) respective asymptotic significance tests. It is found that the tests' levels are often violated in typical finite‐sample situations, whence a parametric bootstrap approach based on max‐stable process models is proposed to obtain more accurate critical values. As a side product, we present an overview of asymptotic results on a variety of common estimators for GEV parameters in a multisample situation of varying record lengths.

A Two-sample Nonparametric Test for Circular Data\u2013 its Exact Distribution and Performance

A nonparametric test labelled ‘Rao Spacing-frequencies test’ is explored and developed for testing whether two circular samples come from the same population. Its exact distribution and performance relative to comparable tests such as the Wheeler-Watson test and the Dixon test in small samples, are discussed. Although this test statistic is shown to be asymptotically normal, as one would expect, this large sample distribution does not provide satisfactory approximations for small to moderate samples. Exact critical values for small samples are obtained and tables provided here, using combinatorial techniques, and asymptotic critical regions are assessed against these. For moderate sample sizes in-between i.e. when the samples are too large making combinatorial techniques computationally prohibitive but yet asymptotic regions do not provide a good approximation, we provide a simple Monte Carlo procedure that gives very accurate critical values. As is well-known, the large number of usual rank-based tests are not applicable in the context of circular data since the values of such ranks depend on the arbitrary choice of origin and the sense of rotation used (clockwise or anti-clockwise). Tests that are invariant under the group of rotations, depend on the data through the so-called ‘spacing frequencies’, the frequencies of one sample that fall in between the spacings (or gaps) made by the other. The Wheeler-Watson, Dixon, and the proposed Rao tests are of this form and are explicitly useful for circular data, but they also have the added advantage of being valid and useful for comparing any two samples on the real line. Our study and simulations establish the ‘Rao spacing-frequencies test’ as a desirable, and indeed preferable test in a wide variety of contexts for comparing two circular samples, and as a viable competitor even for data on the real line. Computational help for implementing any of these tests, is made available online “TwoCircles” R package and is part of this paper.

Design of an efficient algorithm for solution of Bratu differential equations

In this research, we have suggested a combined strategy to calculate and determine the solutions for problems originating in combustion theory and heat transfer, that are known as Bratu differential equations. We aim to suggest and test a soft computing technique using an efficient meta-heuristic the Symbiotic Organism Search (SOS) algorithm and Artificial neural network (ANN) architecture to obtain better solutions for Bratu differential equations by utilizing fewer computational resources and minimal time. We have simulated our computing approach for different cases, and we compare the outcome of our experiments with solutions obtained by the existing state-of-the-art methods. For novelty, we have found an accurate critical value of λ c by using SOS algorithm. Values of TIC, MAD, and NSE confirm that our method is a convenient and potential candidate for handling real-application problems. We found that this ANN-SOS algorithm takes less time and is accurate in getting results of the expected standard.

Phase transitions in normalized cut of social networks

One of the main goals of network analysis and data science is to identify community structures in a network. Community structure is a typical feature of social networks and community detection is considered to be crucial to understand the structure and function of social networks in cyberspace. The community detection problem of social networks can be viewed as a graph partitioning problem whose objective is to identify the external edges as the edge cut that separates the network as two subnetworks by recursive method. The degree-normalized adjacency matrix is more convenient than traditional Laplacian matrix in calculating eigenvalues and eigenvectors. In this work, based on random model we first prove the existence of an abrupt phase transition for community detection in terms of the degree-normalized adjacency matrix with accurate critical value. In detail, the detectability of community detection has changed from high to low when the critical value of phase transition q approaches p1p2 almost surely, where pi(i=1,2) is the intra-community edge connection probability of subnetworks Ci, respectively. Then, the validity of the theoretical results is verified by numerical experiments.

Statistical Methodology for Medical Data: Gestational Age, Birth Weight, and Hand Characteristics

We briefly review the current trend in handling the neonatal baby weight, gestational age, and other related categorical and continuous variable data, through both robust and outlier-based methods. Graphs are generally presented as smooth curves which give a wrong visual impression and totally hide the actual variability of the data, robust methods are applied without considering that they may certainly be affected by asymmetrical contamination, and the outlier-based methods are incorrectly applied without ascertaining if the individual data arrays are normally distributed, free from discordant observations.Aim: To demonstrate our new procedure for handling of neonatal baby data from two case studies.Methodology: The univariate data were handled through the application of discordancy tests in the light of new precise and accurate critical values, and significance tests were applied to both original and discordant outlier-free data arrays. The bivariate data were also handled from identifying and separating discordant outliers and reporting the quality of the coefficients in terms of standard errors. Finally, the supervised multivariate technique of linear discriminant and canonical analysis is successfully applied.Results: The results of significance tests for some cases varied from the use of all data versus censored data. The identification and separation of bivariate discordant outliers drastically improved the quality of regression lines. Linear discriminant and canonical analysis provided high success values for laboratory-controlled experiments.Conclusion: The need of obtaining both central tendency and dispersion parameters in all medical data is established. The reporting of regression coefficients with individual errors is recommended.

A study on the causal effect of urban population growth and international trade on environmental pollution: evidence from China.

This study seeks to contribute to the recent literature by empirically investigating the causal effect of urban population growth and international trade on environmental pollution of China, for the period 1980-2014. The Johansen cointegration confirmed a long-run cointegration association among the utilised variables for the case of China. The direction of causality among the variables was, consequently, investigated using the recent bootstrapped Granger causality test. This bootstrapped Granger causality approach is preferred as it provides robust and accurate critical values for statistical inferences. The findings from the causality analysis revealed the existence of a bi-directional causality between import and urban population. The three most paramount variables that explain the environmental pollution in China, according to the impulse response function, are imports, urbanisation and energy consumption. Our study further established the presence of an N-shaped environmental Kuznets curve relationship between economic growth and environmental pollution of China. Hence, our study recommends that China should adhere to stricter environmental regulations in international trade, as well as enforce policies that promote energy efficiency in the urban residential and commercial sector, in the quest to mitigate environmental pollution issues as the economy advances.

A Fisher’s Criterion-Based Linear Discriminant Analysis for Predicting the Critical Values of Coal and Gas Outbursts Using the Initial Gas Flow in a Borehole

The risk of coal and gas outbursts can be predicted using a method that is linear and continuous and based on the initial gas flow in the borehole (IGFB); this method is significantly superior to the traditional point prediction method. Acquiring accurate critical values is the key to ensuring accurate predictions. Based on ideal rock cross-cut coal uncovering model, the IGFB measurement device was developed. The present study measured the data of the initial gas flow over 3 min in a 1 m long borehole with a diameter of 42 mm in the laboratory. A total of 48 sets of data were obtained. These data were fuzzy and chaotic. Fisher’s discrimination method was able to transform these spatial data, which were multidimensional due to the factors influencing the IGFB, into a one-dimensional function and determine its critical value. Then, by processing the data into a normal distribution, the critical values of the outbursts were analyzed using linear discriminant analysis with Fisher’s criterion. The weak and strong outbursts had critical values of 36.63 L and 80.85 L, respectively, and the accuracy of the back-discriminant analysis for the weak and strong outbursts was 94.74% and 92.86%, respectively. Eight outburst tests were simulated in the laboratory, the reverse verification accuracy was 100%, and the accuracy of the critical value was verified.

The Comparison of Power and Optimization Algorithms on Unit Root Testing with Smooth Transition

The aim of this study is to search for a better optimization algorithm in applying unit root tests that inherit nonlinear models in the testing process. The algorithms analyzed include Broyden, Fletcher, Goldfarb and Shanno (BFGS), Gauss---Jordan, Simplex, Genetic, sequential quadratic programming and extensive grid-search. The simulation results indicate that the derivative free methods, such as Genetic and Simplex, have advantages over hill climbing methods, such as BFGS and Gauss---Jordan, in obtaining accurate critical values for the Leybourne et al. (J Time Ser Anal 19:83---97, 1998) (LNV) and Sollis (J Time Ser Anal 25:409---417, 2004) unit root tests. Besides, we extend our analysis by including exponential smooth transition type of trend function in to unit root testing which is not used in the previous literature. The same result also holds true for our newly proposed unit root test with exponential smooth transition function type of trend model. Furthermore, we realize that there is a gap in the unit root studies that the newly proposed tests are not analyzed between each other's data generating process (DGP). Hence, we investigate the power comparison of different nonlinear unit root test under various DGP including nonlinear unit root tests and find interesting results such as LNV type unit root test can manage to capture state dependent nonlinearity when the transition speed is high. Finally, we have used the Australian real interest rate parity hypothesis to empirically verify the results that we have obtained in the simulation studies.

New critical values for F and their use in the ANOVA and Fisher’s F tests for evaluating geochemical reference material granite G-2 (U.S.A.) and igneous rocks from the Eastern Alkaline Province (Mexico)

Monte Carlo method was used to simulate precise and accurate critical values (with 2 to 7 decimal places) of Fisher´s F test for degrees of freedom (ν1 and ν2) of up to 2000 and confidence levels of 20% to 99.9% for two-sided or two-tailed test (or equivalently to 60% to 99.95% for one-sided or one-tailed test). Unlike the existing literature, we present 15 new critical value tables along with 15 additional tables of the error estimates of individual values. For the two degrees of freedom – horizontal (ν1) as well as vertical (ν2) –the critical values orrespond to 1(1)30(5)100(10)160(20)200(50)400(100)1000 and 6(1)30(5)100(10)160(20)200(50)400 (100)1000(200)2000, respectively, where the numbers before and after the parenthesis are the initial and final values for which critical values were simulated and the numbers in parenthesis indicate the step size how the initial value of degrees of freedom approached to the final one. Thus these critical values consist of 62x62 values for each of the eleven confidence levels. Even though a large number (3844 for each confidence level, amounting to a total of 42284 values for all confidence levels) of new values of F were simulated, values do not exist for many different degrees of freedom in the range of 1-2000. This problem of unavailable critical values was resolved by evaluating regression models based on simple polynomial functions as well as those involving logtransformation of the independent variable. New best-fit equations were thus proposed to estimate the not-tabulated critical values as well as for the estimation of probability of calculated F value. This methodology of log transformations should be useful also for other kinds of applications involving polynomial fitting. We compared these simulated results with commercial as well as freely available software. The new precise and accurate critical values were used to illustrate the application of analysis of variance (ANOVA) and Fisher´s F tests to geochemical data for international geochemical reference material granite G-2 from U.S.A. We also present the methodology to statistically compare geochemical data for ultrabasic, basic and intermediate magmas from eight regions of the Eastern Alkaline Province of Mexico and U.S.A. Finally, we use these as well as the discordant outlier-free data for ultrabasic and basic rocks in multi-dimensional discrimination diagrams to explore the tectonic setting for this volcanic province, which was inferred to be mainly an extensional zone or a continental rift.

Alternative approach for precise and accurate Student´s t critical values and application in geosciences

We applied an alternative Monte Carlo simulation approach to obtain precise and accurate critical values (with 3 to 8 decimal places) for the Student´s t test for normal samples of degrees of freedom up to 6000 and for two-sided confidence levels of 50% to 99.9% and correspondingly for one-sided confidence levels of 75% to 99.95%. As an innovation, unlike the existing literature precision estimates of critical values are also individually reported. Prior to our work, critical values (with 2 or 3 decimal places) were available in tables in the published literature. Twenty-eight regression models were evaluated to obtain the best regression fitting of the tabulated data. All conventional polynomial (from quadratic up to 8th order) regressions failed for this purpose. New equations based on double or triple natural logarithm-transformations are proposed for all not-tabulated degrees of freedom, including fractional values if required as well as for probability computations. More importantly, we suggest that these kinds of log-transformations are likely to be useful for all cases where conventional polynomial regressions fail to perform satisfactorily. To demonstrate the utility of these new critical values and best-fit equations, we provide specific examples of applications in geochemistry, chemistry and medicine. The probability estimates, obtained from the present explicit approach, are consistent with commercial and freely available software. Additionally, a more extensive application of our t values is given for processing inter-laboratory data for geochemical reference materials granites G-1 and G-2 from U.S.A. as well as for evaluating geochemical data for basic rocks from the Canary and Azores Islands

A Power Comparison of Various Tests of Univariate Normality on Ex-Gaussian Distributions

A power analysis of seven normality tests against the Ex-Gaussian distribution (EGd) is presented. The EGd is selected on the basis that it is a particularly well-suited distribution to accommodate positively skewed distributions such as those observed in reaction times data. A pre-assessment of the power of the selected tests across various types of distributions was done via a meta-analysis and a comparison with other power analyses reported in the literature was also performed. General recommendations are given as to which tests should be used to test normality in data suspected to resemble an EG distribution. Additionally, some topics for future research regarding the use of confidence intervals and the computation of accurate critical values are outlined.

Rock critical porosity inversion and S-wave velocity prediction

A critical porosity model is often used to calculate the dry frame elastic modulus by the rock critical porosity value which is affected by many factors. In practice it is hard for us to obtain an accurate critical porosity value and we can generally take only an empirical critical porosity value which often causes errors. In this paper, we propose a method to obtain the rock critical porosity value by inverting P-wave velocity and applying it to predict S-wave velocity. The applications of experiment and log data both show that the critical porosity inversion method can reduce the uncertainty resulting from using an empirical value in the past and provide the accurate critical porosity value for predicting S-wave velocity which significantly improves the prediction accuracy.

Quantifying seasonal export and retention of nutrients in West European lowland rivers at catchment scale

AbstractTo set accurate critical values for the protection of lakes and coastal areas, it is crucial to know the seasonal variation of nutrient exports from rivers. This article presents an improved method for estimating export and in‐stream nutrient retention and its seasonal variation. For 13 lowland river catchments in Western Europe, inputs to surface water and exports were calculated on a monthly basis. The catchments varied in size (21 to 486 km2), while annual in‐stream retention ranged from 23 to 84% for N and 39 to 72% for P. A novel calculation method is presented that quantifies monthly exports from lowland rivers based on an annual load to the river system. Inputs in the calculation are annual emission to the surface waters, average monthly river discharge, average monthly water temperature and fraction of surface water area in the catchment. The method accounts for both seasonal variation of emission to the surface water and seasonal in‐stream retention. The agreement between calculated values and calibration data was high (N: r2 = 0·93; p < 0·001 and P: r2 = 0·81; p < 0·001). Validation of the model also showed good results with model efficiencies for the separate catchments ranging from 31 to 95% (average 76%). This indicates that exports of nitrogen and phosphorus on a monthly basis can be calculated with few input data for a range of West European lowland rivers. Further analysis showed that retention in summer is higher than that in winter, resulting in lower summer nutrient concentrations than that calculated with an average annual input. This implies that accurate evaluation of critical thresholds for eutrophication effects must account for seasonal variation in hydrology and nutrient loading. Our quantification method thus may improve the modelling of eutrophication effects in standing waters. Copyright © 2011 John Wiley & Sons, Ltd.

Testing parametric conditional distributions using the nonparametric smoothing method

This paper proposes a new goodness-of-fit test for parametric conditional probability distributions using the nonparametric smoothing methodology. An asymptotic normal distribution is established for the test statistic under the null hypothesis of correct specification of the parametric distribution. The test is shown to have power against local alternatives converging to the null at certain rates. The test can be applied to testing for possible misspecifications in a wide variety of parametric models. A bootstrap procedure is provided for obtaining more accurate critical values for the test. Monte Carlo simulations show that the test has good power against some common alternatives.

An efficient and direct method for out-of-plane buckling analysis of Y-braced steel frames

Dimensionless design-oriented charts are introduced for customising a new and efficient method of computing the out-of-plane critical buckling load of Y-braced steel frame systems. These charts are derived from extensive parametric studies on the basis of an “exact solution”, within the limits of the Eulerian theory, stability analysis, using a wide array of geometric characteristics of practical interest. Demonstrated with numerical examples, these calculations are shown to yield, in a very efficient way, accurate critical load values of these systems. The charts can be used for practical design of Y-brace elements.

Sample size, lag order and critical values of seasonal unit root tests

A response surface analysis for the distributions of popular tests for seasonal unit roots in quarterly observed time series variables is presented. Five test statistics are considered, along with the most commonly used specifications of the deterministic component in the test regression; allowance is also made for the lag order in the test regression to be determined endogenously, using commonly applied selection methods. Response surface coefficients are reported, permitting simple computation of accurate critical values for 1%-, 5%- and 10%-level tests and probability values for any sample size and lag order. Accurate approximations of the asymptotic distributions are obtained in the process of constructing the response surfaces. Dependence of the critical values and the probability density functions on the sample size and lag order is investigated.

Estimating Procedure Times for Surgeries by Determining Location Parameters for the Lognormal Model

We present an empirical study of methods for estimating the location parameter of the lognormal distribution. Our results identify the best order statistic to use, and indicate that using the best order statistic instead of the median may lead to less frequent incorrect rejection of the lognormal model, more accurate critical value estimates, and higher goodness-of-fit. Using simulation data, we constructed and compared two models for identifying the best order statistic, one based on conventional nonlinear regression and the other using a data mining/machine learning technique. Better surgical procedure time estimates may lead to improved surgical operations.