Surface air temperature change in the Wuyi Mountains,southeast China

Detecting changes in surface air temperature in mid-and low-altitude mountainous regions is essential for a comprehensive understanding of warming trend with altitude.We use daily surface air temperature data from 64 meteorological stations in Wuyi Mountains and its adjacent regions to analyze the spatio-temporal patterns of temperature change.The results show that Wuyi Mountains have experienced significant warming from 1961 to 2018.The warming trend of the mean temperature is 0.20℃/decade,the maximum temperature is 0.17℃/decade,and the minimum temperature is 0.26℃/decade.In 1961-1990,more than 63%of the stations showed a decreasing trend in annual mean temperature,mainly because the maximum temperature decreased during this period.However,in 1971-2000,1981-2010 and 1991-2018,the maximum,minimum and mean temperatures increased.The fastest increasing trend of mean temperature occurred in the southeastern coastal plains,the quickest increasing trend of maximum temperature occurred in the northwestern mountainous region,and the increase of minimum temperature occurred faster in the southeastern coastal and northwestern mountainous regions than that in the central area.Meanwhile,this study suggests that elevation does not affect warming in the Wuyi Mountains.These results are beneficial for understanding climate change in humid subtropical middle and low mountains.

Calculation of Two-Tailed Exact Probability in the Wald-Wolfowitz One-Sample Runs Test

The objectives of this paper are to demonstrate the algorithms employed by three statistical software programs (R, Real Statistics using Excel, and SPSS) for calculating the exact two-tailed probability of the Wald-Wolfowitz one-sample runs test for randomness, to present a novel approach for computing this probability, and to compare the four procedures by generating samples of 10 and 11 data points, varying the parameters n0 (number of zeros) and n1 (number of ones), as well as the number of runs. Fifty-nine samples are created to replicate the behavior of the distribution of the number of runs with 10 and 11 data points. The exact two-tailed probabilities for the four procedures were compared using Friedman’s test. Given the significant difference in central tendency, post-hoc comparisons were conducted using Conover’s test with Benjamini-Yekutielli correction. It is concluded that the procedures of Real Statistics using Excel and R exhibit some inadequacies in the calculation of the exact two-tailed probability, whereas the new proposal and the SPSS procedure are deemed more suitable. The proposed robust algorithm has a more transparent rationale than the SPSS one, albeit being somewhat more conservative. We recommend its implementation for this test and its application to others, such as the binomial and sign test.

Comparison of Two Sample Tests Using Both Relative Efficiency and Power of Test

This paper, comparison of two sample tests, is motivated by the fact that in the test of significant difference between two independent samples, numerous methods can be adopted;each may lead to significant different results;this implies that wrong choice of test statistic could lead to erroneous conclusion. To prevent misleading information, there is a need for proper investigation of some selected methods for test of significant difference between variables/subjects most especially, independent samples. The paper examines the efficiency and sensitivity of four test statistics to ascertain which test performs better. Based on the results, the relative efficiency favours median test as being more efficient than modified median test for both symmetric and asymmetric distributions. In terms of power of test, median test is more sensitive than Modified Median (MMED) test since it has higher power irrespective of the sample sizes for both symmetric and asymmetric distribution. In terms of relative efficiency for asymmetric distribution Modified Mann-Whitney U test is more efficient than Mann-Whitney U test (MMWU), and then for symmetric distribution, Mann-Whitney U test (MMWU) is more efficient than Modified Mann-Whitney in sample size of 5;but for other sample sizes considered Modified Mann-Whitney U test (MMWU) is better than Mann-Whitney. Using power of test for both symmetric and asymmetric distributions, Mann-Whitney is more sensitive than Modified Mann-Whitney U test (MMWU) because it has higher power.

Characterizing prediction errors of a new tree height model for cut-to-length Pinus radiata stems through the Burr TypeⅫdistribution

Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL)stems tend to produce prediction errors whose distributions are not conditionally normal but are rather leptokurtic and heavy-tailed.This feature was merely noticed in previous studies but never thoroughly investigated.This study characterized the prediction error distribution of a newly developed such tree height model for Pin us radiata(D.Don)through the three-parameter Burr TypeⅫ(BⅫ)distribution.The model’s prediction errors(ε)exhibited heteroskedasticity conditional mainly on the small end relative diameter of the top log and also on DBH to a minor extent.Structured serial correlations were also present in the data.A total of 14 candidate weighting functions were compared to select the best two for weightingεin order to reduce its conditional heteroskedasticity.The weighted prediction errors(εw)were shifted by a constant to the positive range supported by the BXII distribution.Then the distribution of weighted and shifted prediction errors(εw+)was characterized by the BⅫdistribution using maximum likelihood estimation through 1000 times of repeated random sampling,fitting and goodness-of-fit testing,each time by randomly taking only one observation from each tree to circumvent the potential adverse impact of serial correlation in the data on parameter estimation and inferences.The nonparametric two sample Kolmogorov-Smirnov(KS)goodness-of-fit test and its closely related Kuiper’s(KU)test showed the fitted BⅫdistributions provided a good fit to the highly leptokurtic and heavy-tailed distribution ofε.Random samples generated from the fitted BⅫdistributions ofεw+derived from using the best two weighting functions,when back-shifted and unweighted,exhibited distributions that were,in about97 and 95%of the 1000 cases respectively,not statistically different from the distribution ofε.Our results for cut-tolength P.radiata stems represented the first case of any tree species where a non-normal error distribution in tree height prediction was described by an underlying probability distribution.The fitted BXII prediction error distribution will help to unlock the full potential of the new tree height model in forest resources modelling of P.radiata plantations,particularly when uncertainty assessments,statistical inferences and error propagations are needed in research and practical applications through harvester data analytics.

A Nonparametric Model Checking Test for Functional Linear Composite Quantile Regression Models

This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model.A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model.The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis,and tends to infinity in probability under the alternative hypothesis,which implies the consistency of the test.Furthermore,it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis.Extensive simulations are reported,and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies.The proposed methods are also applied to two real datasets.

Screening influencing factors of blood stasis constitution in traditional Chinese medicine

Objective To study the influencing factors of blood stasis constitution and provide a basis for treating blood stasis-related diseases by traditional Chinese medicine(TCM) constitution identification.Methods Data were collected using the self-developed TCM constitution identification platform based on B/S model by the project team. The obtained data were divided into blood stasis constitution and normal constitution groups. The differences of the categorical type influencing factors(gender, birth mode, feeding mode within four months of birth, family history, marital status, eating habits, sleeping habits, exercise habits, emotional state, stress situation, and living environment) and the quantitative type influencing factors(sleep time, age,and mother’s age at birth) on the constitution of the two groups were analyzed. In the singlefactor analysis, the Pearson’s chi-square test was selected for the categorical variable, and the independent sample t test and Mann-Whitney U nonparametric test were selected for the quantitative variables according to whether they conformed to the positive-terrestrial distribution;the binary logistic stepwise regression method was selected for the multi-factor analysis.Results The data of 318 cases were collected from the TCM composition identification platform, and 159 cases of blood stasis constitution were used as the experimental group and 159 cases of normal constitution were used as the control group. The Pearson’s chi-square test yielded significant differences(P < 0.05) in the effects of gender, pressure situation, family history, living environment, emotional state, exercise habits, and dietary habits on blood stasis constitution. The independent samples t test yielded differences in sleep duration between the blood stasis constitution and normal constitution populations(P < 0.05), which meant sleep duration of the blood stasis constitution population was less than that of the normal constitution population. The Mann-Whitney U nonparametric test results accepted the original hypothesis that there was no difference in the distribution of age and mother’s age at birth across constitution types(P > 0.05). Binary logistic regression analysis showed that gender, family history, marital status, living environment, exercise habits, and emotional state were risk factors for blood stasis constitution(P < 0.05).Conclusion Gender, family history, living environment, emotional state, and exercise habits were significant influencing factors of blood stasis constitution. Blood stasis constitution populations can pay more attention to these influencing factors in their daily life for the prevention and reconciliation of blood stasis constitution.

Climate Change and Its Effects on Runoff in the North of Tianshan,Xinjiang

[Objective] The aim was to study climate changes in northern Tianshan in Xinjiang and its influences on runoff. [Methed] Based on the runoff data for 54 years of Kenswatt station on Manas River and the climate date of 16 meteorological stations from 1957 to 2007 in the north of Tian- shan in Xinjiang, the climate change and temporal series of the annual runoff were studied by use of nonparametric test, wavelet analysis, R/S analysis and periodic trend superposition model. [ Result] The temperature, precipitation and annual runoff of Manas River increased significantly. The Hurst coefficients of both climate factors and the annual runoff were bigger than 0.5, which indicated that they would still keep an increasing trend. Temperature from 1957 to 1959 was low, precipitation was much, belonging to low temperature and more rain period. 1960s and 1970s were low temperature and less rain period. Temperature in 1980s was close to average value and precipitation was little. Since 1990s, it entered into high temperature and less rain period and was significant during 2000 and 2007. The temperature and precipitation changed in 1995 and 1996. Tempera- ture was＇significant in 11 and 22 years. Precipitation had 5, 8, 14 and 22 years of main cycle. The annual runoff and climate factors in Manasi River were increasing in different times. The annual runoff was related to climate factors, and temperature was closer to annual runoff than precipitation. [ Conclusion] The study provided theoretical basis for the reasonable configuration, ecological protection and agricultural production of water re- sources in north Tianshan in Xinjiang.

Distribution of Sediment Measurements in Lake Michigan as a Case Study: Implications for Estimating Sediment and Water Interactions in Eutrophication and Bioaccumulation Models

Lake Michigan, the sixth largest freshwater lake in the world by surface area, was utilized as a water body for assessment. Field data collected at sampling sites throughout the lake in an intensive monitoring effort were utilized for evaluation of the distribution of sediment measurements. An assessment of sediment nutrient and carbon measurements within Lake Michigan was completed to recognize strata resulting from the hydrodynamics of the system. Nonparametric comparison tests revealed that significant differences exist between measurements of sediment nutrients and organic carbon in the lake using strata based upon water column depth (all results demon-strated a p < 0.05, α = 0.05). Cross-validation analysis was applied to the field-collected samples, revealing that large errors occur when estimating sediment flux of carbon or nutrients at a given location in the lake without considering stratification of the distributions of these measurements. Errors in estimating sediment concentrations of nutrients and carbon specific to a location in the lake demonstrated a statistically significant increase when stratification of sediment measurements wasn’t employed among sites. For example, distributions of errors in estimating all nutrients and organic carbon concentrations, whereby distance squared inverse interpolation methods were applied, demonstrated a statistically significant increase in absence of stratification (all p < 0.001, α = 0.05). These results have implications for characterization, monitoring, and modeling sediment and water interaction as related to eutrophication, as well as to contaminant exposure and bioaccumulation for chemicals within Lake Michigan and large water bodies where stratification of the sediment based upon physics of the system exists.

On the Diversity of Long-Term Temperature Responses to Varying Levels of Solar Activity at Ten European Observatories

We analyze ten of the longest (127 to 230 year-long) time series of European daily temperatures available from five different K&#246;ppen-Geiger climate classes. We split these according to the level of solar cycle activity (H for “higher than median” and L for “lower than median”). This reveals coherent patterns in the temperature differences: when TH-TL?are stacked according to their calendar date, the daily averages from January 1 to December 31st disclose characteristic features in addition to the dominant annual seasonal wave, namely variations up to 2&#176;C lasting for about 1.5 to 3 months. The five observatories at intermediate latitudes in a band from Oxford in the West to Prague in the East (same climate class) have very similar signatures. These similarities are most unlikely to be due to pure chance (confirmed by confidence levels in excess of 99% with the Kolmogorov-Smirnov and Kuiper nonparametric tests). The TH-TL patterns carry a regional signature, modulated by a more local response function. On the other hand, northern European observatories (St Petersburg and Arkhangelsk), those south of the Alps (Milan and Bologna), and the easternmost one in Astrakhan, corresponding to different climate classes, have different signatures. Similarly, preliminary study of long air pressure recordings confirms what emerges from the analysis of temperatures. These new observations lead us to conclude that the climate in different regions presents different responses to variations in solar activity. Moreover, the distributions of the lower, middle, and higher quartiles of the temperature and pressure indices in solar cycles with high versus low activity are significantly different, providing further robust statistical confirmation to this conclusion (confidence level higher to much higher than 99% using the Kuiper test).

Distance-Based Regression Analysis for Measuring Associations

Distance-based regression model,as a nonparametric multivariate method,has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies,genomic analyses,and many other research areas.Based on it,a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim.To the best of our knowledge,the statistical properties of the pseudo-F statistic has not yet been well established in the literature.To fill this gap,the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables.Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large,the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root.The asymptotic null distribution of the new test statistic and power of both tests are also investigated.Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test.Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.

Runoff Variation Law and Its Response to Climate Change in the Headstream Area of the Keriya River Basin,Xinjiang

Based on the runoff and meteorological data of Langan（兰干） Hydrological Station from 1957 to 2009 in Keriya（克里雅） River,the periodicities,abrupt changes,and trends of climate factors and runoff were investigated by wavelet analysis and nonparametric test;then,the future change of the annual runoff was predicted by a periodic trend superposition model.In succession,the influencing volumes of climate change on the annual runoff were separated from the observation values of the an-nual runoff in Keriya River.The results show that（1） temperature series increased significantly,while the annual runoff and precipitation of Keriya River increased insignificantly at the significant level of α=0.05;（2） the common periods of 9 and 15 years existed in the annual runoff evolution process,and the primary periods of temperature and precipitation were 9 and 22 years and 9 and 13 years,respec-tively;（3） the annual runoff did not vary simultaneously with the abrupt change of climate factors in the headstream;the abrupt points of annual runoff and temperature are at 1998 and 1980 year,and that of precipitation is not so significant;and（4） the annual runoff will experience a decrease trend in the future period;the total increasing volume owing to climate change is 23.154×108 m3 in the head-stream during the period of 1999-2009;however,the stream flow has been nearly utilized completely due to the human activities in the mainstream area of Keriya River.

Projection-based High-dimensional Sign Test

This article is concerned with the high-dimensional location testing problem.For highdimensional settings,traditional multivariate-sign-based tests perform poorly or become infeasible since their Type I error rates are far away from nominal levels.Several modifications have been proposed to address this challenging issue and shown to perform well.However,most of modified sign-based tests abandon all the correlation information,and this results in power loss in certain cases.We propose a projection weighted sign test to utilize the correlation information.Under mild conditions,we derive the optimal direction and weights with which the proposed projection test possesses asymptotically and locally best power under alternatives.Benefiting from using the sample-splitting idea for estimating the optimal direction,the proposed test is able to retain type-I error rates pretty well with asymptotic distributions,while it can be also highly competitive in terms of robustness.Its advantage relative to existing methods is demonstrated in numerical simulations and a real data example.

A NEW TEST FOR NORMALITY IN LINEAR AUTOREGRESSIVE MODELS

A nonparametric test for normality of linear autoregressive time series is proposed in this paper.The test is based on the best one-step forecast in mean square with time reverse.Some asymptotic theory is developed for the test,and it is shown that the test is easy to use and has good powers.The empirical percentage points to conduct the test in practice are provided and three examples using real data are included.

GROUP CONTINGENCY TEST FOR TWO OR SEVERAL INDEPENDENT SAMPLES

This paper proposes a new and distribution-free test called ＂Group Contingency＂ test （GC, for short） for testing two or several independent samples. Compared with traditional nonparametric tests, GC test tends to explore more information based on samples, and it＇s location-, scale-, and shapesensitive. The authors conduct some simulation studies comparing GC test with Wilcoxon rank sum test （W）, Kolmogorov-Smirnov test （KS） and Wald-Wolfowitz runs test （WW） for two sample case, and with Kruskal-Wallis （KW） for testing several samples. Simulation results reveal that GC test usually outperforms other methods.