Durbin Test Research Articles

Rank tests for the Latin square design

A rank test for Latin square data is derived. Forms are given for when there are no ties, for when ties occur and mid-ranks are used, and for when ties occur in general. These adjustments are akin to those for the Kruskal-Wallis, Friedman, and Durbin tests. Since substantial block effects may affect ranking, alignment is recommended. The ANOVA F test on the ranks, the rank transform test, is a competitor test. We designate this test, where the data are aligned before ranking, the FART test. The proposed test, implemented as a permutation test, is designated the permutation aligned RL test: the PARL. We also give an approximation to the sampling distribution using the χ 2 distribution, and call this test the CARL. An indicative simulation study assuming the usual parametric model and testing the null hypothesis that the treatment parameter is zero shows that the CARL, PARL, FART, and the F test on the raw data all control their type I errors well and have comparable powers.

Adaptive Robust Subspace Detection Based on GLRT, Rao, Wald, Gradient, and Durbin Tests

Adaptive Robust Subspace Detection Based on GLRT, Rao, Wald, Gradient, and Durbin Tests

An empirical study of the durbin and ANOVA F tests and their contrasts

The Durbin and ANOVA F test on the ranks are competing tests for equality of treatment mean ranks. When the levels of the treatments are ordered, both tests have informative decompositions into orthonormal contrasts that detect linear, quadratic, etc. effects. It is known that the ANOVA F test on the ranks better adheres to the nominal significance level than the Durbin test. Here we investigate whether the same is true for their orthonormal contrasts.

The Determinants of Prices of Fan Tokens as a New Sports Finance Tool

In the Covid-19 era, the income sources of sports clubs decreased, but the importance of fan tokens as new communication, management, and income source for sports clubs increased with Blockchain technology. For this reason, the relationships between fan token prices and club success, transaction volume, and attractiveness factors were examined and the important determinants of fan token prices were tried to be revealed. To determine the most suitable methods for panel data model, first of all, cross-section dependence, homogeneity, and unit root tests were carried out. Then the durbin test was performed and it was concluded that the variables were cointegrated. Finally, the coefficients were examined with the PMG/ARDL test and it was observed that the most important determinants of fan token prices were club success and transaction volume, respectively. While these factors affect fan token prices positively, the effect of the attractiveness factor is seen as less important and negative compared to other factors. In addition, in the error correction model established, the existence of a long-term equilibrium relationship between the variables was confirmed. It was concluded that the short-term deviations returned to the equilibrium after approximately 21 days.

Adaptive detection with training data in partially homogeneous environments for colocated MIMO radar

The issue of adaptive detection is considered for the colocated multi-input multi-output (MIMO) radar in this paper. Meanwhile, the background is partially homogeneous environments (PHE), where the power mismatch is present between the training data and test data. The training data in PHE are utilized to derive effective detectors on the basis of generalized likelihood ratio test, Rao, Wald, Gradient, and Durbin tests. Since the Durbin test-based detector coincides with the Rao test-based detector, the two-step design approach for the Durbin test is used for deriving the new detector. The outcomes of simulation experiments illustrate that the proposed detectors achieve superior effectiveness to existing approaches. Furthermore, the results also show that when the signal mismatch exists, the Wald and Durbin tests maintain robust characteristics. Meanwhile, the Rao test ensures selective property.

Adaptive double subspace target detection based on gradient test: Designs and comparisons

The issue of adaptive detection for double subspace (DOS) signals under the Gaussian noise background is investigated in this paper. The DOS signal has the special structure where the rows and columns of the matrix-valued signal lie in known subspaces with unknown coordinates. To deal with the DOS signal detection problem, two kinds of Gradient tests are proposed in homogeneous environments and partially homogeneous environments. Remarkably, the Durbin test, as well as its two-step version, is also used for the detector design, which is consistent with the existing methods. To evaluate the performance of the proposed methods, both simulated data and real data collected by IPIX radar are used. The results indicate that the Gradient tests ensure the constant false alarm rate property. Furthermore, the proposed detectors obtain relatively robust characteristics and achieve superior performance to existing competitors in some scenarios.

Persymmetric adaptive subspace detection in compound Gaussian sea clutter with generalized inverse Gaussian texture

This paper considers the detection problem of subspace targets in compound Gaussian sea clutter with generalized inverse Gaussian (GIG) texture. Based on the Wald test, the gradient test, and the Durbin test, we propose three novel subspace detectors. And the criterion above are first applied to the detection problem in compound Gaussian (CG) sea clutter with GIG texture. In the first step, assuming that the speckle covariance matrix (CM) and the texture component are unknown to obtain the test statistics of the proposed detectors. In the second step, we exploit the persymmetric property of speckle CM and the maximum a posteriori (MAP) criterion to obtain the estimation of speckle CM and the GIG texture parameters. Moreover, the constant false alarm rate (CFAR) properties of the three proposed detectors have been proven with respect to the speckle CM and the scale parameter of the texture component. We verify the detection performance of the three proposed detectors by the numerical experiments both in simulated data and real sea clutter data, and the simulated results show the proposed detectors are robust in the case of limited training and mismatched signals.

Orthogonal contrasts for both balanced and unbalanced designs and both ordered and unordered treatments

AbstractWe consider designs with t treatments, the ith level of which has ni observations. Four cases are examined: treatment levels both ordered and not, and the design balanced, with all ni equal, and not. A general construction is given that takes observations, typically treatment sums or treatment rank sums, constructs a simple quadratic form and expresses it as a sum of squares of orthogonal contrasts. For the case of ordered treatment levels, the Kruskal–Wallis, Friedman and Durbin tests are recovered by this construction. A dataset where the design is the supplemented balanced, which is an unbalanced design in our terminology, is analyzed. When treatment levels are not ordered the construction also applies. We then focus on Helmert contrasts.

Adaptive Detection of Gaussian Rank-One Signals Using Adaptively Whitened Data and Rao, Gradient and Durbin Tests

We address the problem of detecting a Gaussian rank-one signal using training samples to learn the covariance matrix of the noise present in the samples under test. Towards this end, we propose to use the latter after they have been whitened by the sample covariance matrix of the training samples. As an alternative to the generalized likelihood ratio test, we investigate three simpler alternatives, namely the Rao, gradient and Durbin tests. Closed-form expressions of the corresponding test statistics are derived and the detectors are shown to have a constant false alarm rate. Their performance is assessed via numerical simulations.

Impact on Carbon Intensity of Carbon Emission Trading-Evidence from a Pilot Program in 281 Cities in China.

China’s carbon emissions trading scheme (ETS) is an institutional arrangement that China intends to explore as a means of energy conservation and emission reduction. It is the core of China’s goal of achieving carbon peaking and carbon neutrality. This paper regards the introduction of pilot carbon emission trading policies as a quasi-natural experiment. Propensity Score Matching (PSM), Differences-in-Differences (DID), and spatial Durbin methods were used to evaluate the policy effects of pilot carbon emission trading policies on the carbon intensity of Chinese cities. We empirically tested the impact mechanism using the panel data of 281 cities at the prefecture level and above in China from 2006 to 2019. The results show that (1) the pilot policy of carbon emission trading has significantly reduced the carbon intensity of Chinese cities and shows characteristics of heterogeneity; (2) the dynamic effect test shows that the mitigation effect of the pilot carbon emission trading policy has increased gradually with time; (3) the mediation effect shows that the pilot carbon emission trading policy alleviates urban pollution in the region by improving the level of environmental governance and jointly reduces urban carbon intensity by increasing the level of green technology innovation; (4) the Durbin test suggests that pilot carbon emissions trading policy enforcement can significantly improve the carbon intensity of the area surrounding the city. In summary, the national carbon emissions trading market appears to be a successful experiment that also can contribute to China’s sustainable development. Its promise in achieving the “double carbon” target provides important policy implications.

Adaptive detection based on gradient test and Durbin test in spectrally symmetric interference

In this paper, we consider the problem of detecting a signal in ground clutter dominated environments with a symmetrically structured power spectral density. We take advantage of interference’s spectrum symmetry to develop decision schemes. The gradient test, Durbin test and their two-step (2S) variants are deduced. The 2S-gradient test and the 2S-Durbin test coincide with the 2S generalized likelihood ratio test, and the Durbin test coincide with the Rao test for the same detection problem, while the gradient test is a new detector. Numerical results, based on simulated and real data, show that the gradient test can perform better than the existing ones in sample-starved scenarios, and the detectors exploiting the interference spectrum symmetry outperform traditional detectors without exploiting the interference spectral symmetry.

Nonparametric Analysis of Balanced Incomplete Block Rank Data

Traditional nonparametric analysis of balanced incomplete block rank data usually involves the Durbin test. Here we give an alternative adjustment for the Durbin statistic for when there are ties and mid-ranks are used. The adjusted Durbin statistic is shown to be simply related to the ANOVA F statistic on the ranks, so that the corresponding tests are, in a sense, equivalent. This means both are tests of equality of mean treatment ranks. A simulation study compares the size and power performances of the competing tests. We also apply the nonparametric ANOVA methodology to give tests for univariate moment effects and, when treatments are ordered, for bivariate moment effects. The latter includes umbrella tests.

Multichannel Adaptive Detection Based on Gradient Test and Durbin Test in Deterministic Interference and Structure Nonhomogeneity

In this letter, we consider the problem of detecting a multichannel subspace signal in the presence of deterministic interference and structure nonhomogeneity. We derive the gradient test, Durbin test, and their two-step (2S) variants. The gradient test and its 2S variant have the same form as the existing generalized likelihood ratio test for the same detection problem, whereas the Durbin test and its 2S variant are new detectors. Numerical examples show that the two proposed new detectors, i.e., the Durbin test and its 2S variant, can provide better detection performance in some scenarios. In particular, they are robust to signal mismatch, and can perform well when the structure nonhomogeneity is not serious.

Complex Parameter Rao, Wald, Gradient, and Durbin Tests for Multichannel Signal Detection

In the problem of multichannel signal detection, when it comes to the detector design criteria apart from the generalized likelihood ratio test, the traditional method is to cascade the real and imaginary parts of the parameters, and then substitute them into the real parameter statistics. This method is not succinct, and sometimes may be cumbersome and difficult to handle. Recently, a complex parameter Rao test was introduced by Kay and Zhu without the need of cascading the real and imaginary parts of the complex parameters when there is no nuisance parameter. Inspired by this work, we move a further step toward the complex parameter statistics of the Rao, Wald, gradient, and Durbin tests both with and without nuisance parameters, and derive the relationships between their real and complex parameter statistics. Moreover, for a special Fisher information matrix which often holds in practice, we derive a series of simple forms of the complex parameter statistics for the above four criteria, and discuss their application conditions in linear multivariate complex circular Gaussian distribution. Finally, several application examples are given to confirm the proposed schemes.

Effects of Mortgage Interest Rate on Real Estate Investment in Kenya

As an investment and consumer good, real estate is significant. Like many developing countries, Kenya has struggled to give its citizens access to decent housing that is also affordable. More people are in need of housing due to urbanization, fast population growth, and rural-to-urban migration. Housing supply is less than demand as a result of several of macroeconomic and financial issues that affect real estate investment and, consequently, housing. This study looked into the impact of mortgage interest rates on real estate investment. The study, which covered the 11-year period from 2010 to 2020, used a causal research design and regression analytic research methods based on the Vector Error Correction Model. Data on real estate investments in Kenya The Kenya National Bureau of Statistics (KNBS) and Cytonn quarterly investments reports were obtained from the Central Bank of Kenya. The Ministry of Finance's database on national budgets (KNBS) provided information on mortgage interest rates, A pre-estimation test was run to verify the outcomes. The variables were stationary on the first difference. The VIF test result of 1.62 indicated that there was no multi-collinearity. The 1.9122 Durbin test value suggested that there was no serial correlation. Pairwise Correlation analysis showed a moderate correlation between mortgage interest rate on real estate investment (0.578). The report suggests that in order to incentivize real estate investment, the government should offer mortgage loans at reasonable rates, control property tax rates, and promote public-private partnerships in infrastructure development.

The Effect of Knowledge Management on Managers` Performance of Education Office in Regions 1 and 2 of Kermanshah City

Objective: The purpose of this study is to examine the Effect of Knowledge Management on Managers` Performance. Methodology: The population is all directors of Education Office in Regions 1 and 2 of Kermanshah City, whose number is 145 people. The statistical population-based Morgan – Kerjcie (1970), number is 105 people was chosen as a sample. To select the sample, a simple random sampling method was used. Methodology of the study is descriptive. Standardized questionnaire to collect knowledge management processes and the questionnaire Lee was used. Results: To determine the reliability alpha coefficient was calculated as 0.958, which is indicative of the high level of reliability. For data analysis tests by Kolmogorov - Smirnov ,one-sample t-test, multi-regression and Watson – Durbin test by using the software 19 SPSS was used. Conclusion: The results showed that there is the significant and positive effect between Knowledge Management and Managers` Performance in Education Office in Regions 1 and 2 of Kermanshah City.

A new approach to measuring Overall Liking with the Many-Facet Rasch Model

The 9-point hedonic scale is the most common hedonic rating scale used to provide an assessment of overall liking. Studies have shown that consumer judgements of overall liking could be influenced by their ratings of the liking of flavour, texture, aroma or appearance. However, this is not directly taken into account when using the holistic variable of overall liking. A new approach is proposed for measuring overall liking that is firstly based on initially considering what sensory characteristics (attributes or modalities) defines the latent sensory construct of OVERALL LIKING. The aim of this study was to develop a single measure of Overall Liking that incorporates the relative importance of liking ratings from different sensory characteristics by applying a Many-Facet Rasch model to produce interval-scaled estimates of Overall Liking. A homogeneity test found significant differences (p < 0.01) between the Rasch means estimates of the cured 10 hams that were evaluated by a consumer panel (n = 90), with the two different definitions of the Rasch measure of Overall Liking. No significant differences were found when comparing Rasch measures with raw scores using an intrablock BIB ANOVA and Durbin test. The degree of Relevance, shown on a Many-Facet Wright map, indicated the extent which a variable contributed to the measure of Overall Liking. Of the 10 sensory attributes used for the Individual Attribute Measure, Hardness and Juiciness contributed the most, while Sweetness and Typical Flavour contributed the least. However, the modalities used in rating the Likings of Overall Flavour, Texture, Aroma and Appearance contributed almost to the same extent to Overall Liking in the Total Attribute Measure. The Wright Map also showed that the categories on the 9-point hedonic scale were unequally spaced and the distance between them became increasingly larger the further away from the central category of ‘Neither like nor dislike’.

Adaptive Radar Detectors Based on the Observed FIM

Modified versions of Rao, Wald, and Durbin tests are considered exploiting an estimator of the Fisher Information Matrix (FIM) in place of the exact one. They are asymptotically equivalent (under some technical conditions) to the standard counterparts and rely on the use of the Observed FIM (OFIM), which is proportional to the negative Hessian of the log-likelihood. The developed framework is applied to the problem of adaptive radar detection of a point-like target in homogeneous or partially-homogeneous interference. Remarkably, for both the scenarios, it is shown that Rao, Wald, and Durbin tests with OFIM are statistically equivalent to the Generalized Likelihood Ratio Test (GLRT) for the specific detection problem (namely Kelly's detector for the homogeneous environment and the Adaptive Coherence Estimator (ACE) [S. Kraut and L. L. Scharf, “The CFAR adaptive subspace detector is a scale-invariant GLRT,” IEEE Trans. Signal Process., vol. 47, no. 9, pp. 2538-2541, Sep. 1999.], also known as Adaptive Normalized Matched Filter (ANMF) [E. Conte, M. Lops, and G. Ricci, “Asymptotically optimum radar detection in compound-gaussian clutter,” IEEE Trans. Aerosp. Electron. Syst., vol. 31, no. 2, pp. 617-625, Apr. 1995], for the partially-homogeneous scenario). This provides a new interpretation of the mentioned GLRTs laying the foundations for a better understanding of their theoretical validity.

Anatomical characterization of the brachial plexus in dog cadavers and comparison of three blind techniques for blockade

ObjectivesTo describe the ventral spinal nerve rami contribution to the formation of the brachial plexus (BP), and to compare ease of performing and nerve staining between three blind techniques for BP blockade in dogs. Study designProspective, randomized, blind study. AnimalsA total of 18 dog cadavers weighing 28.2 ± 9.7 kg (mean ± standard deviation). MethodsDogs were randomly assigned to two of three BP treatments: traditional approach (TA), perpendicular approach (PA), and axillary approach (AA). Dye (0.2 mL kg−1) was injected in the left BP using a spinal needle; another BP treatment was used in the right BP. Landmarks (L) included: L1, midpoint between point of the shoulder and sixth cervical (C6) transverse process; L2, scapulohumeral joint; and L3, first rib. For TA, the needle was introduced craniocaudally through L1, medial to the limb and cranial to L3. For PA, the needle was directed perpendicular and caudal to L2, aligned with L1, until cranial to L3. For AA, the needle was directed ventrodorsally, parallel and cranial to L3 until at L1. All BPs were scored for dyeing quality [0 (poor) to 5 (excellent)]. The left BP was dissected for nerve origins. Durbin test was used to compare scores (p < 0.05). ResultsIn all dogs, the musculocutaneous nerve originated from C7 and C8; the radial nerve from C8, the first thoracic vertebra (T1) (16/18 dogs) and C7 (2/18); and the median and ulnar nerves from C8, T1 (17/18) and C7 (1/18). Respective raw scores and adjusted scores for the incomplete block design were not significantly different (p = 0.72; ranks TA 16.5, PA 19.0, AA 18.5). Conclusions and clinical relevanceThe musculocutaneous, median, ulnar and radial nerves originate from C7, C8 and T1. Regardless of the technique, knowledge of anatomy and precise landmarks are relevant for correct dye dispersion.

On Multiple Covariance Equality Testing with Application to SAR Change Detection

This paper deals with the problem of testing the equality of $M$ covariance matrices. We first identify a suitable group of transformations leaving the problem invariant and obtain the corresponding maximal invariant statistic. Then, the Generalized Likelihood Ratio Test (GLRT) is recalled and explicit expressions for Rao, Wald, Gradient, and Durbin tests are provided. Also, equivalences among them and with other well-known tests proposed in open literature (mostly for the real-valued case) are analyzed and compared. Finally, the application of the proposed framework to the relevant signal processing application of multipass Coherent Change Detection (CCD) in polarimetric synthetic aperture radar is demonstrated both on simulated and on live data.