Relevant bibliographies by topics / Hotelling's T^2 statistic

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  2. Dissertations / Theses
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  4. Conference papers

Academic literature on the topic 'Hotelling's T^2 statistic'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Hotelling's T^2 statistic"

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Dembo, Amir, and Qi-Man Shao. "Large and Moderate Deviations for Hotelling's $T^2$-Statistics." Electronic Communications in Probability 11 (2006): 149–59. http://dx.doi.org/10.1214/ecp.v11-1209.

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Sparks, Ross. "Monitoring Highly Correlated Multivariate Processes Using Hotelling's T 2 Statistic: Problems and Possible Solutions." Quality and Reliability Engineering International 31, no. 6 (June 9, 2014): 1089–97. http://dx.doi.org/10.1002/qre.1656.

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Polymenis. "An Application of Univariate Statistics to Hotelling's T2." Journal of Mathematics and Statistics 7, no. 1 (January 1, 2011): 86–94. http://dx.doi.org/10.3844/jmssp.2011.86.94.

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Freeman, Jade, and Reza Modarres. "Efficiency of t-Test and Hotelling's T 2-Test After Box-Cox Transformation." Communications in Statistics - Theory and Methods 35, no. 6 (July 2006): 1109–22. http://dx.doi.org/10.1080/03610920600672203.

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Rencher, Alvin C. "The Contribution of Individual Variables to Hotelling's T 2 , Wilks' Λ, and R 2." Biometrics 49, no. 2 (June 1993): 479. http://dx.doi.org/10.2307/2532560.

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Liu, Weidong, and Qi-Man Shao. "A Cramér moderate deviation theorem for Hotelling’s $T^{2}$-statistic with applications to global tests." Annals of Statistics 41, no. 1 (February 2013): 296–322. http://dx.doi.org/10.1214/12-aos1082.

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Ateş, Can, Özlem Kaymaz, H. Emre Kale, and Mustafa Agah Tekindal. "Comparison of Test Statistics of Nonnormal and Unbalanced Samples for Multivariate Analysis of Variance in terms of Type-I Error Rates." Computational and Mathematical Methods in Medicine 2019 (July 18, 2019): 1–8. http://dx.doi.org/10.1155/2019/2173638.

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In this study, we investigate how Wilks’ lambda, Pillai’s trace, Hotelling’s trace, and Roy’s largest root test statistics can be affected when the normal and homogeneous variance assumptions of the MANOVA method are violated. In other words, in these cases, the robustness of the tests is examined. For this purpose, a simulation study is conducted in different scenarios. In different variable numbers and different sample sizes, considering the group variances are homogeneous σ12=σ22=⋯=σg2 and heterogeneous (increasing) σ12<σ22<⋯<σg2, random numbers are generated from Gamma(4-4-4; 0.5), Gamma(4-9-36; 0.5), Student’s t(2), and Normal(0; 1) distributions. Furthermore, the number of observations in the groups being balanced and unbalanced is also taken into account. After 10000 repetitions, type-I error values are calculated for each test for α = 0.05. In the Gamma distribution, Pillai’s trace test statistic gives more robust results in the case of homogeneous and heterogeneous variances for 2 variables, and in the case of 3 variables, Roy’s largest root test statistic gives more robust results in balanced samples and Pillai’s trace test statistic in unbalanced samples. In Student’s t distribution, Pillai’s trace test statistic gives more robust results in the case of homogeneous variance and Wilks’ lambda test statistic in the case of heterogeneous variance. In the normal distribution, in the case of homogeneous variance for 2 variables, Roy’s largest root test statistic gives relatively more robust results and Wilks’ lambda test statistic for 3 variables. Also in the case of heterogeneous variance for 2 and 3 variables, Roy’s largest root test statistic gives robust results in the normal distribution. The test statistics used with MANOVA are affected by the violation of homogeneity of covariance matrices and normality assumptions particularly from unbalanced number of observations.
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Ben Nouma, Badreddine, Amar Mitiche, Youssef Ouakrim, and Neila Mezghani. "Pattern Classification by the Hotelling Statistic and Application to Knee Osteoarthritis Kinematic Signals." Machine Learning and Knowledge Extraction 1, no. 3 (July 5, 2019): 768–84. http://dx.doi.org/10.3390/make1030045.

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The analysis of knee kinematic data, which come in the form of a small sample of discrete curves that describe repeated measurements of the temporal variation of each of the knee three fundamental angles of rotation during a subject walking cycle, can inform knee pathology classification because, in general, different pathologies have different kinematic data patterns. However, high data dimensionality and the scarcity of reference data, which characterize this type of application, challenge classification and make it prone to error, a problem Duda and Hart refer to as the curse of dimensionality. The purpose of this study is to investigate a sample-based classifier which evaluates data proximity by the two-sample Hotelling T 2 statistic. This classifier uses the whole sample of an individual’s measurements for a better support to classification, and the Hotelling T 2 hypothesis testing made applicable by dimensionality reduction. This method was able to discriminate between femero-rotulian (FR) and femero-tibial (FT) knee osteoarthritis kinematic data with an accuracy of 88.1 % , outperforming significantly current state-of-the-art methods which addressed similar problems. Extended to the much harder three-class problem involving pathology categories FR and FT, as well as category FR-FT which represents the incidence of both diseases FR and FT in a same individual, the scheme was able to reach a performance that justifies its further use and investigation in this and other similar applications.
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Van Dun, Bram, Harvey Dillon, and Mark Seeto. "Estimating Hearing Thresholds in Hearing-Impaired Adults through Objective Detection of Cortical Auditory Evoked Potentials." Journal of the American Academy of Audiology 26, no. 04 (April 2015): 370–83. http://dx.doi.org/10.3766/jaaa.26.4.5.

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Background: Hearing threshold estimation based on cortical auditory evoked potentials (CAEPs) has been applied for some decades. However, available research is scarce evaluating the accuracy of this technique with an automated paradigm for the objective detection of CAEPs. Purpose: To determine the difference between behavioral and CAEP thresholds detected using an objective paradigm based on the Hotelling’s T 2 statistic. To propose a decision tree to choose the next stimulus level in a sample of hearing-impaired adults. This knowledge potentially could increase the efficiency of clinical hearing threshold testing. Research Design: Correlational cohort study. Thresholds obtained behaviorally were compared with thresholds obtained through cortical testing. Study Sample: Thirty-four adults with hearing loss participated in this study. Data Collection and Analysis: For each audiometric frequency and each ear, behavioral thresholds were collected with both pure-tone and 40-msec tone-burst stimuli. Then, corresponding cortical hearing thresholds were determined. An objective cortical-response detection algorithm based on the Hotelling’s T 2 statistic was applied to determine response presence. A decision tree was used to select the next stimulus level. In total, 241 behavioral-cortical threshold pairs were available for analysis. The differences between CAEP and behavioral thresholds (and their standard deviations [SDs]) were determined for each audiometric frequency. Cortical amplitudes and electroencephalogram noise levels were extracted. The practical applicability of the decision tree was evaluated and compared to a Hughson-Westlake paradigm. Results: It was shown that, when collapsed over all audiometric frequencies, behavioral pure-tone thresholds were on average 10 dB lower than 40-msec cortical tone-burst thresholds, with an SD of 10 dB. Four percent of CAEP thresholds, all obtained from just three individual participants, were more than 30 dB higher than their behavioral counterparts. The use of a decision tree instead of a Hughson-Westlake procedure to obtain a CAEP threshold did not seem to reduce test time, but there was significantly less variation in the number of CAEP trials needed to determine a threshold. Conclusions: Behavioral hearing thresholds in hearing-impaired adults can be determined with an acceptable degree of accuracy (mean threshold correction and SD of both 10 dB) using an objective statistical cortical-response detection algorithm in combination with a decision tree to determine the test levels.
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Jiamwattanapong, Knavoot, and Samruam Chongcharoen. "A Two-Sample Test for Mean Vectors in High-Dimensional Data." Applied Science and Innovative Research 1, no. 2 (November 10, 2017): 118. http://dx.doi.org/10.22158/asir.v1n2p118.

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<p><em>Modern measurement technology has enabled the capture of high-dimensional data by researchers and statisticians and classical statistical inferences, such as </em><em>the renowned Hotelling’s T<sup>2</sup> test, are no longer valid when the dimension of the data equals or exceeds the sample size. Importantly, when correlations among variables in a dataset exist, taking them into account in the analysis method would provide more accurate conclusions. In this article, we consider the hypothesis testing problem for two mean vectors in high-dimensional data with an underlying normality assumption. A new test is proposed based on the idea of keeping more information from the sample covariances. The asymptotic null distribution of the test statistic is derived. The simulation results show that the proposed test performs well comparing with other competing tests and becomes more powerful when the dimension increases for a given sample size. The proposed test is also illustrated with an analysis of DNA microarray data. </em></p>
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Dissertations / Theses on the topic "Hotelling's T^2 statistic"

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Williams, James Dickson. "Contributions to Profile Monitoring and Multivariate Statistical Process Control." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/30032.

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The content of this dissertation is divided into two main topics: 1) nonlinear profile monitoring and 2) an improved approximate distribution for the T^2 statistic based on the successive differences covariance matrix estimator. (Part 1) In an increasing number of cases the quality of a product or process cannot adequately be represented by the distribution of a univariate quality variable or the multivariate distribution of a vector of quality variables. Rather, a series of measurements are taken across some continuum, such as time or space, to create a profile. The profile determines the product quality at that sampling period. We propose Phase I methods to analyze profiles in a baseline dataset where the profiles can be modeled through either a parametric nonlinear regression function or a nonparametric regression function. We illustrate our methods using data from Walker and Wright (2002) and from dose-response data from DuPont Crop Protection. (Part 2) Although the T^2 statistic based on the successive differences estimator has been shown to be effective in detecting a shift in the mean vector (Sullivan and Woodall (1996) and Vargas (2003)), the exact distribution of this statistic is unknown. An accurate upper control limit (UCL) for the T^2 chart based on this statistic depends on knowing its distribution. Two approximate distributions have been proposed in the literature. We demonstrate the inadequacy of these two approximations and derive useful properties of this statistic. We give an improved approximate distribution and recommendations for its use.
Ph. D.
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Rupasinghe, Arachchige Don Hasthika Sriyantha. "BOOTSTRAPPING ANALOGS OF THE ONE WAY MANOVA TEST." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/dissertations/1425.

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The classical one way MANOVA model is used to test whether the mean measurements are the same or differ across p groups, and assumes that the covariance matrix of each group is the same. This work suggests using the Olive (2017abc) bootstrap technique to develop analogs of one way MANOVA test. A large sample theory test has also been developed. The bootstrap tests can have considerable outlier resistance, and the tests do not need the population covariance matrices to be equal. The two sample Hotelling's T^2 test is the special case of the one way MANOVA model when p =2.
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Book chapters on the topic "Hotelling's T^2 statistic"

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Rafajłowicz, Ewaryst, and Ansgar Steland. "The Hotelling—Like $$T^2$$ T 2 Control Chart Modified for Detecting Changes in Images having the Matrix Normal Distribution." In Springer Proceedings in Mathematics & Statistics, 193–206. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28665-1_14.

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Tracy, Nola D., John C. Young, and Robert L. Mason. "Some Aspects of Hotelling’s T 2 Statistic for Multivariate Quality Control." In Statistics of Quality, 77–100. CRC Press, 2020. http://dx.doi.org/10.1201/9781003067559-5.

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Babu, Suresh C., and Shailendra N. Gajanan. "Implications of technological change, postharvest technology, and technology adoption for improved food security—application of t-statistic." In Food Security, Poverty and Nutrition Policy Analysis, 27–66. Elsevier, 2022. http://dx.doi.org/10.1016/b978-0-12-820477-1.00029-2.

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JOHANNSEN, PETER, SØREN B. HANSEN, LEIF ØSTERGAARD, and ALBERT H. GJEDDE. "Optimization of H215O Dose and Data Acquisition in Three-Dimensional Activation Studies Using an ECAT EXACT HR-47 PET Camera and Voxel-by-Voxel t -Statistic." In Quantitative Functional Brain Imaging with Positron Emission Tomography, 41–44. Elsevier, 1998. http://dx.doi.org/10.1016/b978-012161340-2/50008-1.

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Conference papers on the topic "Hotelling's T^2 statistic"

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Acharya, Anuja Kumar, Biswajit Sahoo, and Biswa Ranjan Swain. "Object tracking using a new statistical multivariate hotelling's T2 approach." In 2014 IEEE International Advance Computing Conference (IACC). IEEE, 2014. http://dx.doi.org/10.1109/iadcc.2014.6779454.

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Wang, Chau-Shing, Jing-Er Chiu, and Syuan-Fong Jhong. "Fuzzy Inference System based assignable cause diagnosis using Hotelling's T2 control chart patterns." In 2013 10th International Conference on Service Systems and Service Management (ICSSSM). IEEE, 2013. http://dx.doi.org/10.1109/icsssm.2013.6602585.

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Li, FengChia, PengKai Wang, LiLon Yeh, and ShengWen Hong. "Economic process control for multivariate quality characteristics with Hotelling's T2 charts under Gamma shock model." In 2011 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM). IEEE, 2011. http://dx.doi.org/10.1109/ieem.2011.6118169.

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Li, FengChia, PengKai Wang, LiLon Yeh, and ShengWen Hong. "Economic process control for multivariate quality characteristics with Hotelling's T2 charts under Gamma shock model." In 2011 IEEE MTT-S International Microwave Workshop Series on Innovative Wireless Power Transmission: Technologies, Systems, and Applications (IMWS 2011). IEEE, 2011. http://dx.doi.org/10.1109/imws.2011.6115425.

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Liying Jiang, Baojian Xu, Jianhui Xi, Jianguo Cui, and Li Fu. "Improved confidence limits of T2 statistic for monitoring batch processes." In 2012 24th Chinese Control and Decision Conference (CCDC). IEEE, 2012. http://dx.doi.org/10.1109/ccdc.2012.6243070.

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GÓRNICKI, Krzysztof, Agnieszka KALETA, and Aneta CHOIŃSKA. "EXTENSION OF WEIBULL MODEL FOR DESCRIBING OF DRIED APPLE REHYDRATION." In RURAL DEVELOPMENT. Aleksandras Stulginskis University, 2018. http://dx.doi.org/10.15544/rd.2017.026.

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Sample of Ligol variety apples (slices of 3 and 10 mm thickness and cubes of 10 mm thickness) were dried using following methods: natural convection (drying air velocity amounted to 0.01 m/s), forced convection (0.5 and 2 m/s), fluidized bed drying (6 m/s). The drying air temperature was kept at 50, 60, and 70C. The dried apples samples were rehydrated in distilled water at 20, 45, 70, and 95C. The Weibull model given for describing time dependence of the moisture content change was fitted to experimental data and model parameters were determined by multiple regression analysis. The variation of model parameters with characteristic particle dimension (L), drying air velocity (v), drying air temperature (td), and rehydration temperature (tr) described as multiplication type. By using these verification of parameters, extended Weibull model for describing combine effects of L, v, td, tr, and drying time was derived and the parameters of the model were also determined by multiple regression analysis. The accuracies of both models were measured using the determination coefficient (R2), mean bias error (MBE), root mean square error (RMSE), reduced chi-square (2), and t-statistic method. The Weibull model (R2=0.8319-0.9957, MBE=-0.0044-0.0110, RMSE=0.0189-0.1248, 2=0.0004-0.0180, and t-stat=0.0149-0.2875) and the extended Weibull model (R2=0.9130-0.9948, MBE=-0.0209-0.0377, RMSE=0.0230-0.0719, 2=0.0007-0.0057, and t-stat=0.0389-1.2214) described the rehydration characteristics of dried apple satisfactorily. The extended model by taking into account the effect of L, v, td, and tr on its parameters can be considered as more general one.
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Fedorov, Sergey S., Mykhailo V. Gubynskyi, Igor V. Barsukov, Mykola V. Livitan, Oleksiy G. Gogotsi, and Upendra Singh Rohatgi. "Modeling the Operation Regimes in Ultra-High Temperature Continuous Reactors." In ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting collocated with the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/fedsm2014-22161.

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The main advantage of carbon material treatment in electro-thermal furnaces with fluidized bed [EFFB] at 2000–3000C is that they allow producing graphite of high chemical purity, which is especially important in manufacture of ion-lithium batteries. The team conducted extensive research into hydraulic and heat modes of such units and developed a methodology for their design based on the concept of increase in electric resistance with fluidization. The choice of the working space configuration and the operation mode of EFFB are largely determined by the specific electrical resistance [SER] of the fluidized bed. This parameter is a complex function of a number of factors: fluidization character, uniformity of the bed and the temperature, nature and size of the material fractions, current density and furnace atmosphere composition. It is vital to take into account relationships between SER, working temperature T and current density i, which eventually define electrothermal mode of the unit operation. Thus, if graphite size is d = 130μm within temperature range T = 0–2500C and current density i = 0,004–1.0 A/cm2, SER varies in reverse proportion to these parameters Statistic processing of the experimental data allowed to obtain regressive function SER = f (i, t), which we used as the basis of mathematic modeling, heat balance calculation and predicting transitory and operation modes of EFFB with 10kg/hour productivity: SER=0.01.84.711-2.,593*10-2.T-46.854*i+1.205*10-2.T*i,Ω-m′ Resulting volt-ampere characteristics (VACs) of the furnace have maximum values at constant temperature (T = const) which is explained by the non-linear character of the SER function. There exists a technological temperature limit of EFFB responsible for its stable operation. The furnace operation beyond the stability margin depends on the power source characteristics which may cause a sharp power drop or a shorting. The VAC characteristics are determined by the type of material, geometry of the furnace working space, electrode diameter, active zone height, the gap between the electrode and the lining, design of heat insulation and the cooling system. Taking these parameters into consideration, it is possible to conduct a preliminary analysis of the unit stable operation modes as early as during the design stage.
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