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  • Hayter, Anthony J.  (6)
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  • 1
    Online Resource
    Online Resource
    Simultaneous Confidence Tubes in Multivariate Linear Regression
    Wiley ; 2016
    In:  Scandinavian Journal of Statistics Vol. 43, No. 3 ( 2016-09), p. 879-885
    Details
    In: Scandinavian Journal of Statistics, Wiley, Vol. 43, No. 3 ( 2016-09), p. 879-885
    Abstract: Simultaneous confidence bands have been shown in the statistical literature as powerful inferential tools in univariate linear regression. While the methodology of simultaneous confidence bands for univariate linear regression has been extensively researched and well developed, no published work seems available for multivariate linear regression. This paper fills this gap by studying one particular simultaneous confidence band for multivariate linear regression. Because of the shape of the band, the word ‘tube’ is more pertinent and so will be used to replace the word ‘band’. It is shown that the construction of the tube is related to the distribution of the largest eigenvalue. A simulation‐based method is proposed to compute the 1 − α quantile of this eigenvalue. With the computation power of modern computers, the simultaneous confidence tube can be computed fast and accurately. A real‐data example is used to illustrate the method, and many potential research problems have been pointed out.
    Type of Medium: Online Resource
    ISSN: 0303-6898 , 1467-9469
    URL: Issue
    URL: Article
    DOI: 10.1111/sjos.v43.3
    DOI: 10.1111/sjos.12217
    Language: English
    Publisher: Wiley
    Publication Date: 2016
    detail.hit.zdb_id: 186702-7
    detail.hit.zdb_id: 1466951-1
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    Online Resource
  • 2
    Online Resource
    Online Resource
    Critical point and power calculations for the studentized range test for generally correlated means
    Informa UK Limited ; 2001
    In:  Journal of Statistical Computation and Simulation Vol. 71, No. 2 ( 2001-11), p. 85-97
    Details
    In: Journal of Statistical Computation and Simulation, Informa UK Limited, Vol. 71, No. 2 ( 2001-11), p. 85-97
    Type of Medium: Online Resource
    ISSN: 0094-9655 , 1563-5163
    URL: Article
    DOI: 10.1080/00949650108812136
    Language: English
    Publisher: Informa UK Limited
    Publication Date: 2001
    detail.hit.zdb_id: 2004311-9
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    Online Resource
  • 3
    Online Resource
    Online Resource
    Normal probability plots with confidence
    Wiley ; 2015
    In:  Biometrical Journal Vol. 57, No. 1 ( 2015-01), p. 52-63
    Details
    In: Biometrical Journal, Wiley, Vol. 57, No. 1 ( 2015-01), p. 52-63
    Abstract: Normal probability plots are widely used as a statistical tool for assessing whether an observed simple random sample is drawn from a normally distributed population. The users, however, have to judge subjectively, if no objective rule is provided, whether the plotted points fall close to a straight line. In this paper, we focus on how a normal probability plot can be augmented by intervals for all the points so that, if the population distribution is normal, then all the points should fall into the corresponding intervals simultaneously with probability . These simultaneous probability intervals provide therefore an objective mean to judge whether the plotted points fall close to the straight line: the plotted points fall close to the straight line if and only if all the points fall into the corresponding intervals. The powers of several normal probability plot based (graphical) tests and the most popular nongraphical Anderson‐Darling and Shapiro‐Wilk tests are compared by simulation. Based on this comparison, recommendations are given in Section 3 on which graphical tests should be used in what circumstances. An example is provided to illustrate the methods.
    Type of Medium: Online Resource
    ISSN: 0323-3847 , 1521-4036
    URL: Issue
    URL: Article
    DOI: 10.1002/bimj.v57.1
    DOI: 10.1002/bimj.201300244
    RVK:
    WA 15000
    Language: English
    Publisher: Wiley
    Publication Date: 2015
    detail.hit.zdb_id: 131640-0
    detail.hit.zdb_id: 1479920-0
    SSG: 12
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  • 4
    Online Resource
    Online Resource
    Simultaneous inference for several quantiles of a normal population with applications
    Wiley ; 2013
    In:  Biometrical Journal Vol. 55, No. 3 ( 2013-05), p. 360-369
    Details
    In: Biometrical Journal, Wiley, Vol. 55, No. 3 ( 2013-05), p. 360-369
    Abstract: A common statistical problem is to make inference about the mean of a normally distributed population. While the mean and the variance are important quantities, many real problems require information on certain quantiles of the population which combine both the mean and variance. Motivated by two recent applications, we consider simultaneous inference for more than one quantile of interest. In this paper, a set of exact level simultaneous confidence intervals for several quantiles of a normally distributed population is constructed, based on a simple random sample from that population. The critical constants for achieving an exact simultaneous coverage probability can be computed efficiently using numerical quadrature involving only a one‐dimensional integral combined with standard search algorithms. The proposed methods are illustrated with an example. Several further research problems are identified.
    Type of Medium: Online Resource
    ISSN: 0323-3847 , 1521-4036
    URL: Issue
    URL: Article
    DOI: 10.1002/bimj.v55.3
    DOI: 10.1002/bimj.201100232
    RVK:
    WA 15000
    Language: English
    Publisher: Wiley
    Publication Date: 2013
    detail.hit.zdb_id: 131640-0
    detail.hit.zdb_id: 1479920-0
    SSG: 12
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  • 5
    Online Resource
    Online Resource
    Confidence Sets for Statistical Classification (II): Exact Confidence Sets
    MDPI AG ; 2019
    In:  Stats Vol. 2, No. 4 ( 2019-11-07), p. 439-446
    Details
    In: Stats, MDPI AG, Vol. 2, No. 4 ( 2019-11-07), p. 439-446
    Abstract: Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. Liu et al. (2019) proposed a confidence-set-based classifier that classifies a future object into a single class only when there is enough evidence to warrant this, and into several classes otherwise. By allowing classification of an object into possibly more than one class, this classifier guarantees a pre-specified proportion of correct classification among all future objects. However, the classifier uses a conservative critical constant. In this paper, we show how to determine the exact critical constant in applications where prior knowledge about the proportions of the future objects from each class is available. As the exact critical constant is smaller than the conservative critical constant given by Liu et al. (2019), the classifier using the exact critical constant is better than the classifier by Liu et al. (2019) as expected. An example is provided to illustrate the method.
    Type of Medium: Online Resource
    ISSN: 2571-905X
    URL: Article
    DOI: 10.3390/stats2040030
    Language: English
    Publisher: MDPI AG
    Publication Date: 2019
    detail.hit.zdb_id: 2934688-5
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  • 6
    Online Resource
    Online Resource
    Confidence Sets for Statistical Classification
    MDPI AG ; 2019
    In:  Stats Vol. 2, No. 3 ( 2019-06-30), p. 332-346
    Details
    In: Stats, MDPI AG, Vol. 2, No. 3 ( 2019-06-30), p. 332-346
    Abstract: Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. In statistical terms, classification is inference about the unknown parameters, i.e., the true classes of future objects. Hence, various standard statistical approaches can be used, such as point estimators, confidence sets and decision theoretic approaches. For example, a classifier that classifies a future object as belonging to only one of several known classes is a point estimator. The purpose of this paper is to propose a confidence-set-based classifier that classifies a future object into a single class only when there is enough evidence to warrant this, and into several classes otherwise. By allowing classification of an object into possibly more than one class, this classifier guarantees a pre-specified proportion of correct classification among all future objects. An example is provided to illustrate the method, and a simulation study is included to highlight the desirable feature of the method.
    Type of Medium: Online Resource
    ISSN: 2571-905X
    URL: Article
    DOI: 10.3390/stats2030024
    Language: English
    Publisher: MDPI AG
    Publication Date: 2019
    detail.hit.zdb_id: 2934688-5
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