Predictive Distribution of Regression Vector and Residual Sum of Squares for Normal Multiple Regression Model

Khan, Shahjahan

doi:10.1081/sta-200031471

Cited by 16 publications

(11 citation statements)

References 13 publications

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“…All the above studies deal with the prediction distribution of future responses. However, Khan (2004) proposed prediction distributions for the future regression vector (FRV) and future residual sum of squares (FRSS). Here we pursue the same approach to find the optimal β-expectation tolerance regions for the FRV and FRSS using the distribution of appropriate future statistics.…”

Section: Introductionmentioning

confidence: 99%

“…The two sets of responses are connected through the common, shape, regression and scale parameters. Following Khan (2004), we pursue the Bayesian approach to derive the distribution of the FRV and FRSS for the future responses, conditional on a set of realized responses. This is a new development that deals with the predictive inference for the future regression parameters, rather than that of the future responses.…”

Section: Introductionmentioning

confidence: 99%

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Optimal tolerance regions for some functions of multiple regression model with Student-t errors

Khan¹

2006

Journal of Statistics and Management Systems

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This paper considers the multiple regression model to determine optimal β-expectation tolerance regions for the future regression vector (FRV) and future residual sum of squares (FRSS) by using the prediction distributions of some appropriate functions of future responses. It is assumed that the errors of the regression model follow a multivariate Student-t distribution with unknown shape parameter, ν. The prediction distribution of the FRV, conditional on the observed responses, is a multivariate Student-t distribution but its shape parameter does not depend on the unknown degrees of freedom of the Student-t model. Similarly, the prediction distribution of the FRSS is a beta distribution. The optimal β-expectation tolerance regions for the FRV and FRSS have been obtained based on the F -distribution and beta distribution respectively.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal tolerance regions for some functions of multiple regression model with Student-t errors

Khan¹

2006

Journal of Statistics and Management Systems

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“…MODEL OPTIMIZATION AND RESULTS In this section, the main optimization goal is to minimize an error. The residual sum of squares (RSS; also known as sum of squared error, SSE) [11] metric has been chosen to measure error value. It is calculated as a sum of error term values from each sample:…”

Section: Model Constructionmentioning

confidence: 99%

A Database Performance Polynomial Multiple Regression Model

Nowosielski

Kowalski

Kulczycki

2017

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

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Abstract-Modelling of a database performance depending on numerous factors is the first step towards its optimization. The linear regression model with optional parameters was created. Regression equation coefficients are optimized with the Flower Pollination metaheuristic algorithm. The algorithm is executed with numerous possible execution parameter combinations and results are discussed. Potential obstacles are discussed and alternative modelling approaches are mentioned.

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“…To test the null hypothesis on the intercept vector H 0 : β 0 = β 00 (given known vector) against H a : β 0 > β 00 in the multivariate simple regression model (ii) The cdf for m=10, n=20, ρ=0.5, θ j =1.5, j, k=1,2, j ≠ k (for details, see Khan, 2006) when there is non-sample prior information on the slope vector β 1 , the test statistic follows a correlated bivariate F distribution. The ultimate test on H 0 is called the pre-test test (PTT) because it depends on the outcome of the pre-test on the suspected slope; that is, H * 0 = β 1 = β 10 (cf.…”

Section: Application To the Power Function Of The Pttmentioning

confidence: 99%

The Correlated Bivariate NoncentralFDistribution and Its Application

Khan

Pratikno

Ibrahim

et al. 2015

Communications in Statistics - Simulation and Computation

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Abstract:This paper proposes the singly and doubly correlated bivariate noncentral F (BNCF) distributions. The probability density function (pdf) and the cumulative distribution function (cdf) of the distributions are derived for arbitrary values of the parameters. The pdf and cdf of the distributions for different arbitrary values of the parameters are computed, and their graphs are plotted by writing and implementing new R codes. An application of the correlated BNCF distribution is illustrated in the computations of the power function of the pretest test for the multivariate simple regression model (MSRM).Note: The following files were submitted by the author for peer review, but cannot be converted to PDF. You must view these files (e.g. movies) online. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 The bivariate central F (BCF) distribution has been studied by many authors, including Krishaniah (1965a), Amos and Bulgren (1972), Schuurmann et al. (1975), Johnson et al. (1995) and El-Bassiouny and Jones (2009). Krishnaiah (1965b) described the use of the BCF distribution in a problem of simultaneous statistical inference. Krishnaiah (1965c) and Krishnaiah and Armitage (1965) later studied the multivariate central F distribution. Hewett and Bulgren (1971) studied the prediction interval for failure times in certain life testing experiments using the multivariate central F distribution.Many authors have also studied the univariate noncentral F distribution, including Mudholkar et al. (1976), Muirhead (1982, Johnson et al. (1995), and Shao (2005). Johnson et al. (1995 provided the definition of the univariate noncentral F distribution known as the singly noncentral F distribution. The authors also described the doubly noncentral F distribution with (ν 1 , ν 2 ) degrees of freedom and noncentrality parameters λ 1 and λ 2 as the ratio of two independent noncentral chi-square variables, χ Tiku (1966) proposed an approximation to the multivariate noncentral F distribution.In the study of improving the power of a statistical test by pre-testing the uncertain non-sample prior information (NSPI) on the value of a set of parameters (cf. Saleh andSen, 1983, andKhan, 2011a), the cdf of a bivariate noncentral chi-square distribution is used to compute the power function of the test. For large sample studies, the cdf of the bivariate noncentral chi-square (BNCC) distribution is used to compute the power function of the test for testing one subset of regression parameters after pre-testing on another subset of parameters of a multivariate simple regression model (MSRM) (cf. Saleh and Sen, 1983, Yunus andKhan, 2011a). For s...

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Predictive Distribution of Regression Vector and Residual Sum of Squares for Normal Multiple Regression Model

Cited by 16 publications

References 13 publications

Optimal tolerance regions for some functions of multiple regression model with Student-t errors

Optimal tolerance regions for some functions of multiple regression model with Student-t errors

A Database Performance Polynomial Multiple Regression Model

The Correlated Bivariate NoncentralFDistribution and Its Application

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