196,184 research outputs found
A study of partial F tests for multiple linear regression models
Get PDFPartial F tests play a central role in model selections in multiple linear regression models. This paper studies the partial F tests from the view point of simultaneous confidence bands. It first shows that there is a simultaneous confidence band associated naturally with a partial F test. This confidence band provides more information than the partial F test and the partial F test can be regarded as a side product of the confidence band. This view point of confidence bands also leads to insights of the major weakness of the partial F tests, that is, a partial F test requires implicitly the linear regression model holds over the entire range of the covariates in concern. Improved tests are proposed and they are induced by simultaneous confidence bands over restricted regions of the covariates. Power comparisons between the partial F tests and the new tests have been carried out to assess when the new tests are more or less powerful than the partial F tests. Computer programmes have been developed for easy implements of these new confidence band based inferential methods. An illustrative example is provided.<br/
Some new methods for the comparison of two linear regression models
No full textThe frequently used approach to the comparison of two linear regression models is to use the partial F test. It is pointed out in this paper that the partial F test has in fact a naturally associated two-sided simultaneous confidence band, which is much more informative than the test itself. But this confidence band is over the entire range of all the covariates. As regression models are true or of interest often only over a restricted region of the covariates, the part of this confidence band outside this region is therefore useless and to ensure 1 - ? simultaneous coverage probability is therefore wasteful of resources. It is proposed that a narrower and hence more efficient confidence band over a restricted region of the covariates should be used. The critical constant required in the construction of this confidence band can be calculated by Monte Carlo simulation. While this two-sided confidence band is suitable for two-sided comparisons of two linear regression models, a more efficient one-sided confidence band can be constructed in a similar way if one is only interested in assessing whether the mean response of one regression model is higher (or lower) than that of the other in the region. The methodologies are illustrated with two examples
Multiple comparison of several linear regression models
No full textResearch on multiple comparison during the past 50 years or so has focused mainly on the comparison of several population means. Several years ago, Spurrier considered the multiple comparison of several simple linear regression lines. He constructed simultaneous confidence bands for all of the contrasts of the simple linear regression lines over the entire range (-infin, infin) when the models have the same design matrices. This article extends Spurrier's work in several directions. First, multiple linear regression models are considered and the design matrices are allowed to be different. Second, the predictor variables are either unconstrained or constrained to finite intervals. Third, the types of comparison allowed can be very flexible, including pairwise, many–one, and successive. Two simulation methods are proposed for the calculation of critical constants. The methodologies are illustrated with examples
Simulation-based simultaneous confidence bands in multiple linear regression with predictor variables constrained in intervals
No full textThis article presents a method for the construction of a simultaneous confidence band for the normal-error multiple linear regression model. The confidence bands considered have their width proportional to the standard error of the estimated regression function, and the predictor variables are allowed to be constrained in intervals. Past articles in this area gave exact bands only for the simple regression model. When there is more than one predictor variable, only conservative bands are proposed in the statistics literature. This article advances this methodology by providing simulation-based confidence bands for regression models with any number of predictor variables. Additionally, a criterion is proposed to assess the sensitivity of a simultaneous confidence band. This criterion is defined to be the probability that a false linear regression model is excluded from the band at least at one point and hence this false linear regression model is correctly declared as a false model by the band. Finally, the article considers and compares several computational algorithms for obtaining the confidence band
Constant width simultaneous confidence bands for multiple linear regression when predictor variables are constrained in intervals
No full textPooling batches in drug stability study by using constant-width simultaneous confidence bands
No full textOne important study objective in drug stability studies is to estimate the shelf-life of a drug. A key statistical problem involved in this is how to assess the practical equivalence of different batches of the same drug so that different batches can be subgrouped to produce a single shelf-life for the drug. In this paper constant-width simultaneous confidence bands are proposed to quantify the magnitude of difference between different batches, with a particular view to establish the practical equivalence of different batches. This approach is suitable for the situation that the intercepts and slopes of the regression lines for the batches cannot be assumed to be equal. It is shown how constant-width simultaneous confidence bands can be easily constructed for the multiple comparison of several general linear regression models. In particular, it is shown that constant-width simultaneous confidence bands have a better chance to establish the equivalence than, and so are preferable to, the hyperbola-shaped simultaneous confidence bands considered
Gramian matrices in covariance stucture models
No full textCovariance structure models frequently contain
out-of-range estimates that make no sense from
either substantive or statistical points of view.
Negative variance estimates are the most well-known
of these improper solutions, but correlations
that are out of range also occur. Methods to
minimize improper estimates have been accomplished
by reparameterization and estimation under
simple inequality constraints; but these solutions,
discussed previously in this journal (Marsh, 1989),
do not guarantee that the covariance matrices
involved represent variances and covariances of real
numbers, as required. A general approach to avoiding
improper solutions in structural equation
models is proposed. Although this approach does
not resolve inadequacies in the data or theoretical
model that may generate an improper solution, it
solves the long-standing problem of obtaining
proper estimates. Index terms: confirmatory factor
analysis, EQS, Gramian matrices, Heywood cases,
improper solutions, LISREL, structural equation models,
underidentification.Bentler, P. M.; Jamshidian, Mortaza. (1994). Gramian matrices in covariance stucture models. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/116942
Numeraire Invariance and application to Option Pricing and Hedging
Get PDFThis is a short version of the paper of Exchange Options (2007), concentrating on the principle of numeraire invariance. It emphasizes application to unique pricing in arbitrage-free model, the derivation of hedge ratios and the PDE when price ratios are diffusions, explicit representations in the multivariate Poisson model, and the role played by homogeneity.Numeraire invariance, hedging, self-financing trading strategy, predictable representation, unique pricing, arbitrage-free, martingale, homogeneous payoff, Markovian, It\^o's formula, SDE, PDE, geometric Brownian motion, exponential Poisson process
On the combinatorics of iterated stochastic integrals
Get PDFThis paper derives several identities for the iterated integrals of a general semimartingale. They involve powers, brackets, exponential and the stochastic exponential. Their form and derivations are combinatorial. The formulae simplify for continuous or finite-variation semimartingales, especially for counting processes. The results are motivated by chaotic representation of martingales, and a simple such application is given.Semimartingale; iterated integrals; power jump processes; Ito's formula; stochastic exponential; chaotic representation
Dr. Duane M. Jackson, Morehouse College, July 2011
No full textThis video is a conversation with Dr. Duane M. Jackson. Dr. Jackson talks about his paper, "Recall and the Serial Position Effect: The Role of Primacy and Recency on Accounting Students' Performance." Jackie Daniel, AUC Woodruff Library, is the interviewer
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