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SPEAKER: |
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TITLE: |
"Accurate Approximate Likelihood Based Inference" |
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DAY: |
Wednesday, November 4, 1998 |
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TIME: |
3:30 p.m. [Coffee in BSB-202 at 3:00 p.m.] |
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PLACE: |
BSB-108 |
Recent third order approximate inference procedures have evolved either from the saddlepoint method (Daniels 1954, 1987; Barndorff-Nielsen & Cox 1979; Lugannani & Rice 1980) or from the direct analysis and Taylor series expansion of log density functions (Barndorff-Nielsen 1986; Fraser 1990; Fraser & Reid 1995). Tail probabilities at a particular parameter value can be obtained by these methods; however, it is generally restricted to the canonical parameter of the exponential model or to the location parameter of the transformation model. For more general models, Barndorff-Nielsen (1986) proposed a method which depends on the existence of an ancillary statistic.
In this talk, a more general approach to obtain third order approximate inference for any scalar parameter is proposed. The primary idea is based on the results in Fraser & Reid (1995). Examples are given to illustrate the simplicity, accuracy and generality of the proposed procedure.
Dr. Augustine Wong received his Ph.D. degree from the University of Toronto in 1990. He held a two-year postdoctoral position at the University of Waterloo after his Ph.D. studies, followed by one year in a tenure-track position as an Assistant Professor at the University of Alberta. He joined the Department of Mathematics and Statistics at York University as an Assistant Professor in 1993 and has been a tenured Associate Professor in that Department since 1996. He held the position of Director of Statistics in 1997. Dr. Wong is currently spending a sabbatical year at the Fields Institute and the University of Toronto. His present research interests are on applications of the likelihood based inference methods and the averaging method.
The main references that Dr. Wong will use in his talk are listed below. The reference Fraser & Reid (1995) has been placed on reserve at Thode Library (STATS 770: Statistics Seminar).
[1] Barndorff-Nielsen, O.E.(1986), "Inference on Full or Partial Parameters Based on the Standardized Signed Log Likelihood Ratio," BIOMETRIKA 73, pp. 307-322.
[2] Barndorff-Nielsen, O.E. & Cox, D.R. (1979), "Edgeworth and Saddlepoint Approximation With Statistical Applications (With Discussion)," JOURNAL OF THE ROYAL STATISTICAL SOCIETY B 41, pp. 279-312.
[3] Daniels, H.E. (1954), "Saddlepoint Approximation in Statistics," ANNALS OF MATHEMATICAL STATISTICS 25, pp. 631-650.
[4] Daniels, H.E. (1987), "Tail Probability Approximations," INTERNATIONAL STATISTICAL REVIEW 54, pp. 37-48.
[5] Fraser, D.A.S. (1990), "Tail Probabilities From Observed Likelihood," BIOMETRIKA 77, pp. 65-76.
[6] Fraser, D.A.S. & Reid, N. (1995), "Ancillaries and Third-Order Significance," UTILITAS MATHEMATICA 7, pp. 33-53.
[7] Reid, N. (1996), "Likelihood and Higher-Order Approximations to Tail Areas: a Review and Annotated Bibliography," CANADIAN JOURNAL OF STATISTICS 24, pp. 141-166.