Abstract

Professional oboe players almost always have to make their own reeds, which involves a time-consuming process often fraught with wasted effort and discarded results. About one fourth of the total time spent on a reed involves getting it to a stage where it can be tried out on the oboe. Regression analysis was used to aid in making predictions about the ultimate quality of a finished reed based on data available at the initial try-out. The inputs to the regression model consist of several different characteristics of the cane used in making the reeds, and an assessment of the reed in its early stages through this initial try-out on the oboe. The goal to be able to decide whether or not to continue to work on the reed past this stage, based on the predictions of the regression. Thus far, the outcomes predicted by the regression have coincided reasonably closely with the actual outcomes in trials. Several regression models were tried, ranging from pure linear to curvilinear models that include interaction terms and/or squared terms. A particular curvilinear model was deemed the most appropriate.

References

1.
Vernier
,
V. G.
and
Shorter
,
L. C.
, “
Oboe Reed Survey
,”
The Double Reed
, Vol.
13
, No.
3
,
1991
, pp.
27
-
40
.
2.
Abramowitz
,
M.
and
Stegun
,
A.
, Eds.,
Handbook of Mathematical Functions
, National Bureau of Standards, Applied Mathematics Series 55,
1972
.
3.
Kmenta
,
J.
,
Elements of Econometrics
,
Macmillan Publishing Co., Inc.
,
New York
,
1971
.
4.
Lehmann
,
E. L.
,
Nonparametrics: Statistical Methods Based on Ranks
,
Holden-Day, Inc.
,
San Francisco
,
1975
.
5.
Bickel
,
P. J.
, and
Doksum
,
K. A.
,
Mathematical Statistics: Basic Ideas and Selected Topics
,
Holden-Day, Inc.
,
San Francisco
,
1977
.
6.
Feller
,
W.
,
An Introduction to Probability Theory and Its Application
(Vol.
II
),
Wiley
,
San Francisco
,
1971
.
7.
Anderson
,
D. R.
,
Sweeny
,
D. J.
, and
Williams
,
T. A.
,
Introduction to Statistics
,
West Publishing Company
,
St. Paul, MN
,
1991
.
8.
Johnson
,
L. W.
, “
Stochastic Parameter Regression: An Annotated Bibliography
,”
International Statistical Review
 0306-7734, Vol.
45
,
1977
, pp.
257
-
272
.
9.
Johnson
,
L. W.
, “
Stochastic Parameter Regression: an Additional Annotated Bibliography
,”
International Statistical Review
 0306-7734, Vol.
48
,
1980
, pp.
95
-
102
.
10.
Anderson
,
B. D. O.
and
Moore
,
J. B.
,
Optimal Filtering
,
Prentice Hall
,
Englewood Cliffs, NJ
,
1979
.
11.
Spall
,
J. C.
, Ed.,
Bayesian Analysis of Time Series and Dynamic Models
,
Marcel Dekker
,
New York
,
1988
.
12.
Cheng
,
B.
and
Titterington
,
D. M.
, “
Neural Networks: A Review From a Statistical Perspective (with discussion)
,”
Statistical Science
, Vol.
9
,
1994
, pp.
2
-
54
.
13.
Van Monfort
,
K.
,
Estimating in Structural Models with Non-Normal Distributed Variables: Some Alternative Approaches
, M & T Series 12,
DSWO Press
,
Leiden, Holland
,
1988
.
14.
Spall
,
J. C.
, “
The Kantorovich Inequality for Error Analysis of the Kalman Filter with Unknown Noise Distributions
,”
Automatica
 0005-1098, Vol.
31
,
1995
, pp.
1513
-
1517
.
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