Estimation of regression functions with certain monotonicity and concavity/convexity restrictions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Göteborg
Univ.
1994
|
| Schriftenreihe: | Statistiska Institutionen <Göteborg>: Skriftserie
23 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 253 S. graph. Darst. |
| ISBN: | 9122016414 |
Internformat
MARC
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| 100 | 1 | |a Dahlbom, Ulla |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Estimation of regression functions with certain monotonicity and concavity/convexity restrictions |c Ulla Dahlbom |
| 264 | 1 | |a Göteborg |b Univ. |c 1994 | |
| 300 | |a 253 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Statistiska Institutionen <Göteborg>: Skriftserie |v 23 | |
| 502 | |a Zugl.: Göteborg, Univ., Diss., 1994 | ||
| 650 | 4 | |a Estimation theory | |
| 650 | 4 | |a Regression analysis | |
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Datensatz im Suchindex
| _version_ | 1804124375721443328 |
|---|---|
| adam_text | CONTENTS:
page
1. INTRODUCTION 1
2. THE ESTIMATION PROCEDURE 4
2.1. Solutions to some problems 4
2.2. Monotonic increasing and concave regression 8
2.2.1 Fixed bending points 1 0
2.2.2 Changing bending points 1 6
2.3. General adjustments in the estimation method when
changing the concave/convex and the up/down
restrictions 1 9
2.3.1 Changes in the estimation procedure 20
2.3.2 The function systems in the inclusion part 2 2
2.3.3 The changing of p. in the inclusion part 2 4
J a
2.3.4 The changing of order relations between p. ,
and p 2 4
2.3.5 General remarks 2 4
2.4. Sigmoid regression 2 5
3. SIMULATIONS 2 9
4. SOME PROPERTIES FOR THE L.S. ESTIMATION METHOD 3 5
4.1. Convergence of the algorithm 3 5
4.2. Consistency 3 6
4.3. Some properties of the weights of the bending points 3 6
4.4. Some general properties 4 6
BIAS 5 3
5.1. Bias obtained from the estimation method 53
A
5.1.1 Bias of Y(x.) for a related problem 5 3
A
5.2. BiasofY(xk) for isotonic concave up regression
functions 5 6
A
5.2.1 BiasofY(xk) for isotonic concave regression
functions with constant curvature 57
A
5.2.2 BiasofY(x.) for isotonic concave regression
functions with linear functions 5 9
A
5.3. Bias of Y for concave unimodal regression
functions 6 1
A
5.3.1 The influence on bias of Y by the
max J
curvature of the regression function 61
A
5.3.1.1 Bias of Ymax for concave unimodal
regression functions with constant
curvature 6 2
A
5.3.1.2 Bias of Y for symmetric
max J
regression functions with piecewise
linear functions 6 7
A
5.3.2 The influence on bias of Y by the
max J
skewness of the regression function 6 9
5.3.2.1 The influence by the skewness on bias
A
ofY when the regression function
max °
is a third degree polynomial 6 9
5.3.2.2 The influence by the skewness on bias
A
ofY for piecewise linear regression
functions 7 0
A
5.3.3 Illustration of the nature of bias of YmQir
111 a A
by theoretical calculations and by simulations 7 1
A A
5.3.3.1 Comparison between E(Y ) and the
ordered E(Y.) 7 2
5.3.3.2 Distinction between bias caused by
the curvature and bias caused by the
estimation method 7 4
A
5.4. Bias of X for concave unimodal regression
in 3x
functions 7 9
A
5.4.1 Bias of X for symmetric regression functions 7 9
A
5.4.2 The influence on bias of X by the skewness
max J
of the regression function 8 1
A
5.4.2.1 The influence on bias of X by the
skewness when the regression function
is a third degree polynomial 8 1
A
5.4.2.2 The influence on bias of X by the
max J
skewness for regression functions with
piecewise linear functions 8 2
5.5. Bias of the inflection point in sigmoid regression 8 4
5.5.1 Bias of the estimate of the inflection point of
symmetric regression functions 8 4
5.5.2 Bias of the estimate of the inflection point of
non symmetric regression functions 8 6
A
5.5.3 Comparison between bias of Xjnf in sigmoid regression
A
and bias of X using the corresponding
max ° r
slopes between successive observations 8 7
6. VARIANCE 8 9
6.1. The variance of the constructed points for fixed
bending points 8 9
A
6.2. The influence on the variance of Y. by the curvature
of the increasing and concave regression function 92
A
6.2.1 Variance of Y(x.) for increasing and concave
regression functions with constant curvature 93
A
6.2.2 Variance of Y(x.) for increasing and concave
regression functions consisting of linear
functions 95
6.3. Some variance properties of the concave unimodal
A
regression function for stochastic X 9 7
A
6.3.1 The effect on the variance of Y by the
max J
curvature of the concave unimodal regression
function 9 7
A
6.3.1.1 Variance of Y for concave unimodal
max
regression functions with constant
curvature , 9 8
A
6.3.1.2 Variance of Ymax for concave unimodal
regression functions with piecewise
linear functions 99
A
6.3.2 The influence on the variance of X by the
max J
curvature of the concave unimodal regression
function 101
A
6.3.2.1 Variance of X for concave
max
unimodal regression functions with
constant curvature 1 0 2
A
6.3.2.2 Variance of Xmax for concave
unimodal regression functions with
piecewise linear functions 1 03
6.3.3 The influence on the variance of some
estimators by the skewness of the regression
function 106
6.4. Some variance properties of the inflection point of
the sigmoid regression function for stochastic X 106
6.4.1 The variance of the estimated y value of the
inflection point 107
6.4.2 The variance of the estimated x value of the
inflection point 109
A
6.4.3 Comparison between the variance of Xjn, in
A
sigmoid and the variance of X using the
in 2x
corresponding slopes between successive
observations Ill
6.5. Estimation of Var(Y) 1 12
6.5.1 Improvment of the proposed variance estimation
method for regression functions with big
curvature 119
6.5.2 Properties of the proposed variance estimation
method for a regression function with constant
curvature 122
6.5.3 Properties of the proposed variance estimation
method for regression functions with piecewise
linear functions 129
6.5.4 Properties of the proposed variance estimation
method for a skew regression function 132
6.5.5 Properties of the proposed variance estimation
method for sigmoid regression functions 135
THE DISTRIBUTION OF SOME ESTIMATORS 13 8
7.1. The distribution of Y|X 139
A
7.1.1 The distribution of Y|X for increasing and concave
regression functions with constant curvature 139
A
7.1.2 The distribution of Y|X for increasing and concave
regression functions with linear functions 147
7.2. The distribution of the maximum point in concave
unimodal regression 149
A
7.2.1 The influence on the distribution of Ym by
the curvature of the regression function 149
A
7.2.1.1 The distribution of Y for regression
functions with constant curvature 150
A
7.2.1.2 The distribution of Yfflax for symmetric
regression functions with piecewise
linear functions 151
7.2.1.3 Comparison between the cumulative
A
distribution of Ymax and the extreme
value function 152
A
7.2.2 The influence on the distribution of X by
max J
the curvature of the regression function 155
A
7.2.2.1 The distribution of Xmax for regression
functions with constant curvature 155
A
7.2.2.2 The distribution of XmQ, for regression
111 a A
functions with piecewise linear
functions 156
7.2.3 The influence on the distributions of some
estimators by the skewness of the regression
function 1 58
7.3. The estimation of the distribution of the inflection point
in sigmoid regression for stochastic X 159
7.3.1 The distribution of the estimated y value of the
inflection point 160
7.3.2 The distribution of the estimated x value of the
inflection point 162
8. CONFIDENCE INTERVALS 16 4
9. A BIOLOGICAL PROBLEM 1 6 8
9.1 Simulation results in some different situations using
binomially distributed variables with equal weights 178
9.1.1 Comparison of bias obtained for sigmoid
regression to bias obtained in some symmetric
and one non symmetric situations 179
9.1.2 Comparison of the variance obtained using
sigmoid regression to the variance obtained
in some alternative situations 182
9.2 Comparison between sigmoid regression and an ML
estimation method proposed by Schmoyer 186
9.2.1 The ML estimation method proposed by
Schmoyer 1 8 6
9.2.2 An example using Schmoyer s estimation
method 188
9.2.3 General remarks 190
10. COMPARISON BETWEEN THE PROPOSED ESTIMATION
METHOD AND OTHER SIMILAR METHODS 191
10.1. Comparison between concave up and isotonic
regression 191
10.1.1 The LSE method of isotonic regression 192
10.1.2 Comparison of some properties between
concave up and isotonic regression 193
10.1.2.1 Comparision of regression functions
with constant curvature 194
10.1.2.2 Comparision of symmetric regression
functions with linear functions 197
10.1.2.3 Comparison of theoretical results 201
10.1.2.4 Conclusions and remarks 201
10.2. Comparison between concave and unimodal
regression 201
10.2.1 The LSE method of unimodal regression 202
10.2.2 Comparison of some properties of
concave and unimodal regression 203
10.2.2.1 Comparison of estimatesof regression
functions with constant curvature 204
10.2.2.2 Comparison of regression functions
with piecewise linear functions 208
10.2.2.3 Comparison of theoretical results 212
10.2.2.4 Conclusions and remarks 213
10.3. Comparison between concave regression and an
estimation method proposed by Fraser and Massam 214
10.3.1 The estimation method proposed by Fraser
and Massam 21 4
10.3.2 An example using The Fraser and Massam
estimation method 217
10.3.3 The solution obtained from our proposed
estimation method 223
10.4. Comparison between concave regression and an
estimation method proposed by Wu 226
10.4.1 The estimation method proposed by Wu 226
10.4.2 The approximation proposed by Wu 230
10.4.2.1 An example using Wu s
approximation method 23 1
10.4.2.2 Some properties of Wu s
approximation method 23 2
10.5. Comparison between sigmoid regression and some
parametric estimation methods 240
10.5.1 Comparison when the regression function is
symmetric 241
10.5.2 Comparison when the regression function is
non symmetric 244
10.6. Comparison between sigmoid regression, logistic
regression and a discrete alternative to the logistic
regression proposed by Nash 246
10.6.1 The estimation method proposed by Nash 247
10.6.2 Two examples using the discrete alternative
estimation method proposed by Nash 248
REFERENCES 251
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| format | Thesis Book |
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| id | DE-604.BV009998955 |
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| indexdate | 2024-07-09T17:44:40Z |
| institution | BVB |
| isbn | 9122016414 |
| language | English |
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| series | Statistiska Institutionen <Göteborg>: Skriftserie |
| series2 | Statistiska Institutionen <Göteborg>: Skriftserie |
| spelling | Dahlbom, Ulla Verfasser aut Estimation of regression functions with certain monotonicity and concavity/convexity restrictions Ulla Dahlbom Göteborg Univ. 1994 253 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistiska Institutionen <Göteborg>: Skriftserie 23 Zugl.: Göteborg, Univ., Diss., 1994 Estimation theory Regression analysis Schätzung (DE-588)4193791-0 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Regressionsanalyse (DE-588)4129903-6 s Schätzung (DE-588)4193791-0 s DE-604 Statistiska Institutionen <Göteborg>: Skriftserie 23 (DE-604)BV000892564 23 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006628438&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dahlbom, Ulla Estimation of regression functions with certain monotonicity and concavity/convexity restrictions Statistiska Institutionen <Göteborg>: Skriftserie Estimation theory Regression analysis Schätzung (DE-588)4193791-0 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| subject_GND | (DE-588)4193791-0 (DE-588)4129903-6 (DE-588)4113937-9 |
| title | Estimation of regression functions with certain monotonicity and concavity/convexity restrictions |
| title_auth | Estimation of regression functions with certain monotonicity and concavity/convexity restrictions |
| title_exact_search | Estimation of regression functions with certain monotonicity and concavity/convexity restrictions |
| title_full | Estimation of regression functions with certain monotonicity and concavity/convexity restrictions Ulla Dahlbom |
| title_fullStr | Estimation of regression functions with certain monotonicity and concavity/convexity restrictions Ulla Dahlbom |
| title_full_unstemmed | Estimation of regression functions with certain monotonicity and concavity/convexity restrictions Ulla Dahlbom |
| title_short | Estimation of regression functions with certain monotonicity and concavity/convexity restrictions |
| title_sort | estimation of regression functions with certain monotonicity and concavity convexity restrictions |
| topic | Estimation theory Regression analysis Schätzung (DE-588)4193791-0 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Estimation theory Regression analysis Schätzung Regressionsanalyse Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006628438&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000892564 |
| work_keys_str_mv | AT dahlbomulla estimationofregressionfunctionswithcertainmonotonicityandconcavityconvexityrestrictions |