Nonparametric econometrics:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge <<[u.a.]>>
Cambridge Univ. Press
2004
|
| Series: | Themes in modern econometrics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Digital printing |
| Physical Description: | XVIII, 424 S. graph. Darst. |
| ISBN: | 0521586119 0521355648 |
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| _version_ | 1804140640673464320 |
|---|---|
| adam_text | Contents
Preface
page
xvii
1
Introduction
1
2
Methods of Density Estimation
5
2.1
Introduction
5
2.2
Nonparametric Density Estimation
7
2.2.1
A Local Histogram Approach
7
2.2.2
A Formal Derivation of
ƒ ,(*) 9
2.2.3
Rosenblatt-Parzen Kernel Estimator
9
2.2.4
The Nearest Neighborhood Estimator
11
2.2.5
Variable Window-Width Estimators
12
2.2.6
Series Estimators
13
2.2.7
Penalized Likelihood Estimators
15
2.2.8
The Local Log-Likelihood Estimators
17
2.2.9
Summary
19
2.3
Estimation of Derivatives of a Density
19
2.4
Finite-Sample Properties of the Kernel Estimator
20
2.4.1
The Exact Bias and Variance of the Estimator
ƒ 21
2.4.2
Approximations to the Bias and Variance and
Choices of
h
and
К
23
2.4.3
Reduction of
В
ias
29
2.5
Asymptotic Properties of the Kernel Density Estimator
ƒ
with Independent Observations
32
2.5.1
Asymptotic Unbiasedness
33
2.5.2
Consistency
34
2.5.3
Asymptotic Normality
39
2.5.4
Small-Sample Confidence Intervals
42
2.6
Sampling Properties of the Kernel Density Estimator
with Dependent Observations
43
Contents
2.6.1 Unbiasedness 43
2.6.2 Consistency 43
2.6.3
Asymptotic Normality
48
2.6.4
Bibliographical Summary (Approximate and
Asymptotic Results)
48
2.7
Choices of Window Width and Kernel: Further Discussion
49
2.7.1
Choice of
h
49
2.7.2
Choice of Higher Order Kernels
54
2.7.3
Choice of
h
for Density Derivatives
56
2.8
Multivariate Density Estimation
57
2.9
Testing Hypotheses about Densities
60
2.9.1
Comparison with a Known Density Function
61
2.9.2
Testing for Symmetry
67
2.9.3
Comparison of Unknown Densities
68
2.9.4
Testing for Independence
69
2.10
Examples
71
2.10.1
Density of Stock
Märket
Returns
71
2.10.2
Estimating the Dickey-Fuller Density
74
Conditional Moment Estimation
78
3.1
Introduction
78
3.2
Estimating Conditional Moments by Kernel Methods
79
3.2.1
Parametric Estimation
80
3.2.2
Nonparametric Estimation: A Local Regression
Approach
81
3.2.3
Kernel-Based Estimation: A Formal Derivation
83
3.2.4
A General Nonparametric Estimator of
m
(де)
84
3.2.5
Unifying Nonparametric Estimators
86
3.2.6
Estimation of Higher Order Conditional Moments
95
3.3
Finite-Sample Properties
95
3.3.1
Approximate Results: Stochastic jc
96
3.3.2
The Local Linear Regression Estimator
104
3.3.3
Combining Parametric and Nonparametric
Estimators
106
3.4
Asymptotic Properties
108
3.4.1
Asymptotic Properties of the Kernel Estimator
with Independent Observations
108
3.4.2
Asymptotic Properties of the Kernel Estimator
with Dependent Observations
115
3.5
Bibliographical Summary (Asymptotic Results)
116
Contents xi
3.6
Implementing the Kernel Estimator
118
3.6.1
Choice of Window Width
118
3.7
Robust Nonparametric Estimation of Moments
122
3.8
Estimating Conditional Moments by Series Methods
123
3.9
Asymptotic Properties of Series Estimators with
Independent Observations
126
3.10
Asymptotic Properties of Series Estimators with
Dependent Observations
133
3.11
Implementing the Estimator
133
3.12
Imposing Structure on the Conditional Moments
137
3.12.1
Generalized Additive Models
137
3.12.2
Projection Pursuit Regression
139
3.12.3
Neural Networks
140
3.13
Measuring the Affinity of Parametric and
Nonparametric Models
141
3.14
Examples
150
3.14.1
A Model of Strike Duration
150
3.14.2
Earnings-Age Profiles
152
3.14.3
Review of Applied Work on Nonparametric
Regression
157
4
Nonparametric Estimation of Derivatives
160
4.1
Introduction
160
4.2
The Model and Partial Derivative Formulae
161
4.3
Estimation
164
4.3.1
Estimation of Partial Derivatives by Kernel Methods
164
4.3.2
Estimation of Partial Derivatives by Series Methods
167
4.3.3
Estimation of Average Derivatives
167
4.3.4
Local Linear Derivative Estimators
170
4.3.5
Pointwise Versus Average Derivatives
172
4.4
Restricted Estimation and Hypothesis Testing
173
4.4.1
Imposing Linear Equality Restriction on Partial
Derivatives
174
4.4.2
Imposing Linear Inequality Restrictions
175
4.4.3
Hypothesis Testing
176
4.5
Asymptotic Properties of Partial Derivative Estimators
177
4.5.1
Asymptotic Properties of Kernel-Based Estimators
178
4.5.2
Series-Based Estimators
182
4.5.3
Higher Order Derivatives
182
4.5.4
Local Linear Estimators
183
xii Contents
4.6
Asymptotic Properties of Kernel-Based Average
Derivative Estimators
184
4.7
Implementing the Derivative Estimators
189
4.8
Illustrative Examples
190
4.8.1
A Monte Carlo Experiment with a Production
Function
190
4.8.2
Earnings-Age Relationship
192
4.8.3
Review of Applied Work
194
5
Semiparametric Estimation of Single-Equation Models
196
5.1
Introduction
196
5.2
Semiparametric Estimation of the Linear Part of
a Regression Model
198
5.2.1
General Results
198
5.2.2
Diagnostic Tests after Nonparametric Regression
208
5.2.3
Semiparametric Estimation of Some Macro Models
210
5.2.4
The Asymptotic Covariance Matrix of SP
Estimators without Asymptotic Independence
212
5.3
Efficient Estimation of Semiparametric Models in the
Presence of Heteroskedasticity of Unknown Form
214
5.4
Conditions for Adaptive Estimation
217
5.5
Efficient Estimation of Regression Parameters
with Unknown Error Density
225
5.5.1
Efficient Estimation by Likelihood Approximation
225
5.5.2
Efficient Estimation by Kernel-Based Score
Approximation
227
5.5.3
Efficient Estimation by Moment-Based Score
Approximation
230
5.6
Estimation of Scale Parameters
234
5.7
Optimal Diagnostic Tests in Linear Models
234
5.8
Adaptive Estimation with Dependent Observations
235
5.9
M-Estimators
237
5.9.1
Estimation
237
5.9.2
Diagnostic Tests with M-Estimators
242
5.9.3
Sequential M-Estimators
243
5.10
The Semiparametric Efficiency Bound for Moment-Based
Estimators
245
5.10.1
Approximating the SP Efficiency Bound by a
Conditional Moment Estimator
246
5.11
Applications
248
5.11.1
Semiparametric Estimation of a Heteroskedastic
Model
248
Contents xi
5.11.2
Adaptive
Estimation
of a Model of House Prices
250
5.11.3
Review of Other Applications
251
Semiparametric and Nonparametric Estimation of
Simultaneous Equation Models
254
6.1
Introduction
254
6.2
Single-Equation Estimators
255
6.2.1
Parametric Estimation
. 256
6.2.2
Rilstone s Semiparametric Two-Stage Least
Squares Estimator
258
6.3
Systems Estimation
260
6.3.1
A Parametric Estimator
260
6.3.2
The SP3SLS Estimator
261
6.3.3
Newey s Estimator
262
6.3.4
Newey s Efficient Distribution-Free Estimators
264
6.4
Finite-Sample Properties
267
6.5
Nonparametric Estimation
269
6.5.1
Identification
269
6.5.2
Nonparametric Two-Stage Least Squares
(2SLS) Estimation
270
Semiparametric Estimation of Discrete Choice Models
272
7.1
Introduction
272
7.2
Parametric Estimation of Binary Discrete Choice Models
273
7.3
Semiparametric Efficiency Bounds for Binary Discrete
Choice Models
275
7.4
Semiparametric Estimation of Binary Discrete
Choice Models
279
7.4.1
Ichimura s Estimator
280
7.4.2
Klein and Spady s Estimator
283
7.4.3
The
SNP
Maximum Likelihood Estimator
285
7.4.4
Local Maximum Likelihood Estimation
286
7.5
Alternative Consistent SP Estimators
286
7.5.1
Manski s Maximum Score Estimator
286
7.5.2
Horowitz s Smoothed Maximum Score
Estimator
287
7.5.3
Han s Maximum Rank Correlation Estimator
291
7.5.4
Cosslett s Approximate MLE
292
7.5.5
An Iterative Least Squares Estimator
293
7.5.6
Derivative-Based Estimators
294
7.5.7
Models with Discrete Explanatory Variables
295
7.6
Multinomial Discrete Choice Models
296
xiv
Contents
7.7
Some Specification Tests for Discrete Choice Models
297
7.8
Applications
299
8
Semiparametric Estimation of Selectivity Models
300
8.1
Introduction
300
8.2
Some Parametric Estimators
301
8.3
Some Sequential Semiparametric Estimators
304
8.3.1
Cosslett s Dummy Variable Method
306
8.3.2
Powell s Kernel Estimator
306
8.3.3
Newey s Series Estimator
308
8.3.4
Newey s GMM Estimator
310
8.4
Maximum Likelihood-Type Estimators
310
8.4.1
Gallant and Nychka s Estimator
310
8.4.2
Newey s Estimator
311
8.5
Estimation of the Intercept in Selection Models
315
8.6
Applications of the Estimators
315
8.7
Conclusions
316
9
Semiparametric Estimation of Censored Regression Models
317
9.1
Introduction
317
9.2
Some Parametric Estimators
319
9.3
Semiparametric Efficiency Bounds for the Censored
Regression Model
322
9.4
The Kaplan-Meier Estimator of the Distribution Function
of a Censored Random Variable
324
9.5
Semiparametric Density-Based Estimators
326
9.5.1
The Semiparametric Generalized Least Squares
Estimator (SGLS)
327
9.5.2
Estimators Replacing Part of the Sample
328
9.5.3
Maximum Likelihood Type Estimators
329
9.6
Semiparametric Nondensity-Based Estimators
329
9.6.1
Powell s Censored Least Absolute Deviation
(CLAD) Estimator
330
9.6.2
Powell s (1986a) Censored Quantile Estimators
333
9.6.3
Powell s Symmetrically Censored Least
Squares Estimators
333
9.6.4
Newey s Efficient Estimator under Conditional
Symmetry
336
9.7
Comparative Studies of the Estimators
337
10
Retrospect and Prospect
339
Contents xv
A Statistical Methods
342
A.I Probability Concepts
342
A.
1.1
Random Variable and Distribution Function
345
A.
1.2
Conditional Distribution and Independence
347
A.
1.3
Borei
Measurable Functions
348
A.
1.4
Inequalities Involving Expectations
350
A.
1.5
Characteristic Function
(cf.)
351
A.2 Results on Convergence
352
A.2.
1
Weak and Strong Convergence of Random Variables
352
A.2.2 Laws of Large Numbers
354
A.2.3 Convergence of Distribution Functions
355
A.2.4 Central Limit Theorems
357
A.
2.5
Further Results on the Law of Large Numbers
and Convergence in Moments and Distributions
360
A.2.
6
Convergence in Moments
361
A.3 Some Probability Inequalities
365
A.4 Order of Magnitudes (Small
о
and Large O)
368
A.
5
Asymptotic Theory for Dependent Observations
370
A.5.1 Ergodicity
371
A.5.2 Mixing Sequences
372
A.5.3 Near-Epoch Dependent Sequences
376
A.5.4 Martingale Differences and Mixingales
377
A.5
.5
Rosenblatt s
( 1970)
Measure of Dependence
ß„ 379
A.5.6 Stochastic Equicontinuity
379
References
383
Index
419
This book systematically covers a vast literature on nonparametric and semiparametric
statistics and econometrics, including the topics covered in a first-year graduate course,
for example, regression function, heteroskedasticity, simultaneous equations models,
logit-probit, and censored models. Nonparametric and semiparametric methods poten¬
tially offer considerable reward to applied researchers, given the methods ability to
adapt to many unknown features of the data. Professors Pagan and Ullah provide intu¬
itive explanations of difficult concepts, heuristic developments of theory, and empirical
examples emphasizing the usefulness of the modern nonparametric approach.
Adrian Pagan is a Professor of Economics at the Institute of Advanced Studies, Australian
National University. A Fellow of the Econometric Society and Australian Academy of
Social Sciences, he is the coauthor or author of several books and numerous articles in
economics, econometrics, and public policy. Professor Pagan has been coeditor of Journal
of Applied Econometrics and Econometric Theory, and associate editor of
Econométrica
and Journal of Econometrics. He is currently a member of the editorial boards of
Economic Record, Advances in Computational Economics, and Econometric Reviews and
is coeditor of the Themes in Modern Econometrics series for Cambridge University Press.
Aman Ullah
is a Professor and Chair in the Department of Economics at the University of
California, Riverside. A Fellow of the National Academy of Sciences (India), he is the
coauthor, editor, or coeditor of six books and over ninety professional papers in econom¬
ics, econometrics, and statistics. Professor Ullah is a coeditor of the journal Econometric
Reviews and associate editor of Journal of Nonparametric Statistics, Journal of
Quantitative Economics, and Empirical Economics.
|
| any_adam_object | 1 |
| author | Pagan, Adrian R. Ullah, Aman 1946- |
| author_GND | (DE-588)122834666 (DE-588)112170048 |
| author_facet | Pagan, Adrian R. Ullah, Aman 1946- |
| author_role | aut aut |
| author_sort | Pagan, Adrian R. |
| author_variant | a r p ar arp a u au |
| building | Verbundindex |
| bvnumber | BV024620354 |
| classification_rvk | QH 233 |
| ctrlnum | (OCoLC)815876011 (DE-599)BVBBV024620354 |
| discipline | Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV024620354 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:03:12Z |
| institution | BVB |
| isbn | 0521586119 0521355648 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018592378 |
| oclc_num | 815876011 |
| open_access_boolean | |
| owner | DE-83 DE-739 |
| owner_facet | DE-83 DE-739 |
| physical | XVIII, 424 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Themes in modern econometrics |
| spelling | Pagan, Adrian R. Verfasser (DE-588)122834666 aut Nonparametric econometrics Adrian Pagan ; Aman Ullah Cambridge <<[u.a.]>> Cambridge Univ. Press 2004 XVIII, 424 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Themes in modern econometrics Digital printing Nichtparametrische Schätzung (DE-588)4203980-0 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf Semiparametrische Schätzung (DE-588)4232079-3 gnd rswk-swf Parameterschätzung (DE-588)4044614-1 gnd rswk-swf Nichtparametrische Schätzung (DE-588)4203980-0 s Ökonometrie (DE-588)4132280-0 s DE-604 Parameterschätzung (DE-588)4044614-1 s 1\p DE-604 Semiparametrische Schätzung (DE-588)4232079-3 s 2\p DE-604 Ullah, Aman 1946- Verfasser (DE-588)112170048 aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018592378&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018592378&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pagan, Adrian R. Ullah, Aman 1946- Nonparametric econometrics Nichtparametrische Schätzung (DE-588)4203980-0 gnd Ökonometrie (DE-588)4132280-0 gnd Semiparametrische Schätzung (DE-588)4232079-3 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| subject_GND | (DE-588)4203980-0 (DE-588)4132280-0 (DE-588)4232079-3 (DE-588)4044614-1 |
| title | Nonparametric econometrics |
| title_auth | Nonparametric econometrics |
| title_exact_search | Nonparametric econometrics |
| title_full | Nonparametric econometrics Adrian Pagan ; Aman Ullah |
| title_fullStr | Nonparametric econometrics Adrian Pagan ; Aman Ullah |
| title_full_unstemmed | Nonparametric econometrics Adrian Pagan ; Aman Ullah |
| title_short | Nonparametric econometrics |
| title_sort | nonparametric econometrics |
| topic | Nichtparametrische Schätzung (DE-588)4203980-0 gnd Ökonometrie (DE-588)4132280-0 gnd Semiparametrische Schätzung (DE-588)4232079-3 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| topic_facet | Nichtparametrische Schätzung Ökonometrie Semiparametrische Schätzung Parameterschätzung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018592378&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018592378&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT paganadrianr nonparametriceconometrics AT ullahaman nonparametriceconometrics |