105:. When this partition can be achieved it may be possible to complete a Bayesian analysis for the parameters of interest by determining their joint posterior distribution algebraically. The partition allows frequentist theory to develop general estimation approaches in the presence of nuisance parameters. If the partition cannot be achieved it may still be possible to make use of an approximate partition.
85:, the unknown true location of each observation is a nuisance parameter. A parameter may also cease to be a "nuisance" if it becomes the object of study, is estimated from data, or known.
162:
over the nuisance parameters. However, this approach may not always be computationally efficient if some or all of the nuisance parameters can be eliminated on a theoretical basis.
93:
The general treatment of nuisance parameters can be broadly similar between frequentist and
Bayesian approaches to theoretical statistics. It relies on an attempt to partition the
112:
provides a practically useful test because the test statistic does not depend on the unknown variance but only the sample variance. It is a case where use can be made of a
139:
for the parameters of interest which are approximately valid for moderate to large sample sizes and which take account of the presence of nuisance parameters. See
97:
into components representing information about the parameters of interest and information about the other (nuisance) parameters. This can involve ideas about
143:(1977) for some general discussion and Spall and Garner (1990) for some discussion relative to the identification of parameters in linear dynamic (i.e.,
124:
Practical approaches to statistical analysis treat nuisance parameters somewhat differently in frequentist and
Bayesian methodologies.
207:
154:, a generally applicable approach creates random samples from the joint posterior distribution of all the parameters: see
31:
which is unspecified but which must be accounted for in the hypothesis testing of the parameters which are of interest.
197:
279:
258:
244:
108:
In some special cases, it is possible to formulate methods that circumvent the presences of nuisance parameters. The
263:
Spall, J. C. and Garner, J. P. (1990), āParameter
Identification for State-Space Models with Nuisance Parameters,ā
58:(the independent variable): its variance is a nuisance parameter that must be accounted for to derive an accurate
50:
is often not specified or known, but one desires to hypothesis test on the mean(s). Another example might be
159:
176:
294:
144:
82:
39:
155:
98:
158:. Given these, the joint distribution of only the parameters of interest can be readily found by
128:
55:
8:
136:
102:
94:
71:
35:
171:
275:
254:
240:
203:
151:
132:
59:
51:
230:
226:
113:
63:
78:
140:
288:
196:
Wackerly, Dennis; Mendenhall, William; Scheaffer, Richard L. (2014-10-27).
20:
127:
A general approach in a frequentist analysis can be based on maximum
28:
16:
Statistical parameter needed for a model but not of primary interest
67:
43:
109:
221:
Basu, D. (1977), "On the
Elimination of Nuisance Parameters,"
195:
34:
The classic example of a nuisance parameter comes from the
116:. However, in other cases no such circumvention is known.
265:
IEEE Transactions on
Aerospace and Electronic Systems
286:
223:Journal of the American Statistical Association
70:, hypothesis test on the slope's value; see
42:. For at least one normal distribution, the
199:Mathematical Statistics with Applications
88:
235:Bernardo, J. M., Smith, A. F. M. (2000)
119:
287:
272:Essentials of Statistical Inference
13:
270:Young, G. A., Smith, R. L. (2005)
14:
306:
81:, but not always; for example in
249:Cox, D.R., Hinkley, D.V. (1974)
267:, vol. 26(6), pp. 992ā998.
231:10.1080/01621459.1977.10481002
189:
77:Nuisance parameters are often
1:
225:, vol. 77, pp. 355ā366.
182:
54:with unknown variance in the
7:
165:
10:
311:
145:state space representation
83:errors-in-variables models
156:Markov chain Monte Carlo
251:Theoretical Statistics
129:likelihood-ratio tests
89:Theoretical statistics
131:. These provide both
99:sufficient statistics
40:locationāscale family
253:. Chapman and Hall.
202:. Cengage Learning.
137:confidence intervals
120:Practical statistics
103:ancillary statistics
56:explanatory variable
95:likelihood function
72:regression dilution
36:normal distribution
177:Profile likelihood
172:Adaptive estimator
133:significance tests
38:, a member of the
25:nuisance parameter
295:Estimation theory
209:978-1-111-79878-9
152:Bayesian analysis
60:interval estimate
52:linear regression
302:
214:
213:
193:
114:pivotal quantity
79:scale parameters
64:regression slope
310:
309:
305:
304:
303:
301:
300:
299:
285:
284:
237:Bayesian Theory
218:
217:
210:
194:
190:
185:
168:
122:
91:
17:
12:
11:
5:
308:
298:
297:
283:
282:
268:
261:
247:
233:
216:
215:
208:
187:
186:
184:
181:
180:
179:
174:
167:
164:
121:
118:
90:
87:
15:
9:
6:
4:
3:
2:
307:
296:
293:
292:
290:
281:
280:0-521-83971-8
277:
273:
269:
266:
262:
260:
259:0-412-12420-3
256:
252:
248:
246:
245:0-471-49464-X
242:
238:
234:
232:
228:
224:
220:
219:
211:
205:
201:
200:
192:
188:
178:
175:
173:
170:
169:
163:
161:
160:marginalizing
157:
153:
148:
146:
142:
138:
134:
130:
125:
117:
115:
111:
106:
104:
100:
96:
86:
84:
80:
75:
73:
69:
65:
61:
57:
53:
49:
45:
41:
37:
32:
30:
26:
22:
271:
264:
250:
236:
222:
198:
191:
149:
126:
123:
107:
92:
76:
66:, calculate
47:
33:
24:
18:
183:References
147:) models.
21:statistics
239:. Wiley.
29:parameter
289:Category
166:See also
68:p-values
44:variance
274:, CUP.
62:of the
27:is any
278:
257:
243:
206:
110:t-test
46:(s),
276:ISBN
255:ISBN
241:ISBN
204:ISBN
141:Basu
135:and
101:and
23:, a
227:doi
150:In
19:In
291::
74:.
229::
212:.
48:Ļ
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.