Corrections to Theory of Statistics
(Second Printing)

This file was last updated May 21, 2015
If you find errors in the book not listed here or if you wish to offer comments on the book, send them to mark at'' stat.cmu.edu.

This page is constructed mostly from images in .gif files. If you are having trouble reading the images, you might prefer to view a postscript version or a pdf version.
If you find errors in the book not listed here or if you wish to offer comments on the book, send them to mark at'' stat.cmu.edu".

## Contents

### Chapter 1

Section 1.1
• p. 2: A footnote is needed to clarify some notation. (9/23/97)

There is a gif version of revised p. 2 and a postscript version.

• p. 3: line -2: '' should read '' (6/5/03)
Section 1.3
• p. 13 in footnote 10: '' should be  ''
• p. 15 line 14:  '' should be  ''
• p. 17 first line of Example 1.34:  has '' should be  has distribution''
• p. 18 line -12:  '' should be  ''
• p. 19 line 8:  '' should be  '' (2/1/00)
Section 1.5
• p. 39, proof of Lemma 1.67: all of the symbols should be permutations instead, namely . (5/21/15)
• p. 52 line 7:  densities converge to the '' should be  densities converge to the ''
Section 1.6
• p. 52 line -8:  '' should be  '' (7/14/99)
• p. 53 middle expression in (1.92):  '' should be  ''
• p. 54, last line of main text: switch '' and '' (11/17/99)
• p. 55 lines 7 and 18:  '' should be  '' in both places (11/17/99)
• p. 55 line 13: '' should be '' (11/17/99)
• p. 56 line -17:  '' should be  '' (5/1/01)
• p. 56 lin -17: the subscript  '' should be '' (5/1/01)
• p. 56 line -14:  '' should be  ''
• p. 70 line -5: '' should be ''
Section 1.7
• p. 73 problem 3: is used both as a dummy and as a fixed value. In the first line, '' should be '' and in the second line,  should be ''. (1/7/99)
• p. 74 problem 11: after the displayed formula,  '' should be  ''. (2/19/01)
• p. 74 line -2: how many observations'' should be how many observations''
• p. 78 problem 34(c): (refp202)'' should be (b)'' (8/25/97)
• p. 80 problem 43:  is a finite measure'' should read  is a finite measure with no point masses'' (4/24/00)

### Chapter 2

Section 2.1
• p. 84 last line of footnote: predictive'' is misspelled (2/21/00)
• p. 85 second line of Definition 2.8:  '' should be let '' (2/9/99)
• p. 90 line 11:  .'' should be  , where .'' (2/14/00)
• p. 91 line 5:  '' should be  '' (2/23/99)
• p. 95 line -9: density'' should be distribution'' (2/18/99)
Section 2.2
• p. 104: The last paragraph contains some incorrect statements. (2/15/01)

There is a gif version of revised p. 104 and a postscript version.

• p. 108 line -7: The two sides of (2.75) are'' should be The two sides of (2.75) are times''
Section 2.3
• p.114 lines 9-11:  '' should be  '' on all three lines.
• p. 118 line 17:  '' should be  ''
• p. 119 line -7: Example 2.52; see page 100'' should be Example 2.46; see page 97''
• p. 120 line 8:  and '' should be  and ''
Section 2.5
• p. 139 problem 13: in the displayed equation, '' should be  '' (8/27/97)
• p. 140 problem 16 line 3: '' should be ''
• p. 141 problem 24(b): add the sentence Let have a nondegenerate prior distribution.'' (8/27/97)
• p. 143 problem 43:  '' should be
 '' (9/3/97)
• p. 143 problem 46(b) line 2:  '' should be  '' (2/21/00)

### Chapter 3

Section 3.1
• p. 146 line -5: '' should be  ''
• p. 147 line 17: all at least one'' should be at least one''
• p. 147 line 23:  '' should be  '' (3/11/99)
• p. 147 in (3.11): '' should be ''
• p. 147 line -9: '' should be ''
• p. 148 line 1: '' should be ''
Section 3.2
• p. 155 in Example 3.30:  '' should be  '' and  '' should be  ''. (11/4/97)
• p. 159 line -9:  .'' should be  density.'' (9/12/00)
• p. 168 in Example 3.62: the denominator of the displayed formula for should be
• p. 174 line -9: be '' should be let be''
• p. 175 lines 7-8: of the following forms:'' should be equal (æ ) to one of the following forms:'' (11/11/97)
• p. 176 first line after (3.90): '' should be ''
• p. 177 lines -1 and -2: '' should be ''. (9/20/01)
• p. 178 line 12: Theorem 3.91'' should be Proposition 3.91''
• p. 179 line 3: '' should be '' (11/12/97)
Section 3.3
• p. 192 line 20, line 21, footnote 21: Archemedian'' should be Archimedean''
• p. 193 line 4, line 8, line 10, line 15: Archemedian'' should be Archimedean''
• p. 194 line 3: Archemedian'' should be Archimedean''
• p. 196-197: The proof of Lemma 3.130 has an error. Fortunately, a simpler lemma will suffice. (1/21/00)

There are gif versions of revised p. 196 and revised p. 197 and a postscript version.

• p. 198 footnote 30: Archemedian'' should be Archimedean''
• p. 199 lines 6 and 7: '' should be ''
• p. 204 line 22:  '' should be  for ''
• p. 205 in Theorem 3.147: Archemedian'' should be Archimedean''
Section 3.4
• p. 209 problem 10:  '' should be , ,'' (11/12/97)
• p. 210 exercise 18: Suppose that say that , that is,'' should be Suppose that'' (9/18/00)
• p. 212 problem 33: Archemedian'' should be Archimedean''

### Chapter 4

Section 4.1
• p. 215 line -4: '' should be '' and '' should be '' (11/1/00)
• p. 216 line 18: the 0-1 loss is sufficient.'' should be the 0-1 loss might be used.'' (11/1/00)
• p. 217 line -16: '' should be ''
Section 4.2
Section 4.3
• p. 231 Example 4.36 line 2: 0.05 test'' should be 0.95 test'' (5/6/98)
• p. 243 line -9  '' should be  '' (10/10/97)
• p. 246 footnote 17: Lemma 4.78'' should be Corollary 4.80''
• p. 247 second line of proof of Lemma 4.78: remove the phrase which satisfies the preceding inequality constraints'' (10/12/00)
• p. 248 last two lines in Corollary 4.80: '' should be '' on the right-hand sides of both inequalities (4/23/99)
Section 4.4
• p. 254 line 4: '' should be ''
• p. 254 top row of posterior risk table in Example 4.95: '' and '' should be switched. (4/13/99)
Section 4.5
• p. 269 line -5: family'' should be family distribution'' (11/26/97)

• p. 272: A factor was left out of three equations in Example 4.131. In addition, there is a typo on line 12 ( should be ). (4/27/98)

There is a gif version of revised p. 272 and a postscript version.

Section 4.6
• p. 285 problem 2: '' should be '' (9/10/97)
• p. 285 problem 2: '' should be '' (11/1/00)
• p. 286 problem 4: for every prior'' should be for every prior for which there exists a formal Bayes rule,'' (11/1/00)
• p. 286 problem 5:  '' should be  '' (9/5/97)
• p. 286 problem 6: The first displayed equation should be

(11/24/97)
• p. 288 problem 19(d): add the hint Read Example 4.146.'' (1/21/00)
• p. 288 last line of problem 23: level test is the'' should read level one-sided test is a'' (4/21/99)
• p. 290 problem 36: The density should be 0 for . (10/5/01)
• p. 291 first line of problem 42(b): in that'' should be in which'' (10/18/00)
• p. 294 problem 65(c): Prove that'' should be Prove that for all '' (12/23/97)

### Chapter 5

Section 5.1
• p. 298 line 3: estimator that'' should be estimator with finite variance that''
• p. 298 line -2: estimator '' should be estimator with finite variance''
• p. 298 line -1: '' should be  with finite variance'' (11/7/00)
• p. 312 line 1: the difference'' should be half of the difference'' (1/29/98)
Section 5.2
• p. 320 line 9:  '' should be '' (9/16/99)
Section 5.3
• p. 333 in (5.85): '' should be ''
Section 5.4
• p. 341 problem 15(a): Let '' should be Let '' (1/30/98)
• p. 342 problem 26 line 4: add if '' to the end of the sentence
• p. 343 problem 43: -intercept'' should be -intercept'' (9/28/99)

### Chapter 6

Section 6.1
• p. 345 line 7: length'' should be dimension''
• p. 347 lines -8 and -6: '' should be '' in both places (11/17/99)

• p. 348 and 352: There was a common oversight in the proofs of Theorems 6.10 and 6.19. (3/18/98)

There are gif versions of revised p. 348 and revised p. 352 and a postscript version.

• p. 351 line 17: '' should be  ''
• p. 352 last line: real'' should be nonzero''
Section 6.3
• p. 376 lines -4, -3:  will not apply to point hypotheses or to'' should be is not useful for point hypotheses or for''
• p. 380 line 3: test'' should be tests'' (4/2/98)
• p. 385 line 1: '' should be ''

### Chapter 7

Section 7.1
• pp. 394 to 398: In the definitions of small order of '' and large order of ,'' together with their stochastic versions, there is no benefit to allowing to be an arbitrary sequence of real numbers. The definitions should have been written with the requirement that for all . Aside from removing all of the unnecessary absolute values from the s and s that appear on pages 394-398, the following corrections are also needed:
• p. 394, second line of Definition 7.1: sequence of real numbers'' should be sequence of positive numbers''.
• p. 395, line 3:  is real and nonzero'' should be ''.
• p. 395, line 4: the last '' should be ''. (5/19/03)
• p. 395, line 14: sequence of real numbers'' should be sequence of positive numbers''.
• p. 396, second line of Definition 7.3: sequence of numbers'' should be sequence of positive numbers''.(3/5/01)

There is a gif version of revised p. 394, revised p. 395, revised p. 396, revised p. 397, revised p. 398, and a postscript version.

• p. 400: Theorem 7.20 should start with the sentence: Let and be subsets of Euclidean spaces.'' (8/5/97)

• p. 401: The paragraph before Corollary 7.21 is incorrect and there is another minor typo in footnote 7. (8/5/97)

There is a gif version of revised p. 401 and a postscript version.

Section 7.2
• p. 408 last line of statement of Theorem 7.35: put parentheses around (11/24/98)
• p. 411 line 6: Example 7.30'' should be Example 7.39''
• p. 412 line 4: the right-hand side of the equation should be

Section 7.3
• p. 413 line 17:  '' should be ''
• p. 413 line 18: 0.798'' should be 0.637''
• p. 413 Example 7.46 line 4: Then is the'' should read Then is the'' (3/21/00)
• p. 414 lines 9, 19, 22: '' should be  ''
• p. 415 first line of Theorem 7.49: '' should be ''
• p. 415: the conditions of Theorem 7.49 should include the sentence Let be a metric space.'' (8/5/97)
• p. 416 line 7: '' should be  ''
• p. 417 footnote 16 line 3: Usc'' should be USC''
• p. 419 line 8: Insert the sentence Let .'' and the following displayed equation should begin  '' rather than  ''. (10/14/99)
• p. 422 line 15: The th coordinate'' should be The th coordinate'' (2/20/98)
• p. 426 line -4:  is continuous in .'' should read  exists in a neighborhood of for all and .'' (5/9/00)

• p. 427: Several typos appear in the statement and proof of Theorem 7.75. (10/21/99)

There is a gif version of revised p. 427 and a postscript version.

Section 7.4
• p. 431 line 21: at most '' should be at most '' (10/21/99)
• p. 432 line 16: at least '' should be at least '' (10/21/99)
• p. 437 line -6:  '' should be  '' (11/9/99)
• p. 445 first displayed equation in proof of Theorem 7.106: all three s on the right-hand side should be . (1/14/99)
• p. 451 Figure 7.114: the horizontal axis should be labeled '' rather than ''
• p. 454 line 7: '' should be  ''
• p. 455 line 5:  by and by '' should be  by and by '' (3/16/98)
Section 7.5
• p. 459: the conditions of Theorem 7.125 should include the following sentence Assume that the MLE for the parameter space is consistent also.'' (8/5/97)
• p. 462 lines 8 and 14: remove ,0'' from subscript of wherever it appears
• p. 462 line 12:  '' should be  '' (3/10/98)
• p. 463 line -3: matrix'' should be matrix based on one reduced observation''
• p. 467 line 20: '' should be  ''
Section 7.6
• p. 468 problem 10 line 1: '' should be  distribution''
• p. 468 problem 11 (8/14/01)
• line 2: '' should be ''
• line 4: '' should be ''
• line 6: '' should be  ''
• p. 470 problem 24 line 3: '' should be ''
• p. 470 problem 24(a): Should read Show that the relative rate of convergence (defined in Example 7.46 on page 413) of to is 0.'' (3/20/00)
• p. 471 problem 28: prove that'' should be prove that for each fixed ''
• p. 473 problem 43: Consider the joint asymptotic distribution of '' should be Assume that converges in distribution'' (3/3/98)
• p. 474 problem 47: Prove that there exists a subset with such that for every '' should be For each , prove that there exists with such that for every ''
• p. 474 problem 48: add the sentence Assume that has a continuous bounded strictly positive prior density.''
• p. 474 problem 50(a): Use Laplace's'' should be Try to use Laplace's'' (2/20/98)
• p. 475 problem 51: Replace the last sentence by Modify the Laplace approximation of Theorem 7.116 by replacing by and by and by replacing and by observed Fisher information. Prove that the approximate Bayes factor in (4.27) is the same as this modified Laplace approximation divided by .'' (3/16/98)
• p. 475 problem 52 line 2: '' should be  ''

### Chapter 8

Section 8.2
• p. 490 line 1: note first note'' should be first note''
Section 8.6
• p. 527 in (8.63): In the denominator of the fraction on the right-hand side, '' should read ''. (11/27/01)

### Chapter 9

Section 9.2
• p. 557 Theorem 9.44 and second line of proof: All of the 's and 's that appear without subscripts (3 of each) should have subscript 0. (7/1/04)
• p. 558 line 1:  , '' should be  , '' (7/1/04)

### Appendix A

Section A.1
• p. 571 line 8: A collection'' should be A nonempty collection'' (1/11/99)
• p. 575 lines 10-11:  is integrable'' should be the integral of with respect to is defined'' (9/3/97)
Section A.3
• p. 582 line 19: equals '' should be contains '' (5/21/02)
• p. 584 line -2:  '' should be '' (5/19/00)
• p. 585 line -18:  '' should be  '' (5/21/02)
• p. 587 line 2: Let '' should be Let '' (11/28/06)
• p. 587 line 13: with respect to '' should be with respect to '' (1/15/02)
• p. 587 line 13:  '' should be  ''
Section A.4
• p. 588 first line of Proposition A.49: probability'' should be measure'' (5/21/02)
• p. 589 displayed formula in Theorem A.50: '' should be '' (5/21/02)
• p. 592 line 14: -finite'' should finite'' (7/18/02)
Section A.5
• p. 593 line -7 '' should be '' (5/21/02)
• p. 593 line -6 Then let '' should be Then let '' (5/21/02)
• p. 594 line 3  '' should be  '' (5/21/02)
• p. 594 line 8: Lemma A.64'' should be Lemma A.61'' (1/18/99)
• p. 594 line -10:  '' should be '' (1/16/01)
• p. 595 Lemma A.67: Insert the sentence Assume the conditions of Lemma A.64'' at the start. (5/21/02)
• p. 596 line line -12:  '' should be  '' (5/21/02)
Section A.6
• p. 598 line 1: is integrable'' should be and the integral of with respect to is defined'' (9/3/97)
• p. 599 line -21:  '' should be '' (5/21/02)
• p. 599 line -13: All three 's in this displayed equation should be 's. (5/21/02)
• p. 599 lines -9, -8: integrable functions'' should be functions whose integrals are defined'' (9/3/97)
• p. 600 line 23: all '' should be almost all '' (8/5/97)
Section A.7
• p. 603 problem 13: In line 1 measurable spaces'' should be measurable spaces such that contains all singletons''

### Appendix B

Section B.1
• p. 609 line 4: add and '' to the end of the sentence (9/4/01)
Section B.2
• p. 612 line 4: an so'' should be and so'' (5/21/02)
• p. 613 line 9:  '' should be  '' (5/21/02)
Section B.3
• p. 633 line 2 of Theorem B.75: measurable'' should be Borel''
• p. 639: The proofs of two parts of Theorem B.90 have errors, a small typo in the proof of part 3 and an unwarranted claim in part 2. The proof of part 2 is actually made simpler.

There is a gif version of revised p. 639 and a postscript version. (1/29/02)

• p. 643, Example B.100: Insert , with .'' at the end of the first sentence. (10/15/08)
Section B.5
• p.650 line 2 in proof of Theorem B.124:  '' should read  ''. (2/8/02)
Section B.7
• p. 661 line 5: '' should be ''
• p. 661 problem 1: In lines 2-3 the probability that'' should be removed.
Section B.8
• p. 662 problem 6: In line 3 '' should be  ''
• p. 662 problem 7: The displayed formula should be

• p. 673 line 3: '' should be''
• p. 691: Chibb'' should be Chib'' (9/10/01)
• p. 694: Archemedian'' should be Archimedean''