| General Information | - | Schedule of Topics | - | Assignments | - | Textbook Errata |
The following is a list of typographical and mathematical errors in the 1999 edition of Elements of Large-Sample Theory by Erich Lehmann. I thought it might be sort of fun to make this list a class project. Searching for errors has at least three benefits I can think of:
| Location | Correction |
|---|---|
| p. 2, footnote at bottom of page | "connction" should be "connection" |
| p. 7, Lemma 1.1.1 | "symptotically" should be "asymptotically" |
| p. 8, line above (1.1.28) | "formula" should be plural |
| p. 11, Tables 1.2.3 and 1.2.4 | The bottom row in each table should be labeled with the Poisson parameter $\lambda$, not $\gamma$. |
| p. 11, the three lines above Table 1.2.4 | $\gamma=\alpha$ should be $p=\alpha$ and $\gamma=.02$ should be $p=.02$. |
| p. 12, second paragraph, sentence beginning with "The third row..." | Since $\gamma$ should not be in Table 1.2.4, the parenthetical expression "(with $\lambda$ in place of $\gamma$)" seems unnecessary. |
| p. 15, expression (1.3.3) | denominator should be $i^\alpha$, not $i^a$ |
| p. 16, equation (1.3.9) | 1 should not be bold |
| p. 17, Example 1.3.5 | If $\alpha$ is a nonnegative integer, the series has infinite radius of convergence. |
| p. 22, top line | "number" should be plural |
| p. 27, inequality (1.5.3) | Missing $< \epsilon$. Should be $|f(x)-a| < \epsilon$. |
| p. 29, second paragraph | Should read "at $x_0$ is continuous at $x_0$." |
| p. 36, Problem 1.17 | Should be $\gamma^n\to 0$ |
| p. 37, Problem 1.18 in the hint | Should say "Suppose $\gamma > 1$." |
| p. 37, Problem 2.5 | Both terms asymptotically equivalent to $P_n(x)$ should be divided by $x!$. |
| p. 42, Problem 5.1 | Definition 1.5.1 does not apply to this situation. The problem might be rephrased "Extend Definition 1.5.1 and use it to show that..." |
| p. 43, Problem 5.10, second line | lowercase f should be capital |
| p. 43, Problem 5.11, Hint for (i) | The first sentence of the hint is false. Nothing is harmed by deleting it. |
| p. 44, problem 5.14 | The statement is not true. It could be made true by (for example) specifying that the ${b_n}$ are nondecreasing. |
| p. 47, line 6 | "give" should be "gives" |
| p. 52, 5 lines from bottom | should read, "which tends to $a+1$ if..." |
| p. 57, sentence beginning "By Theorem 2.1.1, a sufficient..." | $Y_n$ should be $\delta_n$. |
| p. 58, line above (2.2.11) | relative efficiency is defined in Section 4.3, not 4.2 |
| p. 58, Caption of Table 2.2.1 | word "of" should be omitted |
| p. 59, expression for variance of $\hat\beta$ | numerator of rightmost fraction should be $\sigma^2$, not 1 |
| p. 59, equation (2.2.19) | numerator of second fraction should be $\bar v^2$, not 1 |
| p. 62, limits of summation in (2.2.31) and p. 63, limits of summation below (2.2.34) | Should start with $k=0$, not $k=1$ (this is irrelevant unless $\sigma^2$ is infinite) |
| p. 62, Example 2.2.7 | While there is nothing technically wrong here, the sequences defined are actually (m-1)-dependent in addition to being m-dependent. |
| p. 63, bottom of page in (2.3.1) | Limit is as $n\to\infty$, not $x\to\infty$ |
| p. 65, Example 2.3.3, equation underneath "have cdf $H_n$...' | First F should be P |
| p. 72, Example 2.3.9, equations underneath "then" | First F should be f |
| p. 78, second line from bottom | pronoun "it" has wrong antecedent |
| p. 79, Limit (2.4.13) | In the denominator, the p and q could have subscripted n (this one is a bit questionable, but would probably improve readability) |
| p. 81, Limit (2.4.19) | Convergence in distribution symbol is missing the L |
| p. 81, second to last line | word "the" is repeated |
| p. 82, Table 2.4.2, first column, rows 5, 8, 11, 14, and 17 | $1-G_n(X)$ should be $1-\Phi(X)$ |
| p. 82, equation in middle of page | Numerator of fraction should be $\chi^2_n - n$, not $\chi^2_n$ |
| p. 82, 9 lines from bottom | $\chi^2_{2k}$ should be $\chi^2_k$ |
| p. 83, line above equation (2.4.21) | $\sigma^2$ should be $\sigma^3$ |
| p. 83, equation (2.4.21) | $[1-x^2\phi(x)]$ should be $[1-x^2]\phi(x)$ |
| p. 83, 9 lines from bottom | "Balakrishman" should be "Balakrishnan" |
| p. 86, limit at bottom of page and p. 87, limit at top of page | convergence in distribution symbol is missing L |
| p. 88, limit (2.5.9) | convergence in distribution symbol is missing L |
| p. 89, equation (2.5.11) | $\bar X$ should be under a radical everywhere it appears |
| p. 90, limit at top of page | One of the convergence in distribution symbols is missing L |
| p. 90, both limits in Example 2.5.5; p. 91, first limit in Example 2.5.6 | convergence in distribution symbol is missing L |
| p. 93, equation (2.6.1) | $P$ should be $P_\theta$ (questionable) |
| p. 94, line beginning "For any fixed $n$, ..." | "tends to 0" should be "tends to 1" |
| p. 99, bottom of page; p. 101, equation (2.7.14); p. 102, equation (2.7.16); p. 102, both equations in proof of Theorem 2.7.4; p. 129, Problem 7.5 | expressions such as $o(x)^3$ are not actually defined and should be $o[(x)^3]$. |
| p. 101, sentence above Theorem 2.7.2 | "(A')" should be "(B)" |
| p. 101, equation (2.7.13) | Var X_n should be Var \bar X_n |
| p. 105, three lines above (2.7.29) | "hence by (7.25)" should be "hence by (2.7.25)" |
| p. 106, summary items 1 and 2 | The roles of (A') and (B) are switched. This happens 3 times. |
| p. 110, lines 6-7 | The fact that the $X_i$ are identically distributed is necessary but not sufficient for stationarity |
| p. 111, line above equation (2.8.22) | "(8.20)" should be "(2.8.21)" |
| p. 111, 4 lines below equation (2.8.24) | "(2.8.20)" should be "(2.8.21)" |
| p. 111, equation following "Using the fact that" | $\gamma_{k-1}$ should be $\gamma_k$ |
| p. 117, sentence before equation (2.8.48) | "(2.8.45)" should be "(2.8.46)" |
| p. 119, problem 1.3 at the end of the hint | First, there's a missing ] to match the one before Hint. Second, $|Y_n-c| > b$ should be $|Y_n-c| < b$. |
| p. 120, Problem 2.1 | The statement is false. The absolute value of the sample mean tends to infinity in this case, but with probability 1, the sample mean itself does not converge to any value, finite or infinite. |
| p. 122, Problem 3.5 | "arbitrary" should be "arbitrarily". Also, a right bracket is missing after the hint. |
| p. 125, Problem 4.5, second line of hint | $X_{m-1}$ should be $X_{(m+1)}$ |
| p. 132, Problem 8.16(i) | The equality is not true (however, it is true as an asymptotic equivalence) |
| p. 142, expression 3.1.39 | "for all $n > n_0(\vartheta)$" should be deleted. |
| p. 144, equation (3.1.48) | X and Y are missing bars in denominator |
| p. 150, just above (3.2.15) | "such as sequence" should be "such a sequence". |
| p. 150, statement (3.2.16) | $\infty$ should be 1 |
| p. 151, second to last line | (3.2.31) should be (3.2.13) |
| p. 154, statment (3.2.26) | "assignment" is misspelled |
| p. 162, Table 3.3.1 | "Power at $\Delta=.1$" should be "Power at $\Delta=1$" or "Power at $p-p_0=.1$" |
| p. 162, 4th line below table | "tables" should be "table" |
| p. 162, 7th line below table | "as $p_0$ moves away from 1/2" should be "as $p_0$ moves toward 1/2" |
| p. 163, last line of Theorem 3.3.4 | $\tau^2(\theta_0.\vartheta)$ should be $\hat\tau_n^2$. |
| p. 164, expressions (3.3.23) | convergence in distribution symbols are missing L |
| p. 170, first line of text | 3.2.2 should be 3.3.2 |
| p. 175, 3 lines from bottom | assumptions is misspelled |
| p. 181, 2nd line of Example 3.4.6 | 3.4.3 should be 3.4.4 |
| p. 278, first line and equation (5.1.1) | $\|\underline x, \underline y\|$ should be replaced by $\|\underline x-\underline y\|$ or $d(\underline x,\underline y)$. |
| p. 280, Figure 5.1.1 | Figure (b) has an extra space and $S$ is not defined for either figure |
| p. 281, 2nd equation from bottom | missing comma in $N\left(0,\frac{\sigma^2}{\lambda}\right)$ |
| p. 282, last equation before Example 5.1.2 | misplaced parentheses on the left hand side |
| p. 282, 3rd line of Example 5.1.2 | marginal is misspelled |
| p. 282, last equation before bottom | missing minus signs in exponents of $e$ |
| p. 284, line above (5.1.24) | Theorem 5.1.7 should be Theorem 5.1.8 |
| p. 294, 4th line below (5.2.24) | "tha" should be "the" and "continue" should be "continues" |
| p. 300, matrix in (5.3.2) | The columns are too close together |
| p. 303, equation (5.3.16) | lowercase a on left hand side should be A |
| p. 305, last line of Theorem 5.3.3 | the word "its" is missing between "of" and "off-diagonal" |
| p. 305, line after (5.3.29) | (5.3.27) should be (5.3.28) |
| p. 307, equation (5.3.37) | $|J|$ should be replaced by $|J|^{-1}$ in two places |
| p. 309, first line of item 5 in summary | transformation is misspelled |
| p. 309, summary item 6 | "the Jacobian" should be "the reciprocal of the Jacobian" |
| p. 312, second equation from bottom | large summation symbol should be replaced by normal-sized capital $\Sigma$ |
| p. 317, expression (5.4.34) | $X_iY_i$ should be $(X_i-\xi)(Y_i-\eta)$. Also, convergence in distribution symbol is missing L |
| p. 318, expression (5.4.42) | Convergence in distribution symbol is missing L |
| p. 319, 4th line of item 4 in summary | Convergence in distribution symbol is missing L and capital N (for normal) is missing |
| p. 322, (5.5.14) and the two preceding expressions | Convergence in distribution symbol is missing L |
| p. 328, last equation | Convergence in distribution symbol is missing L |
| p. 329, third line after (5.5.49) | $(0<\rho<1)$ should be $(0<\rho<\infty)$ |
| p. 333, expression (5.6.23) | Convergence in distribution symbol is missing L |
| p. 350, Problem 1.2 (ii) | The function given doesn't work; try something like $f(x_1,x_2)=I(x_1x_2=0)$. |
| p. 351, last line | missing ) in $X_{(n-1)}$. |
| p. 365, equation preceding (6.1.2) | last argument should be $X_{i_a}$, not $X_{i_1}$. |
| p. 366, third line | should begin with $0< {\rm Var}(\phi(X_1))<\infty$ |
| p. 369, Theorems 6.1.2, 6.1.4, 6.2.1 | I cannot verify these theorems without assuming that all the $\sigma^2_i$ are finite. If it's truly possible that $\sigma_1^2<\infty$ and $\sigma_2^2=\infty$ and (6.1.20) still holds, then an example of such behavior would really be helpful. |
| p. 371, last line of text | (1.6.30) should be (6.1.30) |
| p. 382, 6th line after (6.2.3) | $\hat F_n^{-1}$ should be $\hat F_n^{-1}(p)$ |
| p. 389, line after (6.2.41) | "order statistics" should be "order statistic" |
| p. 398, expression (6.2.42) | convergence in distribution symbol is missing L and final ) is missing |
| p. 415, equation (6.4.44) | no space between 3/4 and $(1-z^2)$ |
| p. 425, expression (6.5.14) | missing limit $p$ |
| p. 428, 2nd line | estimator is misspelled |
| pp. 432-433, Equations (6.5.44), (6.5.45), (6.5.47), (6.5.48), and the equation after (6.5.48) | all $\sqrt{n}$ should be $n$ |
| p. 438, Problem 1.17 | Maybe it's just me, but I can't do this problem without assuming $\sigma_2^2<\infty$. I get $E(T_n^*-T_n)^2=Var(T_n)-4\sigma_1^2$, which only goes to zero if $\sigma_2^2$ is finite. |
| p. 454, 3rd line after (7.1.9) | density is misspelled |
| p. 454, Figure 7.1.1 | on x axis, 0 could be -1 and $\theta-c(\theta)$ and $\theta+c(\theta)$ should be on one line. |
| p. 455, 14th line from bottom | densities is misspelled |
| p. 455, 9th line from bottom | "Examples 7.1.1 and 7.1.2" should be "Examples 7.1.2 and 7.1.3" |
| p. 456, 13th line | "Section 7.5" should be "Section 7.4" |
| p. 457, 5th line | 7.1.2 should be 7.1.3 |
| p. 457, line after (7.1.17) | likelihood is misspelled |
| p. 457, 3rd line from bottom | "Section 6.3" should be "Section 7.3" |
| p. 461, first line | "Section 1.3" should be "Section 7.3" |
| p. 463, first equation | equation is wrong; should be \begin{equation*} \frac{\partial}{\partial\theta}\log f_\theta(x) = \frac{3\theta^2(x-\theta^3)}{\sigma_0^2} \end{equation*} |
| p. 463, second equation | $9\theta^4\sigma_0^2$ should be $9\theta^4/\sigma_0^2$ |
| p. 463, line after (7.2.4) | "As was seen in (2.2.17)" should be "As was seen in Example 2.3.7" and "tends" is misspelled |
| p. 463, 4 lines above (7.2.5) | "According to (7.2.7)" should be "According to (7.1.27)" |
| p. 472, 3rd line from bottom | 7.2.1 should be 7.3.1 |
| p. 476, equation (7.3.26) | one of the $\theta_n$ is missing a tilde |
| p. 476, equation above (7.3.29) | denominator of first fraction should be $l''_n(\theta_0)/n$ instead of $l''_n(\theta_0)/\sqrt{n}$ |
| p. 483, header | header has wrong section number and title (should be 7.3) |
| p. 483, line after (7.3.56) | "variables" should be "variable" |
| p. 485, 3 lines before Example 7.4.1 | uniformly is misspelled |
| p. 486, line 14 | uniformly is misspelled |
| pp. 486-487, expressions (7.4.6) and (7.4.7) | convergence in distribution symbols are missing L |
| p. 487, expression (7.4.9) | the 2 and the $a^2$ are switched |
| p. 492, 4th line and p. 495, line below (7.4.33) | Jeffreys should have no apostrophe |
| p. 497, general comment on section 7.5 | Why have underlines for vectors been abandoned? |
| p. 497, equations above (7.5.2) | should be taking the derivatives of the loglikelihood, not the likelihood |
| p. 500, Corollary 7.5.1 | 7.5.1(ii) should be 7.5.1(i) |
| p. 500, equation (7.5.13) | right hand side should be $(J')^{-1}I(\theta)J^{-1}$ |
| p. 501, 5 different places in (M6) and (M7) | $k$ is already the size of the parameter vector, so it should not be used as a dummy |
| p. 502, expression (7.5.19) and last expression on page | convergence in distribution symbols are missing L |
| p. 508, line below (7.5.51) | consistent is misspelled |
| p. 512, line below (7.6.10) | Dirichlet is misspelled |
| p. 513, line above (7.6.16) | 5.4.3 should be 7.5.4 |
| p. 526, line below (7.7.7) | solely is misspelled |
| p. 527, expression (7.7.15) and expression (7.7.16) | $\hat\theta$ is missing a subscript $n$ |
| p. 528, Example 7.7.1, first two lines | $N(0,1)$ should be $N(\theta,1)$ and "Example 7.1.3" should be "Example 7.1.4" |
| p. 528, second equation in Example 7.7.1 | right hand side should be $n\overline x^2$ |
| p. 531, 11 lines from bottom | "second and third factors" should be "third and fourth factors" |
| p. 551, Problem 1.7 | 7.1.2 should be 7.1.3 |
| p. 552, Problem 1.12 | density (7.9.2) is missing a factor of $\theta$ |
| p. 557, Problem 3.13 | This problem is the same as Problem 3.5, p. 556 |
| p. 565, Problem 7.9 | interval is misspelled |
| p. 616, entry for "Bandwidth" | should be included with the B's, not the A's |