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| Kolassa J.E. — Series Approximation Methods in Statistics |
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| Ïðåäìåòíûé óêàçàòåëü |
 formula 175
 approximation 103 150 187
 distribution 48
Absolute error 37 63 67 81
Adjusted profile log likelihood 145
Albers, Bickel, and van Zwet, 1976 54 197
Albert and Anderson, 1984 158
Analytic statistical model 1
Ancillary 178
Andrews and Stafford, 1993 199
Asymptotic expansion 6
Asymptotic methods 1
Bahadur and Ranga Rao, 1960 91—92 95
Bak and Newman, 1996 vi 11 71
Barndorff — Nielsen’s formula 1 171 175 182—188 190 192
Barndorff–Nielsen and Cox, 1979 140 169 171
Barndorff–Nielsen and Cox, 1984 171
Barndorff–Nielsen and Cox, 1989 1 47—48
Barndorff–Nielsen and Kluppelberg, 1999 82
Barndorff–Nielsen, 1978 70 157 187
Barndorff–Nielsen, 1980 175 179 182 188
Barndorff–Nielsen, 1983 175 187—188
Barndorff–Nielsen, 1984 185
Barndorff–Nielsen, 1986 101 187
Barndorff–Nielsen, 1990a 101
Barndorff–Nielsen, 1990b 187
Bartlett, 1953 167—168
Bartlett, 1955 167
Bartlett’s correction 165 167—168 171 184 193
Bayesian paradigm 191
Beek, 1972 26
Berman, et. al., 1990 163
Bernoulli distribution 12
Bernoulli number 30 55 61
Bernoulli polynomials 51
Berry — Esseen theorem 9 25
Bhattacharya and Denker, 1990 1
Bhattacharya and Rao, 1976 1 45 53 125 166—167
Billingsley, 1986 13 16 19 111
binomial 108
Binomial distribution 12
Blackwell and Hodges, 1959 67 77—78 127
Blackwell — Hodges formula 161
Blaesild and Jensen, 1985 81
Bleistein, 1966 104
Bochner and Martin, 1948 126
Bootstrap 49
Cauchy distribution 12 29
Central limit theorem 31 40 166
Chambers, 1967 44 59 116
Characteristic function v 7—16 21 25 29—30 37—39 41 55—56 111 124
Clarkson and Jennrich, 1991 159—160
Conditional distributions 139 145
Conditional inference 139
Conditional profile log likelihood 142
Contingency tables 154
Converge with probability 1 2
Convergence almost surely 2
Convergence in distribution 2
Convergence in mean 2
Convergence in probability 2
Convolution 8 18
Cordeiro and Paula, 1989 171
Cornish and Fisher, 1937 47
Cornish — Fisher expansion 31 47—48 54 62
Cox and Reid, 1987 142
Cox and Snell, 1981 198
Cox, 1980 180
Cramer, 1925 4
Cramer, 1946 14
Cramer’s condition 40 46 124 166
Cumulant generating function 9 64 68—71 77—78 82—85 106 113 149 193—195
Cumulants 9—10
Cumulative distribution functions 28
Curved exponential family 179 184—185
Daniels, 1954 63 67—69 71—72 75 80—81
Daniels, 1958 175
Daniels, 1983 189
Daniels, 1987 89 94 135
Davis, 1976 32
Davison and Hinkley, 1988 193—194
Davison, 1986 192
Davison, 1988 150 157
DiCiccio and Martin, 1991 129
DiCiccio, Hall, and Romano, 1991 175
DiCiccio, Martin, and Young, 1993 141
Directed log likelihood ratio statistic 185
di–gamma function 176
Double exponential distribution 29
Double saddlepoint density approximation 140 154
Double saddlepoint distribution function approximation 147—150 156
Durbin, 1980 83 175 177
Edgeworth series 28 31—32 36 51—55 58—60 62—67 72—73 75 77 80 89 91 94 166—167
Efron, 1975 179 196—197
Efron, 1982 193
Empirical likelihood 175
Esseen, 1945 51 166
Esseen, 1956 26
Esseen’s series 51 60 125 167
Estimating equations 189
Euler — Maclaurin summation formula 57—58
Expected information 168
Exponential distribution 29 128
Exponential empirical likelihood 193
Exponential family 63—64 117 139 148—149 168 175 178 184—187 193
Exponential random variables 142
Feller, 1971 v 19 21 38 51
Field and Ronchetti, 1990 1 190
Fisher and Cornish, 1960 48
Fisher information 175 179 196
Fisher, 1925 195—196
Fisher, 1934 178 187
Fourier inversion 19 32 71 115
Fourier transform 7
Fraser, 1968 188
Fraser, 1979 188
Fraser, Reid, and Wong, 1991 141—142
Frydenberg and Jensen, 1989 173
Fubini’s Theorem 17—18 90
Gamma distribution 68 81—83 88 172 175 203
Geman and Geman, 1984 162
Generalized lattice 114 147 149
Gibbs — Skovgaard algorithm 162
Gram — Charlier series 34
Hall, 1983 48
Hall, 1992 1
Haynsworth and Goldberg, 1965 30 51 57
Hermite polynomial 35 37 67 116—118
Hettmansperger, 1984 54 62
High contact 56
Hocking, 1985 143 153
Hodges and Lehmann, 1970 195 197
Hypergeometric distribution 154—155
Invariant 10 48 54 91
Inverse gaussian distribution 30 81—82 88 203
Inverting characteristic functions 16
Jacobsen, 1989 157—158
Jeffreys, 1962 75
Jensen, 1988 80—81 92
Jensen, 1992 101
Jensen, 1995 1
Jing and Robinson, 1994 68 119 127—129 141 150
| Jing and Wood, 1996 193
Kass, 1988 123
Kass, Tierney, and Kadane, 1990 191
Kendall, Stuart, and Ord, 1987 9—10 12
Kolassa and McCullagh, 1990 58 166
Kolassa and Tanner, 1994 157 159—160 162
Kolassa, 1989 125 134 167
Kolassa, 1991 67
Kolassa, 1992 62 107
Kolassa, 1994 162
Kolassa, 1995 162
Kolassa, 1996a 127
Kolassa, 1996b 97 107 150
Kolassa, 1996c 195 198
Kolassa, 1997 150 157
Kolassa, 2001 162
Kolassa, 2003a 94 107 114 116 131
Kolassa, 2003b 166
Kolassa, 2004 145 162
Kolassa, 2005 97
Kong and Levin, 1996 55
Koning and Does, 1988 48
Konishi, Niki, and Gupta, 1988 49
Laplace transform 8 33
Laplace’s method 123 191
Lattice 127
Lattice distribution 12 27—28 40 48—49 51—53 55—58 106 166—167 172 195
Lawley, 1956 171
Le Cam, 1969 1
Legendre transform 66 83 119 128
Levin and Kong, 1990 167
Levin, 1990 142
Likelihood ratio statistic 101 126 167 182
Logistic distribution 29 78—79 85 96
Logistic regression 49 55 163 172 188
Lognormal distribution 30
Lugannani and Rice approximation 95—97 194
Lugannani and Rice, 1980 95 135 146
M-estimate 189 194
Mardia, 1970 119
Mathews and Walker, 1964 72
Maximum likelihood estimator 63 167 175 189—190 196
McCullagh and Cox, 1986 171
McCullagh and Nelder, 1989 162
McCullagh and Tibshirani, 1990 145
McCullagh, 1984 182
McCullagh, 1986 119
McCullagh, 1987 v 9—10 32—33 35 118 171 182
Moment generating function 8—9 29 32 38 68 109—110
Monotone Convergence Theorem 15
Multivariate Blackwell–Hodges approximations 140
Multivariate cumulant generating function 110 117
Multivariate Edgeworth series 165—166
Multivariate moment generating function 109
Multivariate saddlepoint density 125 154
Multivariate saddlepoints 146
Newton — Raphson method 85
Non-independently distributed variables 44—46 195
Normal correlation 182
Normal distribution 11 68
Normalize 64 83
numeric integration 89
Observed information 168 175 179
Path of steepest descent 72
Permutation tests 194
Petrov, 1975 100
Pfaff and Pfanzagl, 1985 197
Pfanzagl, 1980 197
Phillips, 1983 127—128
Pitman efficiency 197
Poisson regression 188
Poisson variables 154
Posterior moments 191
Praskova–Vizkova, 1976 55
Press, et. al., 1986 161
Prior distribution 191
Pseudo-cumulant 33—35 37
Pseudo-moments 33—35 37 59 115 118
Rao, 1960 166—167
Rao, 1961 166—167
Rao, 1962 196
Rao, 1963 196
Regularity conditions 40
Reid, 1988 v 165 171 175 187
Reid, 1996 1 90
Relative error 42 44 63 67 81—82
Riemann — Lebesgue theorem 41 72
Robinson, 1982 55 92 95 107 135 195
Routledge and Tsao, 1995 135
Rudin, 1973 18
Rudin, 1976 vi 29
Saddlepoint 63 65 73
Saddlepoint cumulative distribution function approximations 90 106
Saddlepoint density approximation 63—72 81 147
Score statistic 165 167
Secant approximation 104
Secant method 86
Semi-invariant 9—10
Sequential saddlepoint approximation 141 157
Serfling, 1980 1—2 167 189
Series Theorem 23 38—39 124
Sheppard’s correction 55 58—59 61 167
Sign test 12
simple linear regression 44 46
Singular distribution 40 195
Skates, 1993 104
Skovgaard, 1987 135 145 148 150—151 155 157 163
Skovgaard, 1989 1
Skovgaard, 1990 1
Smoothing Theorem 20—22 25 38—40 124—125
Spearman’s Rank Correlation 48 54
Stafford and Andrews, 1993 199
Statistical curvature 196
Steepness 70
Strawderman, Casella, and Wells, 1996 163
Sufficiency 178
Taniguchi, 1991 198
Tanner, 1996 162
Temme, 1982 99
Temme’s Theorem 150 153
Thisted, 1988 89
Tierney and Kadane, 1986 191—192
Tierney, Kass, and Kadane, 1989 127—128
Transformation family 188
Turnbull, Brown, and Hu, 1974 192
Uniform distribution 12 68
Uniform error 94
Uniform relative error 63 78 92
Wald statistic 165
Wallace, 1958 3
Wang, 1990a 194
Wang, 1990b 133 135
Waterman and Lindsay, 1996 162
Watson’s lemma 75 86 91—92 96 107 119 147
Weak convergence 19
Widder, 1946 8
Wilcoxon signed rank statistic 54
Withers, 1988 49
Wong and Li, 1992 192
Wong, 1992 196
Yang and Kolassa, 2002 96 148
Yarnold, 1972 167
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