Bhattacharya R.N., Rao R.R. — Normal Approximation and Asymptotic Expansions :: Электронная библиотека попечительского совета мехмата МГУ

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Bhattacharya R.N., Rao R.R. — Normal Approximation and Asymptotic Expansions

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Название: Normal Approximation and Asymptotic Expansions

Авторы: Bhattacharya R.N., Rao R.R.

Аннотация:

This monograph presents in a unified way various refinements of the classical central limit theorem for independent random vectors and includes recent research on the subject. Most of the multidimensional results in this area are fairly recent, and significant advances over the last 15 years have led to a fresh outlook. The increasing demands of application (e.g., to the large sample theory of statistics) indicate that the present generality is useful. It is rather fortunate that in our context precision and generality go hand in hand.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: reprinted edition

Год издания: 1986

Количество страниц: 291

Добавлена в каталог: 12.04.2010

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Предметный указатель

Absolutely continuous, function      263
Absolutely continuous, signed measure      269
Asymptotically best constant in Berry — Esseen theorem      110 240
Bernoulli numbers, polynomials      272
Berry — Esseen theorem      104
Borel sigma-field of a metric space      2
Boundary of a set      4
Bounded Lipschitzian distance      17
Bounded variation of a function      263
Cauchy's estimate      68 69
Cauchy's formula      28
Central limit theorem, classical      186
Central limit theorem, multidimensional      183
Characteristic function of a probability measure      42
Chebyshev's inequality, one sided      103
Closed half space      20
Continuity set      4
Convex hull of a set      23
Convex set      20
Convolution, of finite signed measures      43
Convolution, of functions      42
Covariance matrix      261
Covariance matrix, average      59
Cramer — Edgeworth polynomials      51 52
Cramer — Levy theorem      44
Cramer's condition      207
Cumulants, $\nu th$       46
Degenerate distribution      226
Difference operators      262
Distribution function, of a finite signed measure      54 261
Distribution function, of a random vector      262
Distribution of a random vector      261
Euler — Maclaurin sum formula, in multidimension      275
Euler — Maclaurin sum formula, in one dimension      273
Face of a polyhedron      25
Formula in lattice case      230
Fourier inversion, theorem      41
Fourier transform      40
Fourier — Stieltjes transform      42
Fundamental domain of a lattice      229
Hausdorff distance      19
Hoelder inequality, generalized      48
Hyperplane      20
Indicator function of a set      4
Induced signed measure      43
Inner product, in ${C}^{k}$       40
Inner product, in ${L}^{2}({R}^{k})$       40
Lattice      224
Lattice point problem      242

Lattice, distribution      226
Lattice, minimal      227
Lattice, random vector      226
Liapounov coefficient      59
Liapounov's central limit theorem, multidimensional extension      185
Lindeberg's central limit theorem, multidimensional extension      183
Local central limit theorem for densities      189
Local expansion, for densities      192 194
Local expansion, for the lattice case      231
Logarithm, principal branch      45
Mean central limit theorem      172
Mean of a random vector      260
Moment, $\nu th$       44
Moment, absolute      45
Norm, in ${C}^{k}$       40
Norm, in ${L}^{p}({R}^{k})$       40
Norm, of a matrix      124
Norm, of a matrix, of a finite signed measure      3
Normal distribution      50
Normal distribution, density      50
Oscillation, average modulus of      97
Oscillation, of a function      4
Oscillation, of a function on a set      7
Parseval's relation      44
Period      227
Period lattice      228
Plancherel theorem      41
Polya's result      23
Polyhedron      25
Prokhorov distance      5
Q-continuous function      4
Riemann — Lebesgue lemma      41
Scheffe's theorem      6
Schwartz, function      265
Schwartz, space      274
Singular measure on ${R}^{k}$       270
Standard normal distribution      51
Standard normalization      160
Strongly non-lattice distribution      221
Support of a (signed) measure      2
Surface, area      27
Surface, integral      27
Uniformity class, of functions      6
Uniformity class, of sets      6
Uniqueness theorem for the Fourier — Stieltjes transform      43
Variation, of a finite signed measure - positive, negative, total      2
Variation, of a function on a set      263
Weak, convergence      3
Weak, topology      3

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