Small Sample AsymptoticsIMS, 1990 - 151 pagine |
Parole e frasi comuni
accuracy apply Approx approximate density approximate the density asymptotic expansion Barndorff-Nielsen Biometrika Cauchy centering central limit theorem chapter compute confidence intervals conjugate density consider constant contaminated normal cumulant generating function Daniels defined denote density f density of Tn derive developed Durbin Edgeworth approximation Edgeworth expansion equation evaluate exact density example Exhibit exponential family finite fn(t fn(t)dt fn(to fn/fn formula Gamma distribution given gn(t Hampel hand side Helstrom Huber iid random variables large deviations linear M-estimates mean moment generating function Monte Carlo multivariate normal approximation normal distribution numerical integration observations obtain order statistics parameter path of steepest percentiles probability problem regression relative error robust robust statistics Ronchetti saddlepoint approximation saddlepoint techniques shows small sample approximation small sample asymptotics solution standard normal steepest descent T₁ tail area approximation term of order test statistic underlying density underlying distribution upper tail area values θο
Brani popolari
Pagina 133 - Bickel, PJ, Gotze, F., and van Zwet, WR (1986), "The Edgeworth Expansion For U-statistics of Degree Two", Annals of Statistics 14, 1463-1484.
Pagina 138 - Henrici, P. 1977 Applied and computational complex analysis, vol. 2. New York: Wiley.
Pagina 138 - Approximate Evaluation of Detection Probabilities in Radar and Optical Communications", IEEE Transactions on Aerospace and Electronic Systems, AES-14, 4, 630-640.
Pagina 138 - Calculating error probabilities for intersymbol and cochannel interference" , IEEE Transactions on Communications, vol.
Pagina 57 - Restrict attention to statistics which can be written as a functional T of the empirical distribution function Fn...
Pagina 15 - Now we can apply the same arguments as in the proof of Theorem 2.2 to the integral on the right hand side of (2.18) and the result follows.
Pagina 136 - Easton, GS, and Ronchetti, E. (1986), "General Saddlepoint Approximations With Applications to L-statistics", Journal of the American Statistical Association 86, 420-430.
Pagina 140 - Distribution of the Ratio of Quadratic Forms in Normal Variables - Numerical Methods", SI AM Journal of Scientific and Statistical Computing 5, 476-488.
Pagina 77 - Hampel argues effectively that the most natural and simple quantity to study is the derivative of the logarithm of the density, namely f'n/fn- There are at least four reasons why this seems reasonable.
Pagina 28 - To summarize: if it is possible to deform the path of integration and express the integral as...