Series Approximation Methods in Statistics: 88 (Lecture Notes in Statistics)

This book was originally compiled for a course I taught at the University of Rochester in the fall of , and is intended to give advanced Lecture Notes in Statistics. © Series Approximation Methods in Statistics Pages
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Edgeworth developed a similar expansion as an improvement to the central limit theorem. Let F n denote the cumulative distribution functions of the variables X n. Then by the central limit theorem,.

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If we expand in terms of the standard normal distribution, that is, if we set. The Edgeworth series is developed similarly to the Gram—Charlier A series, only that now terms are collected according to powers of n. Again, after inverse Fourier transform, the density function F n follows as. The first five terms of the expansion are [5]. Blinnikov and Moessner have given a simple algorithm to calculate higher-order terms of the expansion. Note that in case of a lattice distributions which have discrete values , the Edgeworth expansion must be adjusted to account for the discontinuous jumps between lattice points.

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Take and the sample mean. We can use several distributions for:. On the moment problem. Moment-based approximations of distributions using mixtures: Reconstruction of probability density functions. On L 1 -convergence of statistical kernel estimators of distribution densities. Estimation of the mixing distribution in the Poisson mixture models. Uncensored and censored samples.

Hausdorff moment problem via fractional moments. The Problem of Moments. Recherches sur les fractions continues. Toulouse 8 J1—J; A5—A Counterexamples in Probability , 2nd ed. Krein condition in probabilistic moment problems. Stieltjes classes for moment indeterminate probability distributions.

Numerical inversion of the Laplace transform via fractional moments.

Maclaurin series of cos(x)

Identifiability of finite mixtures. The inversion of the Laplace integral and the related moment problem.

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Statistical Society, Series A , , , Wolfson, Interval-based versus decision theoretic criteria for the choice of sample size, The Statistician , 46, , Lloyd, When do best confidence limits exist? Srinivasan, An approach to the construction of parametric confidence bands on cumulative distribution functions, Biometrika , 59, , Meier, Nonparametric estimation for incomplete observations, Jurnal of the American Statistical Association , 53, , A goal programming-based software for real estate assessment, European Journal of Operational Research , , , Sahai, A second bibliography on estimation and testing procedures for non-normal Samples, Statistica Applicata: Italian Journal of Applied Statistics , 5, , Gallo, Poisson regression analysis in clinical research, Journal of Biopharmaceutical Statistics , 5, , Seo, Fourier transformation can improve quadrature efficiency of Laplace distribution, Computational Statistics , 16, , Foutz, Kolmogorov-type tests of goodness-of-fit against stochastic ordering, Communications in Statistics: Theory and Method , 26, , Meeuwsen, Testing the mean of asymmetric population: Johnson;s modified t test revisited, Communication in Statistics: Simulation and Computation , 17, , Byar, Percentage point of the asymptotic distribution of one and two sample statistics for truncated and censored data, Technometrics , 17, , Kleiber, Long memory vs.

Moore, Combining information for prediction in linear regression, Metrika , 56, , Theory Relat Fields , , , Yuen, A note on minimizing absolute percentage error in combined forecasts, Computers and Operations Research , 28, , Zidek, Bayesian multivariate spatial interpolation with data missing by design, Journal of the Royal Statistical Society , 59 2 , P. Na, Test for parameter change in stochastic processes based on conditional least-squares estimator, Journal of Multivariate Analysis 93, , Utev, Comparison of individual risk models, Insurance: Editor , Contribution to Probability and Statistics , Yang, Nonparametric likelihood ratio confidence bands for quantile functions from incomplete survival data, Annals of Statistics , 24, , Pakes, On the number of near-maximum insurance claims, Insurance: Lim and Loh, A comparison of tests of equality of variances, Computational Statistics and Data Analysis , 22, , Cai, Some thoughts on averaging techniques in stochastic dynamics, Probabilistic Engineering Mechanics , 15, , Pan, A new method for selection of population distribution and parameter estimation, Reliability Engineering and System Safety , 60, , Journal of the American Statistical Association , 88, , Rao, On minimum distance estimation of location bases on the Kolmogorov statistic, Communication in Statistics: Theory and Methods , 11, , Rubin, Ellipsoidally symmetric extensions of the general location model for mixed categorical and continuos data, Biometrika , 85, , Maritz, A note on the problem of statistical calibration, App.

Maritz, An analysis of the linear-calibration controversy from the perspective of compound estimation, Technometrics , 24, , Variance Reduction, Statistics and Probability Letters , 47, , Koenderink, Estimation of torsion, Journal of Applied Statistics , 26, , Permaul, Transition from partial factors method to simulation based reliability assessment in structural design, Probabilistic Engineering Mechanics , 14, , Pardo, Choosing the best Rukhin goodness-of-fit statistics, Computational Statistics and Data Analysis , 49, , Rakes, The effect of sample size and variability of data on the comparative performance of artificial neural networks and regression, Computers and Operation Research , 25, , The transformation method, Mathematical Programming , 75, , A modified Kolmogorov-Smirnov test sensitive to tail alternative, Annals of Statistics , 20, , Wong, Forming inferences about some intraclass correlation coefficients, Psychological Methods , 1, , Sun, Towards an omnibus distribution-free goodness-of-fit test for the Cox model, Statistica Sinica , 6, , Sun, Transformations of Gaussian random fields to Brownian sheet and non-parametric change-point tests, Statistics and Probability Letters , 28, , Escobar, An algorithm to compute the cdf of the product of two normal random variables, Communications in Statistics: B , 23, , Statistical applications, Applied Mathematics Letters , 13, , Borcard, Partialling out the spatial component of ecological variation: Questions and propositions in the linear modelling framework, Environmental and Ecological Statistics , 5, , Mielke and Yao, Empirical coverage tests, J.

Simula , 35, , Simulation and Computation , B8, , Pham, Stochastic optimization under constraints , Stochastic Processes and their Applications, 93, , Gastwirth, Hybrid test for the hypothesis of symmetry, Journal of Applied Statistics , 25, , Estimating the conditional bias, Metrika , 55, , Moulton L, and N.

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Halsey, A mixture model with detection limits for regression analyses of antibody response to vaccine, Biometrics , 51, , Lin, Independence characterizations and testing normality against restricted skewness-kurtosis alternatives, Journal of Statistical Planning and Inference , , , Reid, Comparison of test statistics via expected lengths of associated confidence intervals, Journal of Statistical Planning and Inference , 97, , Nagelkerke, A note on a general definition of the coefficient of determination, Biometrika , 78, , A comparative study, Technometrics , 26, , Wellington, Multiple objective optimization problems in statistics, International Transactions in Operational Research , 9, - , Smith, Application of a method for the efficient computation of posteriori distributions, App.

Back to basics, Statistics and Computing , 4, , Paula, Wald one-sided test using generalized estimating equations approach, Computational Statistics and Data Analysis , 36, , Banerjee, Testing the equality of distributions of random vectors with categorical components, Computational Statistics and Data Analysis , 37, , Comparison of eleven methods, Statistics in Medicine , 17, , Madsen, A generalization of some classical time series tools, Computational Statistics and Data Analysis , 37, , Fang, Detecting influential observations in growth curve model with unstructured covariance, Comput.


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