Statistics for Spatial Data.

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

25. Multiple Imputation for Nonresponse in Surveys. By D. B. Rubin. ISBN 0 471 08705 X. Wiley, Chichester, 1987. 258 pp. £30.25.

Multiple Imputation for Nonresponse in Surveys

Statistical Analysis with Missing Data

Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

We consider estimating density functions which have support on [0, ∞) using some gamma probability densities as kernels to replace the fixed and symmetric kernel used in the standard kernel density estimator. The gamma kernels are non-negative and have naturally varying shape. The gamma kernel estimators are free of boundary bias, non-negative and achieve the optimal rate of convergence for the mean integrated squared error. The variance of the gamma kernel estimators at a distance x away from the origin is O(n−4/5x−1/2) indicating a smaller variance as x increases. Finite sample comparisons with other boundary bias free kernel estimators are made via simulation to evaluate the performance of the gamma kernel estimators.

Probability Density Function Estimation Using Gamma Kernels

Beta kernel estimators for density functions

We propose tests for sphericity and identity of high-dimensional covariance matrices. The tests are nonparametric without assuming a specific parametric distribution for the data. They can accommodate situations where the data dimension is much larger than the sample size, namely the “large p, small n” situations. We demonstrate by both theoretical and empirical studies that the tests have good properties for a wide range of dimensions and sample sizes. We applied the proposed test on a microarray dataset on Yorkshire Gilts and tested for the covariance structure for the expression levels for sets of genes.

/pdf/tests-for-high-dimensional-covariance-matrices-1dxom456gv.pdf

Tests for High-Dimensional Covariance Matrices

By learning the PM2.5 readings and meteorological records from 2010–2015, the severity of PM2.5 pollution in Beijing is quantified with a set of statistical measures. As PM2.5 concentration is highly influenced by meteorological conditions, we propose a statistical approach to adjust PM2.5 concentration with respect to meteorological conditions, which can be used to monitor PM2.5 pollution in a location. The adjusted monthly averages and percentiles are employed to test if the PM2.5 levels in Beijing have been lowered since China's State Council set up a pollution reduction target. The results of the testing reveal significant increases, rather than decreases, in the PM2.5 concentrations in the years 2013 and 2014 as compared with those in year 2012. We conduct analyses on two quasi-experiments—the Asia-Pacific Economic Cooperation meeting in November 2014 and the annual winter heating—to gain insight into the impacts of emissions on PM2.5. The analyses lead to a conclusion that a fundamental shift from mainly coal-based energy consumption to much greener alternatives in Beijing and the surrounding North China Plain is the key to solving the PM2.5 problem in Beijing.

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2015.0257

Assessing Beijing's PM2.5 pollution: Severity, weather impact, APEC and winter heating

Standard empirical likelihood confidence intervals for quantiles are identical to sign-test intervals They have relatively large coverage error, of size $n^{-1/2}$, even though they are two-sided intervals We show that smoothed empirical likelihood confidence intervals for quantiles have coverage error of order $n^{-1}$, and may be Bartlett-corrected to produce intervals with an error of order only $n^{-2}$ Necessary and sufficient conditions on the smoothing parameter, in order for these sizes of error to be attained, are derived The effects of smoothing on the positions of endpoints of the intervals are analysed, and shown to be only of second order

/pdf/smoothed-empirical-likelihood-confidence-intervals-for-84a2aw7961.pdf

Song Xi Chen

Papers

Probability Density Function Estimation Using Gamma Kernels

Beta kernel estimators for density functions

Tests for High-Dimensional Covariance Matrices

Assessing Beijing's PM2.5 pollution: Severity, weather impact, APEC and winter heating

Smoothed empirical likelihood confidence intervals for quantiles