Abstract
This chapter provides brief introductions to a number of important topics which have not been touched upon in the rest of the book, namely, (1) classification of an observation in one of several groups, (2) principal components analysis which splits the data into orthogonal linear components in the order of the magnitudes of their variances, and (3) sequential analysis in which observations are taken one-by-one until the accumulated evidence becomes decisive.
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References
Bhattacharya, A., & Bhattacharya, R. (2012). Nonparametric inference on manifolds: With applications to shape spaces. IMS monograph (Vol. 2). Cambridge: Cambridge University Press.
Bhattacharya, A., & Dunson, D. B. (2010). Nonparametric Bayesian density estimation on manifolds with applications to planar shapes. Biometrika, 97, 851–865.
Bhattacharya, A., & Dunson, D. B. (2012). Nonparametric Bayes classification and hypothesis testing on manifolds. Journal of Multivariate Analysis, 111, 1–19.
Bhattacharya, A., & Waymire, E. C. (2007). A Basic course in probability theory. New York, Springer.
Bishop, C. (2006). Principal component analysis. In Pattern recognition and machine learning (information science and statistics) (pp. 561–570). New York: Springer.
Chernoff, H. (1972). Sequential analysis and optimal design. Regional conferences in applied mathematics (Vol. 8). Philadelphia: SIAM.
Ferguson, T. S. (1967). Mathematical statistics: A decision theoretic approach. New York: Academic Press.
Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Annals of Statistics, 1(2), 209–230.
Ferguson, T. S. (1974). Prior distributions on spaces of probability measures. Annals of Statistics, 4(4), 615–629.
Ghosal, S. (2010). Dirichlet process, related priors and posterior asymptotics. In N. L. Hjort et al. (Eds.), Bayesian nonparametrics (pp. 36–83). Cambridge: Cambridge University Press.
Ghosh, J. K., & Ramamoorthi, R. V. (2002). Bayesian nonparametrics. New York: Springer.
Hastie, T., Tibshirani, R., & Friedman, J. H., (2001). The elements of statistical learning. New York: Springer.
Hjont, N. L., Holmes, C., Müller, P., & Walker, S. G., (Eds.). (2010). Bayesian nonparametrics. Cambridge: Cambridge University Press.
Lehmann, E. L. (1959). Testing statistical hypothesis. New York: Wiley.
Rao, C. R. (1965). Linear statistical inference and its applications. New York: Wiley.
Sen, P. K. (1981). Sequential nonparametrics. New York: Wiley.
Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statistica Sinica, 4, 639–650.
Siegmund, D. (1985). Sequential analysis: Tests and confidence intervals. New York: Springer.
Siegmund, D. (1992). Sequential analysis: Tests and confidence intervals. New York: Springer.
Vapnik, V. N. (1998). Statistical learning theory. New York: Springer.
Wald, A. (1947). Sequential analysis. New York: Wiley.
Wasserman, L. (2003). All of statistics: A concise course in statistical inference. New York: Springer.
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Bhattacharya, R., Lin, L., Patrangenaru, V. (2016). Miscellaneous Topics. In: A Course in Mathematical Statistics and Large Sample Theory. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-4032-5_15
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DOI: https://doi.org/10.1007/978-1-4939-4032-5_15
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