Recent Publications

          Books


         1. Asymptotic Statistics (with M. Denker), Birkhauser, DMV Lecture Series (May, 1990).

      2. Random Dynamical Systems (2007) (with M. Majumdar). Cambridge University Press.

      3. A Basic Course in Probability Theory (2007) (with E.C. Waymire). Springer.

      4. Stochastic Processes with Applications (2009) (with E.C. Waymire). SIAM Classics in Applied Mathematics 61 (SIAM reprint with Errata). Original edition published in 1990 by John Wiley, New York. 

       5. Normal Approximation and Asymptotic Expansions (with R. Ranga Rao) (2010). SIAM Classics in Applied Mathematics 64 (Revised Reprint). Original edition by Wiley, New York (1976). Russian Edition (1982). Revised Reprint by Krieger, Florida(1986).

       6. Nonparametric Inference on Manifolds with Applications to Shape Spaces (2012) (with A. Bhattacharya). IMS Monograph Series #2, Cambridge University Press, Cambridge, UK.

       7. A Course in Mathematical Statistics and Large Sample Theory (2016) (With L.Lin and V.Patrangenaru). Springer Series in Statistics. To appear.

 
           Articles

          18. Majoring kernels and stochastic cascades with applications to incompressible Navier-Stokes equations (with L. Chen, S. Dobson, R. Guenther, C. Orum, M. Ossiander, E. Thomann, E. Waymire) (2003) Trans. Amer. Math. Soc. 355, 5003-5040.
    
       17. Semi-Markov cascade representations of local solutions to 3-D incompressible Navier-Stokes equations (with L. Chen, S. Dobson, R. Guenther, C. Orum, M. Ossiander, E. Thomann, E. Waymire). (2005) In Probability and Partial Differential Equations in Modern Applied Mathematics, IMA vol. 140, Springer, 27-40.

       16. Stability in distribution of randomly perturbed quadratic maps as Markov processes (with M. Majumdar). (2004) Ann. Appl. Probab. 14, no. 4, 1802–1809.

       15. Phase changes with time and multi-scale homogenizations of a class of anomalous diffusions. (2005) In Probability and partial differential equations in Modern Applied Mathematics. IMA Vol. Math. Appl., 140, Springer, New York, 11-26.

       14.  Large sample theory of intrinsic and extrinsic sample means on manifolds. I (with V.  Patrangenaru). (2003) Ann. Statist. 31, no. 1, 1–29.

       13. Large sample theory of intrinsic and extrinsic sample means on manifolds. II (with V.  Patrangenaru). (2005) Ann. Statist. 33, no. 3, 1225–1259.

       12. Consistency and asymptotic normality of the estimated effective doses in bioassay (with M. Kong). (2007) J. Statist. Plann. Inference 137, no. 3, 643–658.

       11. Statistics on Riemannian manifolds: asymptotic distribution and curvature (with A. Bhattacharya). (2008) Proc. Amer. Math. Soc. 136, no. 8, 2959–2967.

       10. Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging (with A. Bandulasiri, V. Patrangenaru). (2009) J. Multivariate Anal. 100, no. 9, 1867–1882.

       9. An adaptive nonparametric method in benchmark analysis for bioassay and environmental studies (with L. Lin). (2010) Statist. Probab. Lett. 80, no. 23-24, 1947–1953.

       8. Limit theorems for monotone Markov processes (with M. Majumdar, N. Hashimzade). (2010) Sankhya A 72, no. 1, 170–190.

       7. On the speed of convergence of multidimensional diffusions to equilibrium (with A. Wasielak). (2012) Stoch. Dyn. 12, no. 1, 1150003, 19 pp.

       6. A nonparametric theory of statistics on manifolds (2013). In Limit theorems in probability, statistics and number theory-In Honor of Friedrich Gotze; 173-206.

       5. Recent progress in the nonparametric estimation of monotone curves—with applications to bioassay and environmental risk assessment. (2013) Comput. Statist. Data Anal. 63, 63–80.

      4. Problems of ruin and survival in economics: Applications of limit theorems in probability (with Discussions) (with M. Majumdar, L. Lin) (2013). Sankhya B 75, no. 2, 190–194.

      3. Statistics on manifolds and landmarks based image analysis: a nonparametric theory with applications (with V. Patrangenaru). (2014) J. Statist. Plann. Inference 145, 1–22.

      2.   Nonparametric benchmark dose estimation with continuous dose-response data.    Scandinavian Journal of Statistics 42 (2015), 713--731 (with Lin, L and  Piegorsch, W).

     1.  Omnibus CLTs for Fr\'echet means and nonparametric inference on non-Euclidean spaces.   Proceedings of the American Mathematical Society(2016). To appear. Arxiv:1306.5806 . (with Lin, L).