Rabi Bhattacharya

Rabi Bhattacharya's AcademicInfluence.com Rankings

Rabi Bhattacharya

Mathematics

#5293

World Rank

#7461

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Measure Theory

#1620

World Rank

#1999

Historical Rank

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Mathematics

Why Is Rabi Bhattacharya Influential?

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According to Wikipedia, Rabindra Nath Bhattacharya is a mathematician/statistician at the University of Arizona. He works in the fields of probability theory and theoretical statistics where he has made fundamental contributions to long-standing problems in both areas. Most notable are his solution to the multidimensional rate of convergence problem for the central limit theorem in his Ph.D. thesis published in the Bulletin of the American Mathematical Society and further elaborated in a research monograph written jointly with R. Ranga Rao and the solution of the validity of the formal Edgeworth expansion in collaboration with J.K. Ghosh in 1978. He has also contributed significantly to the theory and application of Markov processes, including numerous co-authored papers on problems in groundwater hydrology with Vijay K. Gupta, and in economics with Mukul Majumdar. Most recently his research has focused on nonparametric statistical inference on manifolds and its applications. He is a co-author of three graduate texts and four research monographs. A comprehensive selection of Bhattacharya's work is available in a special 2016 Contemporary Mathematicians volume published by Birkhäuser. He is married to Bithika Gouri Bhattacharya, with a daughter, a son, and four grandchildren.

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Rabi Bhattacharya's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Normal Approximation and Asymptotic Expansions (1976) (1086)
ON THE VALIDITY OF THE FORMAL EDGEWORTH EXPANSION (1978) (598)
LARGE SAMPLE THEORY OF INTRINSIC AND EXTRINSIC SAMPLE MEANS ON MANIFOLDS—II (2003) (429)
Stochastic processes with applications (1990) (342)
On the functional central limit theorem and the law of the iterated logarithm for Markov processes (1982) (242)
The Hurst effect under trends (1983) (215)
Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions (1978) (152)
A basic course in probability theory (2007) (127)
Convolution effect in the determination of composition profiles and diffusion coefficients by microprobe step scans (1988) (109)
Nonparametric Inference on Manifolds: With Applications to Shape Spaces (2015) (89)
Nonparametric statistics on manifolds with applications to shape spaces (2008) (82)
Normal Approximations and Asymptotic Expansions. (1977) (81)
Stability in Distribution for a Class of Singular Diffusions (1992) (81)
Nonparametic estimation of location and dispersion on Riemannian manifolds (2002) (79)
A statistical approach to estimate the 3D size distribution of spheres from 2D size distributions (2005) (77)
Random Dynamical Systems: Theory and Applications (2007) (69)
On geometric ergodicity of nonlinear autoregressive models (1995) (68)
ASYMPTOTICS OF A CLASS OF MARKOV PROCESSES WHICH ARE NOT IN GENERAL IRREDUCIBLE (1988) (66)
Random Walk (2011) (59)
A Central Limit Theorem for Diffusions with Periodic Coefficients (1985) (57)
Omnibus CLTs for Fr\'echet means and nonparametric inference on non-Euclidean spaces (2013) (57)
Solute Dispersion in Multidimensional Periodic Saturated Porous Media (1986) (52)
Continuity Correction (2011) (50)
Random exchange economies (1973) (49)
Statistics on Riemannian manifolds: asymptotic distribution and curvature (2008) (49)
Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations (2003) (49)
Controlled semi-Markov models, the discounted case (1989) (48)
Second Order and $L^p$-Comparisons between the Bootstrap and Empirical Edgeworth Expansion Methodologies (1989) (48)
Refinements of the Multidimensional Central Limit Theorem and Applications (1977) (48)
A theoretical explanation of solute dispersion in saturated porous media at the Darcy Scale (1983) (47)
Random Dynamical Systems: Acknowledgment (2007) (45)
On a Class of Stable Random Dynamical Systems: Theory and Applications (2001) (44)
Foundation theories of solute transport in porous media: a critical review (1979) (43)
Asymptotics of solute dispersion in periodic porous media (1989) (41)
On a Theorem of Dubins and Freedman (1999) (37)
Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging (2009) (35)
Extrinsic analysis on manifolds is computationally faster than intrinsic analysis with applications to quality control by machine vision (2012) (34)
Random dynamical systems: a review (2003) (34)
Ergodicity of nonlinear first order autoregressive models (1995) (33)
Speed of convergence of the n-fold convolution of a probability measure on a compact group (1972) (32)
Recurrence and ergodicity of diffusions (1982) (29)
Consistency and asymptotic normality of the estimated effective doses in bioassay (2007) (29)
An Exposition of Götze's Estimation of the Rate of Convergence in the Multivariate Central Limit Theorem (2010) (28)
Random Iterations of Two Quadratic Maps (1993) (28)
On the stochastic foundations of the theory of water flow through unsaturated soil (1976) (27)
Probability, statistics, and their applications : papers in honor of Rabi Bhattacharya (2003) (26)
A Course in Mathematical Statistics and Large Sample Theory (2016) (25)
Benchmark Dose Analysis via Nonparametric Regression Modeling (2014) (25)
A New Derivation of the Taylor-Aris Theory of Solute Dispersion in a Capillary (1983) (24)
On moment conditions for valid formal Edgeworth expansions (1988) (24)
A class of U- statistics and asymptotic normality of the number of k- clusters (1992) (23)
CONTROLLED SEMI-MARKOV MODELS UNDER LONG-RUN AVERAGE REWARDS (1989) (23)
On Errors of Normal Approximation (1975) (22)
Nonparametric estimation of benchmark doses in environmental risk assessment (2012) (22)
Rates of Weak Convergence for the Multidimensional Central Limit Theorem (1970) (21)
Multiscale diffusion processes with periodic coefficients and an application to solute transport in porous media (1999) (21)
Berry-Esseen bounds for the multi-dimensional central limit theorem (1968) (20)
Statistics on manifolds and landmarks based image analysis: A nonparametric theory with applications (2014) (20)
An adaptive nonparametric method in benchmark analysis for bioassay and environmental studies. (2010) (19)
Rates of Weak Convergence and Asymptotic Expansions for Classical Central Limit Theorems (1971) (18)
On the Taylor-Aris theory of solute transport in a capillary (1984) (18)
An Approach to the Existence of Unique Invariant Probabilities for Markov Processes ∗ (1999) (17)
NONPARAMETRIC BENCHMARK ANALYSIS IN RISK ASSESSMENT: A COMPARATIVE STUDY BY SIMULATION AND DATA ANALYSIS. (2011) (16)
Random Dynamical Systems (2007) (16)
Ergodicity and central limit theorems for a class of Markov processes (1988) (14)
A molecular approach to the foundations of the theory of solute transport in porous media: I. Conservative solutes in homogeneous isotropic saturated media (1981) (14)
Speed of convergence to equilibrium and to normality for diffusions with multiple periodic scales (1999) (14)
Limit theorems for monotone Markov processes (2010) (12)
Recent Results on Refinements of the Central Limit Theorem (1972) (12)
Dynamical systems subject to random shocks: An introduction (2003) (12)
Asymptotic Behavior of Several Dimensional Diffusions (1981) (11)
On a Statistical Theory of Solute Transport in Porous Media (1979) (11)
Time-scales for Gaussian approximation and its breakdown under a hierarchy of periodic spatial heterogeneities (1995) (11)
Fokker-Planck Equations (2004) (11)
Correction Note: Correction to "Criteria for Recurrence and Existence of Invariant Measures for Multidimensional Diffusions" (1980) (10)
Recent progress in the nonparametric estimation of monotone curves - With applications to bioassay and environmental risk assessment (2013) (10)
Stability in distribution of randomly perturbed quadratic maps as Markov processes (2004) (9)
A note on the distribution of integrals of geometric Brownian motion (2001) (9)
Extrinsic Data Analysis on Sample Spaces with a Manifold Stratification (2011) (9)
Toward an analytical theory of water flow through inhomogeneous porous media (1977) (8)
Correction to "On the Validity of the Formal Edgeworth Expansion" (1980) (8)
Iterated random maps and some classes of Markov processes (2001) (8)
On geometric ergodicity of nonlinear autoregressive models [Statist. Probab. Lett. 22 (1995) 311–315]☆ (1999) (8)
STOCHASTIC EQUIVALENCE OF CONVEX ORDERED DISTRIBUTIONS AND APPLICATIONS (2000) (8)
A Central Limit Theorem for Frechet Means (2013) (7)
A Markovian Stochastic Basis for the Transport of Water Through Unsaturated Soil (1976) (7)
NONPARAMETRIC INFERENCE ON NON-EUCLIDEAN SPACES (2015) (7)
Proxy and instrumental variable methods in a regression model with one of the regressors missing (1993) (6)
On characterizing the probability of survival in a large competitive economy (2001) (6)
Random Iteration of I.I.D. Quadratic Maps (2001) (6)
Random Dynamical Systems: Dynamical Systems (2007) (6)
Nonparametric Benchmark Dose Estimation with Continuous Dose‐Response Data (2015) (6)
Semi-Markov Cascade Representations of Local Solutions to 3-D Incompressible Navier-Stokes (2005) (6)
On the Order of Magnitude of Cumulants of Von Mises Functionals and Related Statistics (1983) (5)
Random iterates of monotone maps (2010) (5)
Correction: “Asymptotics of a class of Markov processes which are not in general irreducible” [Ann. Probab. 16 (1988), no. 3, 1333–1347; MR 89m:60148] (1997) (5)
Estimating the probability mass of unobserved support in random sampling (2000) (4)
Introduction to General Methods of Estimation (2016) (4)
Some exact solutions of Einstein–Dirac–Maxwell zero mass scalar equations (1983) (4)
Majorizing Kernels & Stochastic Cascades With Applications To Incompressible (2002) (4)
ON THE SPEED OF CONVERGENCE OF MULTIDIMENSIONAL DIFFUSIONS TO EQUILIBRIUM (2012) (3)
Differential Geometry for Model Independent Analysis of Images and Other Non-Euclidean Data: Recent Developments (2018) (3)
Weak Convergence of Probability Measures on Metric Spaces (2016) (3)
A Nonparametric Theory of Statistics on Manifolds (2013) (3)
On Global Stability of Some Stochastic Economic Processes: A Synthesis (1980) (3)
On the central limit theorem for diffusions with almost periodic coefficients (1988) (3)
Nonparametric Analysis of Non-Euclidean Data on Shapes and Images (2018) (3)
Extrinsic analysis on manifolds (2012) (2)
Cramér-Edgeworth Expansions (1990) (2)
Kolmogorov’s Extension Theorem and Brownian Motion (2016) (2)
1. Random Walk and Brownian Motion (2009) (2)
1. Weak Convergence of Probability Measures and Uniformity Classes (2010) (2)
Withdrawn: Statistics on manifolds andlandmarks based image analysis: A nonparametric theory with applications (2013) (2)
Random Walk, Brownian Motion, and Martingales (2021) (2)
Independence, Conditional Expectation (2016) (2)
Rejoinder To: Problems of Ruin and Survival in Economics: Applications of Limit Theorems in Probability (2013) (1)
Comment on Solute dispersion in multidimensional periodic saturated porous media by Vijay K. Gupta (1987) (1)
Rejoinder to the Discussion (2014) (1)
FLOW THROUGH POROUS MEDIA. RECENT DEVELOPMENTS (1983) (1)
Nonparametric Inference for Extrinsic Means on Size-and-Shape Manifolds with Applications in Medical Imaging (2008) (1)
A hierarchy of Gaussian and non-Gaussian asymptotics of a class of Fokker-Planck equations with multiple scales (1997) (1)
Acknowledgment of Priority (1984) (1)
The Nonparametric Bootstrap (2016) (1)
Problems of ruin and survival in economics (2013) (1)
Sustainability in the Stochastic Ramsey Model (2015) (1)
Bienaymé–Galton–Watson Simple Branching Process and Extinction (2021) (1)
Phase Changes with Time and Multi-Scale Homogenizations of a Class of Anomalous Diffusions (2005) (1)
Problems of ruin and survival in economics: applications of limit theorems in probability (2013) (1)
Fréchet Means and Nonparametric Inference on Non-Euclidean Geometric Spaces (2016) (1)
Phase changes with time for a class of autonomous multiscale diffusions (2002) (1)
First Passage Time Distributions for Brownian Motion with Drift and a Local Limit Theorem (2021) (1)
Markov Chain Monte Carlo (MCMC) Simulation and Bayes Theory (2016) (1)
On the physical interpretation of the soil water diffusivity in terms of the theory of markov processes (1976) (1)
Nonparametric Inference on Manifolds: Nonparametric Bayes inference on manifolds (2012) (1)
Nonparametric curve estimation under monotonicity constraint (2013) (1)
Equity and Sustainability: An Exposition (2020) (1)
Classical Central Limit Theorems (2016) (1)
Random Walk, Brownian Motion, and the Strong Markov Property (2021) (0)
Sustainability in the Stochastic Ramsey Model (2015) (0)
4. Continuous-Parameter Markov Chains (2009) (0)
Martingales and Stopping Times (2016) (0)
A Historical Note on Brownian Motion (2016) (0)
Superiority of Bayes estimators over the MLE in high dimensional multinomial models and its implication for nonparametric Bayes theory (2019) (0)
Nonparametric Inference on Manifolds: Landmark-based shape spaces (2012) (0)
Failure of a Credit System: Implications of the Large Deviation Theory (2010) (0)
Classical Zero–One Laws, Laws of Large Numbers and Large Deviations (2016) (0)
Book Review: Limit theorems of probability theory: Sequences of independent random variables (1997) (0)
5. Asymptotic Expansions—Lattice Distributions (2010) (0)
Some Elements of the Theory of Markov Processes and Their Convergence to Equilibrium (2016) (0)
Special Topic: The Geometric Random Walk and the Binomial Tree Model of Mathematical Finance (2021) (0)
Sufficient Statistics, Exponential Families, and Estimation (2016) (0)
0. A Probability and Measure Theory Overview (2009) (0)
Special Topic: Bienaymé–Galton–Watson Simple Branching Process and Excursions (2021) (0)
7. An Application of Stein's Method (2010) (0)
Stationary Processes and Discrete Parameter Markov Processes (2022) (0)
Reply [to Comment on Solute dispersion in multidimensional periodic saturated porous media by Vij (1987) (0)
Random Dynamical Systems: Bibliography (2007) (0)
The planar shape space ??k2 (2012) (0)
ArcSine Law Asymptotics (2021) (0)
Random Dynamical Systems: Special Structures (2007) (0)
Martingales: Definitions and Examples (2021) (0)
2. Discrete-Parameter Markov Chains (2009) (0)
Special Topic: Fractional Brownian Motion and/or Trends: The Hurst Effect (2021) (0)
Special Topic: Optimal Stopping Rules (2021) (0)
Nonparametric Analysis of Shapes with Applications to Morphometrics and Medical Diagnostics (2007) (0)
Brownian Motion: The LIL and Some Fine-Scale Properties (2016) (0)
Nonparametric Inference on Manifolds: Differentiable manifolds (2012) (0)
Stiefel manifolds Vk,m (2012) (0)
Strong Markov Property, Skorokhod Embedding, and Donsker’s Invariance Principle (2016) (0)
6. Two Recent Improvements (2010) (0)
Multiple Testing and the False Discovery Rate (2016) (0)
The Brownian Bridge (2021) (0)
Intrinsic analysis on manifolds (2012) (0)
The Simple Random Walk I: Associated Boundary Value Distributions, Transience, and Recurrence (2021) (0)
Tests in Parametric and Nonparametric Models (2016) (0)
Real projective spaces and projective shape spaces (2012) (0)
6. Dynamic Programming and Stochastic Optimization (2009) (0)
Affine shape spaces A??km (2012) (0)
Stochastic Calculus for Point Processes and a Martingale Characterization of the Poisson Process (2021) (0)
What Is a Stochastic Process? (2021) (0)
Reprints: Part I (2016) (0)
The Simple Random Walk II: First Passage Times (2021) (0)
Large Sample Theory of Estimation in Parametric Models (2016) (0)
Statistics Based on Ranking Methods (1985) (0)
Ruin probabilities in models of resource management and insurance: A synthesis (2015) (0)
Edgeworth Expansions and the Bootstrap (2016) (0)
7. An Introduction to Stochastic Differential Equations (2009) (0)
Expansions of Distributions of Statitics Admitting Stochastic Expansions (1990) (0)
Special Topic: Branching Random Walk, Polymers, and Multiplicative Cascades (2021) (0)
Asymptotic expansions in statistics: A review of methods and applications (2011) (0)
4. Asymptotic Expansions—Nonlattice Distributions (2010) (0)
Reflection similarity shape spaces R??km (2012) (0)
Markov Processes, Fokker–Planck Equations for (2006) (0)
Fundamental Stochastic Models of the Transport of Water and Solutes Through Saturated and Unsaturated Porous Media: Project Completion Report (1977) (0)
Parametric models on Sd and ??k2 (2012) (0)
Consistency and Asymptotic Distributions of Statistics (2016) (0)
Nonparametric Curve Estimation (2016) (0)
The Functional Central Limit Theorem (FCLT) (2021) (0)
Kendall's similarity shape spaces ??km (2012) (0)
Correction [to "`On the stochastic foundations of the theory of water flow through unsaturated soil' by R. N. Bhattacharya, V. K. Gupta, and G. Sposito"] (1977) (0)
Estimating the Average Diameter of a Population of Spheres from Observed Diameters of Random Two-Dimensional Sections (2003) (0)
Location and spread on metric spaces (2012) (0)
3. Birth—Death Markov Chains (2009) (0)
5. Brownian Motion and Diffusions (2009) (0)
Seminar on stochastic processes, 1982: E. Çinlar, K.L. Chung, R.K. Getoor, Editors Birkhäuser, Boston, 1983 (1985) (0)
Application of the Markovian Hypothesis to the Theory of Soil Water Movement: Reply to Criticism (1977) (0)
The Upcrossings Inequality and (Sub)Martingale Convergence (2021) (0)
STATISTICS ON RIEMANNIAN MANIFOLDS (2006) (0)
Special Topic: A Comprehensive Renewal Theory for General Random Walks (2021) (0)
The Poisson Process, Compound Poisson Process, and Poisson Random Field (2021) (0)
Growth of Supercritical Bienaymé–Galton–Watson Simple Branching Processes (2021) (0)
Continuous Parameter Martingales (2021) (0)
Second Order Efficiency (1990) (0)
Brownian Motion on the Half-Line: Absorption and Reflection (2021) (0)
Special Topic: Ruin Problems in Insurance (2021) (0)
Optional Stopping of (Sub)Martingales (2021) (0)
Coupling Methods for Markov Chains and the Renewal Theorem for Lattice Distributions (2021) (0)
Invariant Distributions: Estimation and Computation (2007) (0)
2. Fourier Transforms and Expansions of Characteristics Functions (2010) (0)
Nonparametric Bayes regression, classification and hypothesis testing on manifolds (2012) (0)
Random Dynamical Systems: Markov Processes (2007) (0)
Random Dynamical Systems: Appendix (2007) (0)
Random Series of Independent Summands (2016) (0)
Special Topic: Incompressible Navier–Stokes Equations and the Le Jan–Sznitman Cascade (2021) (0)
Random Dynamical Systems: Discounted Dynamic Programming Under Uncertainty (2007) (0)
An Exposition of G\"otze's Estimation of the Rate of Convergence in the Multivariate Central Limit Theorem (2010) (0)
Fourier Series, Fourier Transform, and Characteristic Functions (2016) (0)
Modification of Leitmann's “optimum pursuit problem” (1970) (0)
Cornish-Fisher Expansions (1990) (0)
Random Maps, Distribution, and Mathematical Expectation (2016) (0)
The Kolmogorov–Chentsov Theorem and Sample Path Regularity (2021) (0)
On some problems in internal ballistics (1975) (0)
Book Reviews (2017) (0)
3. Bounds for Errors of Normal Approximation (2010) (0)
Multidimensional Random Walk (2021) (0)
Bootstrp and Edgeworth Expansion (1990) (0)

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