Non-Parametric functional estimation (Density, distribution function and quantile estimation by kernel and Berstein polynomial methods and their application in finance. Bootstrap methods for kernel estimators)\b
Nonparametric estimation of 100(1 − p)% expected shortfall: p → 0 as sample size is increased Santanu Dutta, Suparna Biswas Communications in Statistics Simulation and Computation, 2018 Expected shortfall (ES) is a well-known measure of extreme loss associated with a risky asset or portfolio. For any 0 < p < 1, the 100(1 − p) percent ES is defined as the mean of the conditional loss distribution, given the event that the loss exceeds (1 − p)th quantile of the marginal loss distribution. Estimation of ES based on asset return data is an important problem in finance. Several nonparametric estimators of the expected shortfall are available in the literature. Using Monte Carlo simulations, we compare the accuracy of these estimators under the condition that p → 0 as n → ∞ for several asset return time series models, where n is the sample size. Not much seems to be known regarding the properties of the ES estimators under this condition. For p close to zero, the ES measures an extreme loss in the right tail of the loss distribution of the asset or portfolio. Our simulations and real-data analysis provide insight into the effect of varying p with n on the performance of nonparametric ES estimators.
Extreme quantile estimation based on financial time series Santanu Dutta, Suparna Biswas Communications in Statistics Simulation and Computation, 2017 Estimation of market risk is an important problem in finance. Two well-known risk measures, viz., value at risk and median shortfall, turn out to be extreme quantiles of the marginal distribution of asset return. Time series on asset returns are known to exhibit certain stylized facts, such as heavy tails, skewness, volatility clustering, etc. Therefore, estimation of extreme quantiles in the presence of such features in the data seems to be of natural interest. It is difficult to capture most of these stylized facts using one specific time series model. This motivates nonparametric and extreme value theory-based estimation of extreme quantiles that do not require exact specification of the asset return model. We review these quantile estimators and compare their known properties. Their finite sample performance are compared using Monte Carlo simulation. We propose a new estimator that exhibits encouraging finite sample performance while estimating extreme quantile in the right tail region.
Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths Santanu Dutta, Koushik Saha Communications in Statistics Theory and Methods, 2017 We obtain the rates of pointwise and uniform convergence of multivariate kernel density estimators using a random bandwidth vector obtained by some data-based algorithm. We are able to obtain faster rate for pointwise convergence. The uniform convergence rate is obtained under some moment condition on the marginal distribution. The rates are obtained under i.i.d. and strongly mixing type dependence assumptions.
Distribution function estimation via Bernstein polynomial of random degree Santanu Dutta Metrika, 2016 The problem of distribution function (df) estimation arises naturally in many contexts. The empirical and the kernel df estimators are well known. There is another df estimator based on a Bernstein polynomial of degree m. For a Bernstein df estimator, plays the same role as the bandwidth in a kernel estimator. The asymptotic properties of the Bernstein estimator has been studied so far assuming m is non random, chosen subjectively. We propose algorithms for data driven choice of m. Such an m is a function of the data, i.e. random. We obtain the convergence rates of a Bernstein df estimator, using a random m, for i.i.d., strongly mixing and a broad class of linear processes. The estimator is shown to be consistent for any stationary, ergodic process satisfying some conditions. Using simulations and analysis of real data the finite sample performance of the different df estimators are compared.
Cross-validation Revisited Santanu Dutta Communications in Statistics Simulation and Computation, 2016 Data-based choice of the bandwidth is an important problem in kernel density estimation. The pseudo-likelihood and the least-squares cross-validation bandwidth selectors are well known, but widely criticized in the literature. For heavy-tailed distributions, the L1 distance between the pseudo-likelihood-based estimator and the density does not seem to converge in probability to zero with increasing sample size. Even for normal-tailed densities, the rate of L1 convergence is disappointingly slow. In this article, we report an interesting finding that with minor modifications both the cross-validation methods can be implemented effectively, even for heavy-tailed densities. For both these estimators, the L1 distance (from the density) are shown to converge completely to zero irrespective of the tail of the density. The expected L1 distance also goes to zero. These results hold even in the presence of a strongly mixing-type dependence. Monte Carlo simulations and analysis of the Old Faithful geyser data suggest that if implemented appropriately, contrary to the traditional belief, the cross-validation estimators compare well with the sophisticated plug-in and bootstrap-based estimators.
Excess over threshold distribution function estimation: S. Dutta, P. Dahal S Dutta, P Dahal Metrika, 1-21 , 2026 2026
Anti-racist reorientations to land through gardening with newcomer youth of color R Lognon, C Khandelwal, M Sanyal, S Dutta, P Banerjee, P Sengupta Frontiers in Climate 7, 1639059 , 2025 2025 Citations: 2
Non parametric estimation of parameters in using safety first criteria TK Powdel, S Dutta Communications in Statistics-Simulation and Computation, 1-18 , 2025 2025
Modeling long term return distribution and nonparametric market risk estimation S Dutta, TK Powdel Sankhya B 85 (Suppl 1), 257-289 , 2023 2023 Citations: 4
Kernel based estimation of the distribution function for length biased data A Bose, S Dutta Metrika 85 (3), 269-287 , 2022 2022 Citations: 4
Comparing the market risk of Indian balanced, small & midcap and large cap funds S Biswas, S Dutta October , 2019 2019 Citations: 1
Nonparametric estimation of 100(1 − p )% expected shortfall: p → 0 as sample size is increased S Dutta, S Biswas Communications in Statistics-Simulation and Computation 47 (2), 338-352 , 2018 2018 Citations: 9
Extreme quantile estimation based on financial time series S Dutta, S Biswas Communications in Statistics-Simulation and Computation 46 (6), 4226-4243 , 2017 2017 Citations: 14
Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths S Dutta, K Saha Communications in Statistics-Theory and Methods 46 (6), 2708-2723 , 2017 2017 Citations: 2
Distribution function estimation via Bernstein polynomial of random degree S Dutta Metrika 79 (3), 239-263 , 2016 2016 Citations: 8
Cross-validation revisited S Dutta Communications in Statistics-Simulation and Computation 45 (2), 472-490 , 2016 2016 Citations: 42
Consistency of multivariate density estimators using random bandwidths S Dutta, K Saha Communications in Statistics-Theory and Methods 45 (2), 252-266 , 2016 2016
Assessing market risk of Indian index funds S Biswas, S Dutta Global Business Review 16 (3), 511-523 , 2015 2015 Citations: 12
Local smoothing for kernel distribution function estimation S Dutta Communications in Statistics-Simulation and Computation 44 (4), 878-891 , 2015 2015 Citations: 11
Bandwidth selection for kernel based interval estimation of a density S Dutta Journal of Data Science 12 (3), 405-416 , 2014 2014 Citations: 1
Local smoothing using the bootstrap S Dutta Communications in Statistics-Simulation and Computation 43 (2), 378-389 , 2014 2014 Citations: 7
Pointwise and uniform convergence of kernel density estimators using random bandwidths S Dutta, A Goswami Statistics & Probability Letters 83 (12), 2711-2720 , 2013 2013 Citations: 3
A review of Indian index funds SS Sarkar, S Dutta, P Dutta Global Business Review 14 (1), 89-98 , 2013 2013 Citations: 15
Density estimation using bootstrap bandwidth selector A Bose, S Dutta Statistics & Probability Letters 83 (1), 245-256 , 2013 2013 Citations: 8
Estimation of the MISE and the optimal bandwidth vector of a product kernel density estimate S Dutta Journal of Statistical Planning and Inference 141 (5), 1817-1831 , 2011 2011 Citations: 8
MOST CITED SCHOLAR PUBLICATIONS
Cross-validation revisited S Dutta Communications in Statistics-Simulation and Computation 45 (2), 472-490 , 2016 2016 Citations: 42
The effect of literacy and bank penetration on financial inclusion in India: a statistical analysis S Dutta, P Dutta Tezpur University, Napaam , 2011 2011 Citations: 20
A review of Indian index funds SS Sarkar, S Dutta, P Dutta Global Business Review 14 (1), 89-98 , 2013 2013 Citations: 15
Extreme quantile estimation based on financial time series S Dutta, S Biswas Communications in Statistics-Simulation and Computation 46 (6), 4226-4243 , 2017 2017 Citations: 14
Mode estimation for discrete distributions S Dutta, A Goswami Mathematical Methods of Statistics 19 (4), 374-384 , 2010 2010 Citations: 14
Assessing market risk of Indian index funds S Biswas, S Dutta Global Business Review 16 (3), 511-523 , 2015 2015 Citations: 12
Local smoothing for kernel distribution function estimation S Dutta Communications in Statistics-Simulation and Computation 44 (4), 878-891 , 2015 2015 Citations: 11
Nonparametric estimation of 100(1 − p )% expected shortfall: p → 0 as sample size is increased S Dutta, S Biswas Communications in Statistics-Simulation and Computation 47 (2), 338-352 , 2018 2018 Citations: 9
Distribution function estimation via Bernstein polynomial of random degree S Dutta Metrika 79 (3), 239-263 , 2016 2016 Citations: 8
Density estimation using bootstrap bandwidth selector A Bose, S Dutta Statistics & Probability Letters 83 (1), 245-256 , 2013 2013 Citations: 8
Estimation of the MISE and the optimal bandwidth vector of a product kernel density estimate S Dutta Journal of Statistical Planning and Inference 141 (5), 1817-1831 , 2011 2011 Citations: 8
Local smoothing using the bootstrap S Dutta Communications in Statistics-Simulation and Computation 43 (2), 378-389 , 2014 2014 Citations: 7
Modeling long term return distribution and nonparametric market risk estimation S Dutta, TK Powdel Sankhya B 85 (Suppl 1), 257-289 , 2023 2023 Citations: 4
Kernel based estimation of the distribution function for length biased data A Bose, S Dutta Metrika 85 (3), 269-287 , 2022 2022 Citations: 4
Pointwise and uniform convergence of kernel density estimators using random bandwidths S Dutta, A Goswami Statistics & Probability Letters 83 (12), 2711-2720 , 2013 2013 Citations: 3
A Statistical Analysis of Daily Nifty Returns, During 2001-11 S Dutta International Journal of Research in Commerce, It & Management 1 (4), 133-137 , 2011 2011 Citations: 3
Anti-racist reorientations to land through gardening with newcomer youth of color R Lognon, C Khandelwal, M Sanyal, S Dutta, P Banerjee, P Sengupta Frontiers in Climate 7, 1639059 , 2025 2025 Citations: 2
Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths S Dutta, K Saha Communications in Statistics-Theory and Methods 46 (6), 2708-2723 , 2017 2017 Citations: 2
Ranking MFIS in India: using TOPSIS S Dutta, P Dutta INTERNATIIONAL JOURNAL OF RESEARCHIIN COMMERCE, IT AND MANAGEMENT 1 (3) , 2011 2011 Citations: 2
Comparing the market risk of Indian balanced, small & midcap and large cap funds S Biswas, S Dutta October , 2019 2019 Citations: 1
