@article{bhattacharyya_richardson_flores_2006, title={Unit roots: Periodogram ordinate}, volume={76}, ISSN={["1879-2103"]}, DOI={10.1016/j.spl.2005.09.011}, abstractNote={The periodogram ordinate is used to define an asymptotic test for the testing problem H0:α=1 vs. HA:|α|<1 under appropriate assumptions on the model Yt=αYt-1+εt-θεt-1, where θ is near one. A drift term is also included in the model. An independent and identically distributed error structure as well as one exhibiting long memory are studied.}, number={6}, journal={STATISTICS & PROBABILITY LETTERS}, author={Bhattacharyya, BB and Richardson, GD and Flores, PV}, year={2006}, month={Mar}, pages={641–651} }
@article{boissy_bhattacharyya_li_richardson_2005, title={Parameter estimates for fractional autoregressive spatial processes}, volume={33}, ISSN={["0090-5364"]}, DOI={10.1214/009053605000000589}, abstractNote={A binomial-type operator on a stationary Gaussian process is introduced in order to model long memory in the spatial context. Consistent estimators of model parameters are demonstrated. In particular, it is shown that d N - d = O P ((Log N) 3 /N ), where d = (d 1 , d 2 ) denotes the long memory parameter.}, number={6}, journal={ANNALS OF STATISTICS}, author={Boissy, Y and Bhattacharyya, BB and Li, X and Richardson, GD}, year={2005}, month={Dec}, pages={2553–2567} }
@article{bhattacharyya_ren_richardson_zhang_2003, title={Spatial autoregression model: strong consistency}, volume={65}, ISSN={["0167-7152"]}, DOI={10.1016/j.spl.2003.07.004}, abstractNote={Abstract Let ( α n , β n ) denote the Gauss–Newton estimator of the parameter (α,β) in the autoregression model Zij=αZi−1,j+βZi,j−1−αβZi−1,j−1+eij. It is shown in an earlier paper that when α=β=1, {n 3/2 ( α n −α, β n −β)} converges in distribution to a bivariate normal random vector. A two-parameter strong martingale convergence theorem is employed here to prove that n r ( α n −α, β n −β)→ 0 almost surely when r 3 2 .}, number={2}, journal={STATISTICS & PROBABILITY LETTERS}, author={Bhattacharyya, BB and Ren, JJ and Richardson, GD and Zhang, J}, year={2003}, month={Nov}, pages={71–77} }
@article{bhattacharyya_li_pensky_richardson_2000, title={Testing for unit roots in a nearly nonstationary spatial autoregressive process}, volume={52}, ISSN={["0020-3157"]}, DOI={10.1023/A:1004184932031}, number={1}, journal={ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS}, author={Bhattacharyya, BB and Li, X and Pensky, M and Richardson, GD}, year={2000}, month={Mar}, pages={71–83} }
@article{bhattacharyya_richardson_franklin_1997, title={Asymptotic inference for near unit roots in spatial autoregression}, volume={25}, DOI={10.1214/aos/1031594738}, abstractNote={Asymptotic inference for estimators of (α n , β n ) in the spatial autoregressive model z ij (n) = α n z i-1 , j (n) + β n Z i,j-1 (n) - α n β n Z i-1 , j-1 (n) + e ij obtained when α n and β n are near unit roots. When α n and β n are reparameterized by α n = e c/n and β n = e d/n , it is shown that if the one-step Gauss-Newton estimator of λ 1 α n + λ 2 β n is properly normalized and embedded in the function space D([0,1] 2 ), the limiting distribution is a Gaussian process. The key idea in the proof relies on a maximal inequality for a two-parameter martingale which may be of independent interest. A simulation study illustrates the speed of convergence and goodness-of-fit of these estimators for various sample sizes.}, number={4}, journal={Annals of Statistics}, author={Bhattacharyya, B. B. and Richardson, G. D. and Franklin, L. A.}, year={1997}, pages={1709–1724} }