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Published: 26 October 2023

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1

Gupta, Vijay, and Ravi P. Agarwal. Convergence Estimates in Approximation Theory. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02765-4.

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2

Senatov, V. V. Qualitative effects in the estimates of the convergence rate in the central limit theorem in multidimensional spaces. Moscow: Maik Nauka/Interperiodica Publishing, 1996.

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3

M, Křížek, Neittaanmäki P, and Stenberg R. 1953-, eds. Finite element methods: Superconvergence, post-processing, and a posteriori estimates. New York: M. Dekker, 1998.

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4

Newey, Whitney K. Convergence rates for series estimators. Cambridge, Mass: Dept. of Economics, Massachusetts Institute of Technology, 1993.

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5

Newey, Whitney K. Convergence rates & asymptotic normality for series estimators. Cambridge, Mass: Dept. of Economics, Massachusetts Institute of Technology, 1995.

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6

Ferger, D. On the almost sure convergence of maximum likelihood-type estimators for a change point. Dresden: Technische Universität Dresden, Institut für Mathematische Stochastik, 2004.

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7

J, Kavanagh Michael, Armstrong Laboratory (U.S.), and State University of New York at Albany., eds. Transferability of skills: Convergent, postdictive, criterion-related, and construct validation of cross-job retraining time estimates. Brooks AFB, TX: U.S. Air Force, Armstrong Laboratory, 1997.

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8

Agarwal, Ravi P., and Vijay Gupta. Convergence Estimates in Approximation Theory. Springer London, Limited, 2014.

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9

Agarwal, Ravi P., and Vijay Gupta. Convergence Estimates in Approximation Theory. Springer, 2016.

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10

Convergence Estimates In Approximation Theory. Springer International Publishing AG, 2014.

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11

Convergence estimates for multidisciplinary analysis and optimization. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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12

Li, Jingzhi, and Michael V. Klibanov. Inverse Problems and Carleman Estimates: Global Uniqueness, Global Convergence and Experimental Data. de Gruyter GmbH, Walter, 2021.

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13

Li, Jingzhi, and Michael V. Klibanov. Inverse Problems and Carleman Estimates: Global Uniqueness, Global Convergence and Experimental Data. de Gruyter GmbH, Walter, 2021.

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14

Inverse Problems and Carleman Estimates: Global Uniqueness, Global Convergence and Experimental Data. de Gruyter GmbH, Walter, 2021.

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15

Krizek, Michel. Finite Element Methods: Superconvergence, Post-Processing, and a Posterior Estimates. CRC Press LLC, 2017.

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16

Finite Element Methods: Superconvergence, Post-Processing, and a Posterior Estimates. CRC Press LLC, 2017.

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17

Isett, Philip. Preparatory Lemmas. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0014.

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This chapter prepares for the proof by introducing a method concerning the general rate of convergence of mollifiers. The lemma takes into account the multi-index, the moment vanishing conditions, and smooth functions. An explanation for reducing the number of minus signs appearing in the proof is offered. The case N = 2 of the above lemma suffices for the proof of the main theorem. The chapter considers another way to work out the details relating to the lemma, which will be repeatedly used in the remainder of the proof. In particular, it describes functions whose integrals are not normalized to 1, but which satisfy the same type of estimates as ∈subscript Element.
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18

Mas, André, and Besnik Pumo. Linear Processes for Functional Data. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.3.

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This article provides an overview of the basic theory and applications of linear processes for functional data, with particular emphasis on results published from 2000 to 2008. It first considers centered processes with values in a Hilbert space of functions before proposing some statistical models that mimic or adapt the scalar or finite-dimensional approaches for time series. It then discusses general linear processes, focusing on the invertibility and convergence of the estimated moments and a general method for proving asymptotic results for linear processes. It also describes autoregressive processes as well as two issues related to the general estimation problem, namely: identifiability and the inverse problem. Finally, it examines convergence results for the autocorrelation operator and the predictor, extensions for the autoregressive Hilbertian (ARH) model, and some numerical aspects of prediction when the data are curves observed at discrete points.
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19

Cheng, Russell. Embedded Distributions: Two Numerical Examples. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0007.

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This chapter illustrates use of (i) the score statistic and (ii) a goodness-of-fit statistic to test if an embedded model provides an adequate fit, in the latter case with critical values calculated by bootstrapping. Also illustrated is (iii) calculation of parameter confidence intervals and CDF confidence bands using both asymptotic theory and bootstrapping, and (iv) use of profile log-likelihood plots to display the form of the maximized log-likelihood and scatterplots for checking convergence to normality of estimated parameter distributions. Two different data sets are analysed. In the first, the generalized extreme value (GEVMin) distribution and its embedded model the simple extreme value (EVMin) are fitted to Kevlar-fibre breaking strength data. In the second sample, the four-parameter Burr XII distribution, its three-parameter embedded models, the GEVMin, Type II generalized logistic and Pareto and two-parameter embedded models, the EVMin and shifted exponential, are fitted to carbon-fibre strength data and compared.
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20

Davidson, James. Stochastic Limit Theory. 2nd ed. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192844507.001.0001.

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This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first provides a handbook and reference for the underlying mathematics (Part I, Chapters 1–6), statistical theory (Part II, Chapters 7–11), and stochastic process theory (Part III, Chapters 12–18). The second half provides a treatment of the main convergence theorems used in analysing the large sample behaviour of econometric estimators and tests. These are the law of large numbers (Part IV, Chapters 19–22), the central limit theorem (Part V, Chapters 23–26), and the functional central limit theorem (Part VI, Chapters 27–32). The focus in this treatment is on the nonparametric approach to time series properties, covering topics such as nonstationarity, mixing, martingales, and near‐epoch dependence. While the approach is not elementary, care is taken to keep the treatment self‐contained. Proofs are provided for almost all the results.
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21

Wang, Bin. Intraseasonal Modulation of the Indian Summer Monsoon. Oxford University Press, 2018. http://dx.doi.org/10.1093/acrefore/9780190228620.013.616.

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The strongest Indian summer monsoon (ISM) on the planet features prolonged clustered spells of wet and dry conditions often lasting for two to three weeks, known as active and break monsoons. The active and break monsoons are attributed to a quasi-periodic intraseasonal oscillation (ISO), which is an extremely important form of the ISM variability bridging weather and climate variation. The ISO over India is part of the ISO in global tropics. The latter is one of the most important meteorological phenomena discovered during the 20th century (Madden & Julian, 1971, 1972). The extreme dry and wet events are regulated by the boreal summer ISO (BSISO). The BSISO over Indian monsoon region consists of northward propagating 30–60 day and westward propagating 10–20 day modes. The “clustering” of synoptic activity was separately modulated by both the 30–60 day and 10–20 day BSISO modes in approximately equal amounts. The clustering is particularly strong when the enhancement effect from both modes acts in concert. The northward propagation of BSISO is primarily originated from the easterly vertical shear (increasing easterly winds with height) of the monsoon flows, which by interacting with the BSISO convective system can generate boundary layer convergence to the north of the convective system that promotes its northward movement. The BSISO-ocean interaction through wind-evaporation feedback and cloud-radiation feedback can also contribute to the northward propagation of BSISO from the equator. The 10–20 day oscillation is primarily produced by convectively coupled Rossby waves modified by the monsoon mean flows. Using coupled general circulation models (GCMs) for ISO prediction is an important advance in subseasonal forecasts. The major modes of ISO over Indian monsoon region are potentially predictable up to 40–45 days as estimated by multiple GCM ensemble hindcast experiments. The current dynamical models’ prediction skills for the large initial amplitude cases are approximately 20–25 days, but the prediction of developing BSISO disturbance is much more difficult than the prediction of the mature BSISO disturbances. This article provides a synthesis of our current knowledge on the observed spatial and temporal structure of the ISO over India and the important physical processes through which the BSISO regulates the ISM active-break cycles and severe weather events. Our present capability and shortcomings in simulating and predicting the monsoon ISO and outstanding issues are also discussed.
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