Built on

[author] Shin, JaehyeokJ., Ramdas, AadityaA. and Rinaldo, AlessandroA. (2019b). On the bias, risk and consistency of sample means in multi-armed bandits. arXiv preprint arXiv:1902.00746. \endbibitem
Original
1902
Earlier work this paper cites.
[author] Fontaine, XavierX., Perrault, PierreP., Valko, MichalM. and Perchet, VianneyV. (2019). Online A-Optimal Design and Active Linear Regression. arXiv preprint arXiv:1906.08509. \endbibitem
Original
1906
Earlier work this paper cites.
[author] Deshpande, YashY., Javanmard, AdelA. and Mehrabi, MohammadM. (2019). Online debiasing for adaptively collected high-dimensional data. arXiv preprint arXiv:1911.01040. \endbibitem
Original
1911
Earlier work this paper cites.
[author] Hadad, VitorV., Hirshberg, David AD. A., Zhan, RuohanR., Wager, StefanS. and Athey, SusanS. (2019). Confidence intervals for policy evaluation in adaptive experiments. arXiv preprint arXiv:1911.02768. \endbibitem
Original
1911
Earlier work this paper cites.
[author] Lai, Tze LeungT. L. (1994). Asymptotic properties of nonlinear least squares estimates in stochastic regression models. The Annals of Statistics 22 1917–1930. \endbibitem
1930
Earlier work this paper cites.
[author] Thompson, William RW. R. (1933). On the likelihood that one unknown probability exceeds another in view of the evidence of two samples. Biometrika 25 285–294. \endbibitem
1933
Earlier work this paper cites.
[author] White, John SJ. S. (1958). The limiting distribution of the serial correlation coefficient in the explosive case. The Annals of Mathematical Statistics 1188–1197. \endbibitem
1958
Earlier work this paper cites.
{binproceedings}
1972
Earlier work this paper cites.
[author] Goodwin, GCG. and Payne, RLR. (1977). Dynamic system identification experiment design and data analysis. Mathematics in Science and Engineering, Volume 136. Elsevier. \endbibitem
1977
Earlier work this paper cites.
[author] Dickey, David AD. A. and Fuller, Wayne AW. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American statistical association 74 427–431. \endbibitem
1979
Earlier work this paper cites.

Similar

[author] Lai, T LT. L. and Robbins, HerbertH. (1979). Adaptive design and stochastic approximation. The Annals of Statistics 7 1196–1221. \endbibitem
1979
Cited alongside, same era.
[author] Lai, T L_etcT. L., Robbins, HerbertH. and Wei, C ZiC. Z. (1979). Strong consistency of least squares estimates in multiple regression II. Journal of Multivariate Analysis 9 343–361. \endbibitem
1979
Cited alongside, same era.
[author] Lai, Tze LeungT. L. and Wei, Ching ZongC. Z. (1982). Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. The Annals of Statistics 10 154–166. \endbibitem
1982
Cited alongside, same era.
[author] Zhang, Kelly WK. W., Janson, LucasL. and Murphy, Susan AS. A. (2020). Inference for Batched Bandits. arXiv preprint arXiv:2002.03217. \endbibitem
Original
2002
Cited alongside, same era.

Then

[author] Box, George EPG. E., Jenkins, Gwilym MG. M., Reinsel, Gregory CG. C. and Ljung, Greta MG. M. (2015). Time series analysis: forecasting and control. John Wiley & Sons. \endbibitem
2015
Later among the works it cites.
[author] Villar, Sofía SS. S., Bowden, JackJ. and Wason, JamesJ. (2015). Multi-armed bandit models for the optimal design of clinical trials: benefits and challenges. Statistical science: a review journal of the Institute of Mathematical Statistics 30 199. \endbibitem
2015
Later among the works it cites.
{binproceedings}
2018
Later among the works it cites.
[author] Kaufmann, EmilieE. and Koolen, WouterW. (2018). Mixture martingales revisited with applications to sequential tests and confidence intervals. arXiv preprint arXiv:1811.11419. \endbibitem
Original
2018
Later among the works it cites.
{binproceedings}
2018

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2021

Near-optimal inference in adaptive linear regression

Khamaru, Koulik, Deshpande, Yash, Lattimore, Tor et al.

Understand

When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior.

As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality can lead to erroneous results.
We propose a family of online debiasing estimators to correct these distributional anomalies in least squares estimation.
Our proposed methods take advantage of the covariance structure present in the dataset and provide sharper estimates in directions for which more information has accrued.

Built on

[author] Shin, JaehyeokJ., Ramdas, AadityaA. and Rinaldo, AlessandroA. (2019b). On the bias, risk and consistency of sample means in multi-armed bandits. arXiv preprint arXiv:1902.00746. \endbibitem
Original
1902
Earlier work this paper cites.
[author] Fontaine, XavierX., Perrault, PierreP., Valko, MichalM. and Perchet, VianneyV. (2019). Online A-Optimal Design and Active Linear Regression. arXiv preprint arXiv:1906.08509. \endbibitem
Original
1906
Earlier work this paper cites.
[author] Deshpande, YashY., Javanmard, AdelA. and Mehrabi, MohammadM. (2019). Online debiasing for adaptively collected high-dimensional data. arXiv preprint arXiv:1911.01040. \endbibitem
Original
1911
Earlier work this paper cites.
[author] Hadad, VitorV., Hirshberg, David AD. A., Zhan, RuohanR., Wager, StefanS. and Athey, SusanS. (2019). Confidence intervals for policy evaluation in adaptive experiments. arXiv preprint arXiv:1911.02768. \endbibitem
Original
1911
Earlier work this paper cites.
[author] Lai, Tze LeungT. L. (1994). Asymptotic properties of nonlinear least squares estimates in stochastic regression models. The Annals of Statistics 22 1917–1930. \endbibitem
1930
Earlier work this paper cites.
[author] Thompson, William RW. R. (1933). On the likelihood that one unknown probability exceeds another in view of the evidence of two samples. Biometrika 25 285–294. \endbibitem
1933
Earlier work this paper cites.
[author] White, John SJ. S. (1958). The limiting distribution of the serial correlation coefficient in the explosive case. The Annals of Mathematical Statistics 1188–1197. \endbibitem
1958
Earlier work this paper cites.
{binproceedings}
1972
Earlier work this paper cites.
[author] Goodwin, GCG. and Payne, RLR. (1977). Dynamic system identification experiment design and data analysis. Mathematics in Science and Engineering, Volume 136. Elsevier. \endbibitem
1977
Earlier work this paper cites.
[author] Dickey, David AD. A. and Fuller, Wayne AW. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American statistical association 74 427–431. \endbibitem
1979
Earlier work this paper cites.

Similar

[author] Lai, T LT. L. and Robbins, HerbertH. (1979). Adaptive design and stochastic approximation. The Annals of Statistics 7 1196–1221. \endbibitem
1979
Cited alongside, same era.
[author] Lai, T L_etcT. L., Robbins, HerbertH. and Wei, C ZiC. Z. (1979). Strong consistency of least squares estimates in multiple regression II. Journal of Multivariate Analysis 9 343–361. \endbibitem
1979
Cited alongside, same era.
[author] Lai, Tze LeungT. L. and Wei, Ching ZongC. Z. (1982). Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. The Annals of Statistics 10 154–166. \endbibitem
1982
Cited alongside, same era.
[author] Zhang, Kelly WK. W., Janson, LucasL. and Murphy, Susan AS. A. (2020). Inference for Batched Bandits. arXiv preprint arXiv:2002.03217. \endbibitem
Original
2002
Cited alongside, same era.

Then

[author] Box, George EPG. E., Jenkins, Gwilym MG. M., Reinsel, Gregory CG. C. and Ljung, Greta MG. M. (2015). Time series analysis: forecasting and control. John Wiley & Sons. \endbibitem
2015
Later among the works it cites.
[author] Villar, Sofía SS. S., Bowden, JackJ. and Wason, JamesJ. (2015). Multi-armed bandit models for the optimal design of clinical trials: benefits and challenges. Statistical science: a review journal of the Institute of Mathematical Statistics 30 199. \endbibitem
2015
Later among the works it cites.
{binproceedings}
2018
Later among the works it cites.
[author] Kaufmann, EmilieE. and Koolen, WouterW. (2018). Mixture martingales revisited with applications to sequential tests and confidence intervals. arXiv preprint arXiv:1811.11419. \endbibitem
Original
2018
Later among the works it cites.
{binproceedings}
2018

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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[author] Abbasi-Yadkori, YasinY., Pál, DavidD. and Szepesvári, CsabaC. (2011). Online least squares estimation with self-normalized processes: An application to bandit problems. arXiv preprint arXiv:1102.2670. \endbibitem

Original

2011

Cited alongside, same era.

[author] Åström, Karl JK. J. (2012). Introduction to stochastic control theory. Courier Corporation. \endbibitem

2012

Cited alongside, same era.

[author] Boucheron, S.S., Lugosi, G.G. and Massart, P.P. (2013). Concentration inequalities: A nonasymptotic theory of independence. Oxford University Press, Oxford, UK. \endbibitem

2013

Cited alongside, same era.

{binproceedings}

2013

Cited alongside, same era.

{binproceedings}

2014

Cited alongside, same era.

[author] Howard, Steven RS. R., Ramdas, AadityaA., McAuliffe, JonJ. and Sekhon, JasjeetJ. Time-uniform, nonparametric, non-asymptotic confidence sequences. The Annals of Statistics To appear. \endbibitem

Cited in the paper.

{binproceedings}

Cited in the paper.

[author] Zhang, Kelly WK. W., Janson, LucasL. and Murphy, Susan AS. A. Statistical Inference with M-Estimators on Adaptively Collected Data. \endbibitem

Original

Cited in the paper.

Later among the works it cites.

[author] Vershynin, RomanR. (2018). High-dimensional probability: An introduction with applications in data science 47. Cambridge university press. \endbibitem

2018

Later among the works it cites.

[author] Wainwright, Martin JM. J. (2019). High-dimensional statistics: A non-asymptotic viewpoint. Cambridge University Press. \endbibitem

2019

Later among the works it cites.

[author] Lattimore, TorT. and Szepesvári, CsabaC. (2020). Bandit algorithms. Cambridge University Press. \endbibitem

2020

Later among the works it cites.

[author] Lattimore, T.T. (2023). A Lower Bound for Linear and Kernel Regression with Adaptive Covariates. arXiv. \endbibitem

2023

Closest in time.