Optimal adaptive sampling for a symmetric two-state continuous time Markov chain

References

• Aït-Sahalia, Y., Mykland, P. A., Zhang, L. (2005). How often to sample a continuous-time process in the presence of market microstructure noise. The Review of Financial studies 18(2):351–416. doi:10.1093/rfs/hhi016
   Web of Science ®Google Scholar
• Anderson, T. W., Taylor, J. B. (1976). Some experimental results on the statistical properties of least squares estimates in control problems. Econometrica 44 (6):1289–1302. doi:10.2307/1914261
   Web of Science ®Google Scholar
• Arcidiacono, P., Bayer, P., Blevins, J. R., Ellickson, P. B. (2016). Estimation of dynamic discrete choice models in continuous time with an application to retail competition. The Review of Economic Studies 83 (3):889–931. doi:10.1093/restud/rdw012
   Web of Science ®Google Scholar
• Bandi, F. M., Russell, J. R. (2008). Microstructure noise, realized variance, and optimal sampling. The Review of Economic Studies 75(2):339–369. doi:10.1111/j.1467-937X.2008.00474.x
   Web of Science ®Google Scholar
• Becker, G., Kersting, G. (1983). Design problems for the pure birth process. Advances in Applied Probability 15 (2):255–273. doi:10.2307/1426436
   Web of Science ®Google Scholar
• Bergstrom, A. R. (1990). Continuous Time Econometric Modelling. Oxford: Oxford University Press.
   Google Scholar
• Billingsley, P. (1961). Statistical Inference for Markov Processes. Chicago: University of Chicago Press.
   Google Scholar
• Blevins, J. R. (2017). Identifying restrictions for finite parameter continuous time models with discrete time data. Econometric Theory 33(3):739–754. doi:10.1017/S0266466615000353
   Web of Science ®Google Scholar
• Chernoff, H. (1953). Locally optimal designs for estimating parameters. The Annals of Mathematical Statistics 24 (4):586–602. doi:10.1214/aoms/1177728915
   Google Scholar
• Chernoff, H. (1959). Sequential design of experiments. The Annals of Mathematical Statistics 30 (3):755–770. doi:10.1214/aoms/1177706205
   Google Scholar
• Davidson, J. (1994). Stochastic Limit Theory: An Introduction for Econometricians. Oxford: OUP.
   Google Scholar
• Doraszelski, U., Judd, K. L. (2012). Avoiding the curse of dimensionality in dynamic stochastic games. Quantitative Economics 3(1):53–93. doi:10.3982/QE153
   Web of Science ®Google Scholar
• Ehrenfeld, S. (1962). Some experimental design problems in attribute life testing. Journal of the American Statistical Association 57(299):668–679. doi:10.1080/01621459.1962.10500555
   Web of Science ®Google Scholar
• Elfving, G. (1937). Zur theorie der Markoffschen ketten.
   Google Scholar
• Hong, H., Li, W., Wang, B. (2015). Estimation of dynamic discrete models from time aggregated data. Journal of Econometrics 188(2):435–446. doi:10.1016/j.jeconom.2015.03.009
   Web of Science ®Google Scholar
• Israel, R. B., Rosenthal, J. S., Wei, J. Z. (2001). Finding generators for markov chains via empirical transition matrices, with applications to credit ratings. Mathematical Finance 11(2):245–265. doi:10.1111/1467-9965.00114
   Web of Science ®Google Scholar
• Kiefer, J., Wolfowitz, J. (1952). Stochastic estimation of the maximum of a regression function. The Annals of Mathematical Statistics 23 (3):462–466. doi:10.1214/aoms/1177729392
   Google Scholar
• Kingman, J. F. C. (1962). The imbedding problem for finite Markov chains. Zeitschrift fr Wahrscheinlichkeitstheorie Und Verwandte Gebiete 1(1):14–24. doi:10.1007/BF00531768
   Google Scholar
• Lai, T. L., Robbins, H. (1982). Iterated least squares in multiperiod control. Advances in Applied Mathematics 3 (1):50–73. doi:10.1016/S0196-8858(82)80005-5
   Google Scholar
• Merton, R. C. (1990). Continuous-Time Finance. Massachusetts: Blackwell.
   Google Scholar
• Pagendam, D. E., Pollett, P. K. (2010). Locally optimal designs for the simple death process. Journal of Statistical Planning and Inference 140 (11):3096–3105. doi:10.1016/j.jspi.2010.04.017
   Web of Science ®Google Scholar
• Phillips, P. C. B. (1976). The estimation of linear stochastic differential equations with exogenous variables. In Statistical Inference in Continuous Time Models, Amsterdam: North Holland, pp. 135–173.
   Google Scholar
• Robbins, H., Monro, S. (1951). A stochastic approximation method. The Annals of Mathematical Statistics 22 (3):400–407. doi:10.1214/aoms/1177729586
   Google Scholar
• Van der Vaart, A. W. (2010). Time Series. Lecture notes: http://www.math.leidenuniv.nl/avdvaart/timeseries/dictaat.pdf.
   Google Scholar
• Yu, J. (2012). Bias in the estimation of the mean reversion parameter in continuous time models. Journal of Econometrics 169(1):114–122. doi:10.1016/j.jeconom.2012.01.004
   Web of Science ®Google Scholar
• Yu, J. (2014). Econometric analysis of continuous time models: a survey of Peter Phillip’s work and some new results. Econometric Theory 30(4):737–774.
   Web of Science ®Google Scholar
• Zhou, Q., Yu, J. (2015). Asymptotic theory for linear diffusions under alternative sampling schemes. Economics Letters 128:1–5. doi:10.1016/j.econlet.2014.12.015
   Web of Science ®Google Scholar