Mean Square Convergence Rates for Maximum Quasi-Likelihood Estimators
Published Online:12 Jan 2014https://doi.org/10.1287/12-SSY086
References
- , Some experimental results on the statistical properties of least squares estimates in control problems. Econometrica, 44(6): 1289–1302, 1976.Google Scholar
- , Revenue Management with Incomplete Demand Information. In J. J. Cochran, editor, Encyclopedia of Operations Research. Wiley, 2011.Google Scholar
- , An inverse matrix adjustment arising in discriminant analysis. The Annals of Mathematical Statistics, 22(1): 107–111, 1951. MR0040068Google Scholar
- , Dynamic pricing without knowing the demand function: risk bounds and near-optimal algorithms. Operations Research, 57(6): 1407–1420, 2009. MR2597918Link, Google Scholar
- , Positive Definite Matrices. Princeton University Press, Princeton, 2007. MR2284176Google Scholar
- , Dynamic pricing under a general parametric choice model. Operations Research, 60(4): 965–980, 2012. MR2979434Link, Google Scholar
- , Strong consistency of maximum quasi-likelihood estimate in generalized linear models via a last time. Statistics & Probability Letters, 45(3): 237–246, 1999. MR1718035Google Scholar
- , Strong consistency of maximum quasi-likelihood estimators in generalized linear models with fixed and adaptive designs. The Annals of Statistics, 27(4): 1155–1163, 1999. MR1740117Google Scholar
- , Probability Theory: Independence, Interchangeability, Martingales. Springer Verlag, New York, third edition, 2003.Google Scholar
- , Self-Normalized Processes: Limit Theory and Statistical Applications. Springer Series in Probability and its Applications. Springer, New York, first edition, 2009. MR2488094Google Scholar
- , Dynamic pricing with multiple products and partially specified demand distribution. Mathematics of Operations Research, Forthcoming, 2013.Google Scholar
- , Simultaneously learning and optimizing using controlled variance pricing. Management Science, Forthcoming, 2013.Google Scholar
- , Topology. Allyn and Bacon, Boston, 1966. MR0193606Google Scholar
- , Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. The Annals of Statistics, 13(1): 342–368, 1985. MR0773172Google Scholar
- , Generalized Linear Models: A Unified Approach. Sage Publications, Thousand Oaks, CA, 2001.Google Scholar
- , Woodroofe’s one-armed bandit problem revisited. The Annals of Applied Probability, 19(4): 1603–1633, 2009. MR2538082Google Scholar
- , Quasi-Likelihood and Its Application. Springer Series in Statistics. Springer Verlag, New York, 1997. MR1461808Google Scholar
- , Dynamic pricing with an unknown linear demand model: asymptotically optimal semi-myopic policies. Working paper, University of Chicago, http://faculty.chicagobooth.edu/bora.keskin/pdfs/DynamicPricingUnknownDemandModel.pdf, 2013.Google Scholar
- , Iterated least squares in multiperiod control. Advances in Applied Mathematics, 3(1): 50–73, 1982. MR0646499Google Scholar
- , Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. The Annals of Statistics, 10(1): 154–166, 1982. MR0642726Google Scholar
- , Topologie et equations fonctionelles. Annales Scientifiques de l’École Normale Supérieure, 51: 45–78, 1934. MR1509338Google Scholar
- , Probability Theory I. Springer Verlag, New York, Berlin, Heidelberg, 4th edition, 1977a. MR0651017Google Scholar
- , Probability Theory II. Springer Verlag, New York, Berlin, Heidelberg, 4th edition, 1977b. MR0651017Google Scholar
- , Quasi-likelihood functions. The Annals of Statistics, 11(1): 59–67, 1983. MR0684863Google Scholar
- , Generalized Linear Models. Chapman & Hall, London, 1983. MR0727836Google Scholar
- , Generalized linear models. Journal of the Royal Statistical Society, Series A (General), 135(3): 370–384, 1972.Google Scholar
- , Iterative Solution of Nonlinear Equations in Several Variables, volume 30 of SIAM’s Classics in Applied Mathematics. Society for, Industrial and Applied Mathematics, Philadelphia, 2000. MR1744713Google Scholar
- , Optimal experimental design and some related control problems. Automatica, 44(2): 303–325, 2008. MR2530779Google Scholar
- , Linearly parameterized bandits. Mathematics of Operations Research, 35(2): 395–411, 2010. MR2674726Link, Google Scholar
- , Eliminating multiple root problems in estimation. Statistical Science, 15(4): 313–332, 2000. MR1819708Google Scholar
- , Improved convergence rates for tail probabilities. Bulletin of the Transilvania University of Brasov – Series III: Mathematics, Informatics, Physics, 2(51): 137–142, 2009. MR2642502Google Scholar
- , Baum-Katz-Nagaev type results for martingales. Journal of Mathematical Analysis and Applications, 336(2): 1489–1492, 2007. MR2353031Google Scholar
- , A note on the uniqueness of the quasi-likelihood estimator. Statistics & Probability Letters, 38(2): 125–130, 1998. MR1627914Google Scholar
- , Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika, 61(3): 439–447, 1974. MR0375592Google Scholar
- , Rate of strong consistency of maximum quasi-likelihood estimator in multivariate generalized linear models. Communications in Statistics – Theory and Methods, 37(19): 3115–3123, 2008. MR2467755Google Scholar
- , Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models. Science in China Series A: Mathematics, 47(6): 882–893, 2004. MR2127216Google Scholar
- , On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models. Science in China Series A: Mathematics, 51(7): 1287–1296, 2008. MR2417495Google Scholar
- , Asymptotic properties of quasi-maximum likelihood estimates in generalized linear models. Communications in Statistics – Theory and Methods, 40(24): 4417–4430, 2011. MR2864166Google Scholar
- , Asymptotic properties in generalized linear models with natural link function and adaptive designs. Advances in Mathematics (China), 42(1): 121–127, 2013. MR3098890Google Scholar

