# Non-parametric lower bounds and information functions

Conference item

Novak, S. 2018. Non-parametric lower bounds and information functions.

*ISNPS-Third Conference of the International Society for Nonparametric Statistics (ISNPS).*Avignon, France 11 - 16 Jun 2016 Springer. pp. 69-83 https://doi.org/10.1007/978-3-319-96941-1

Title | Non-parametric lower bounds and information functions |
---|---|

Authors | Novak, S. |

Abstract | We argue that common features of non-parametric estimation appear in parametric cases as well if there is a deviation from the classical regularity condition. Namely, in many non-parametric estimation problems (as well as some parametric cases) unbiased finite-variance estimators do not exist; neither estimator converges locally uniformly with the optimal rate; there are no asymptotically unbiased with the optimal rate estimators; etc.. |

Conference | ISNPS-Third Conference of the International Society for Nonparametric Statistics (ISNPS) |

Page range | 69-83 |

ISSN | 2194-1009 |

ISBN | |

Hardcover | 9783319969404 |

Publisher | Springer |

Publication dates | |

Print | 16 Oct 2018 |

Online | 09 Mar 2018 |

Publication process dates | |

Deposited | 25 Oct 2016 |

Accepted | 01 Jan 2016 |

Completed | 16 Jun 2016 |

Output status | Published |

Accepted author manuscript | |

First submitted version | |

Copyright Statement | Final Accepted Version: This is a pre-copyedited version of a contribution published in Nonparametric Statistics: 3rd ISNPS, Avignon, France, June 2016, Editors: Patrice Bertail, Pierre-André Cornillon, Eric Matzner-Lober, Delphine Blanke, published by Springer International Publishing. The definitive authenticated version is available online via https://doi.org/10.1007/978-3-319-96941-1 |

Additional information | Novak S.Y. (2016) Non-parametric lower bounds and information functions. – In: Abstr. ISNPS-3 Conf., Avignon, p. 131. |

Digital Object Identifier (DOI) | https://doi.org/10.1007/978-3-319-96941-1 |

Language | English |

Book title | Nonparametric Statistics: 3rd ISNPS, Avignon, France, June 2016 |

https://repository.mdx.ac.uk/item/86qx5

## Download files

##### 54

total views##### 15

total downloads##### 0

views this month##### 0

downloads this month

## Export as

## Related outputs

##### On Poisson approximation

Novak, S. 2024. On Poisson approximation.*Journal of Theoretical Probability.*https://doi.org/10.1007/s10959-023-01310-4

##### Poisson approximation. Addendum

Novak, S. 2021. Poisson approximation. Addendum.*Probability Surveys.*18, pp. 272-275. https://doi.org/10.1214/21-PS2

##### On the T-test

Novak, S. 2022. On the T-test.*Statistics & Probability Letters.*189. https://doi.org/10.1016/j.spl.2022.109562

##### Compound Poisson approximation

Čekanavičius, V. and Novak, S. 2022. Compound Poisson approximation.*Probability Surveys.*19, pp. 271-350. https://doi.org/10.1214/22-PS8

##### Poisson approximation in terms of the Gini-Kantorovich distance

Novak, S. 2021. Poisson approximation in terms of the Gini-Kantorovich distance.*Extremes.*24 (1), pp. 64-87. https://doi.org/10.1007/s10687-020-00392-1

##### On the T-test

Novak, S. 2020. On the T-test.##### Poisson approximation

Novak, S. 2019. Poisson approximation.*Probability Surveys.*16, pp. 228-276. https://doi.org/10.1214/18-PS318

##### On the accuracy of poisson approximation

Novak, S. 2019. On the accuracy of poisson approximation.*Extremes.*22 (4), pp. 729-748. https://doi.org/10.1007/s10687-019-00350-6

##### On the length of the longest head run

Novak, S. 2017. On the length of the longest head run.*Statistics & Probability Letters.*30, pp. 111-114. https://doi.org/10.1016/j.spl.2017.06.020

##### Inference about the Pareto--type distribution

Novak, S. 1992. Inference about the Pareto--type distribution.*Transactions of the Eleventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes.*Prague 26 - 31 Aug 1990 pp. 251-258

##### On the joint limiting distribution of the first and the second maxima

Novak, S. and Weissman, I. 1998. On the joint limiting distribution of the first and the second maxima.*Communications In Statistics. Stochastic Models.*14 (1-2), pp. 311-318. https://doi.org/10.1080/15326349808807473

##### On blocks and runs estimators of extremal index

Weissman, I. and Novak, S. 1998. On blocks and runs estimators of extremal index.*Journal of Statistical Planning and Inference.*66 (2), pp. 281-288. https://doi.org/10.1016/S0378-3758(97)00095-5

##### Time intervals of constant sojourn of a homogeneous Markov chain in a fixed subset of states

Novak, S. 1988. Time intervals of constant sojourn of a homogeneous Markov chain in a fixed subset of states.*Siberian Mathematical Journal.*29 (1), pp. 100-109. https://doi.org/10.1007/BF00975021

##### Asymptotic properties of the distribution of the length of the longest head run

Novak, S. 1988.*Asymptotic properties of the distribution of the length of the longest head run.*Thesis Russian Academy of Sciences Institute of Mathematics (Novosibirsk)

##### Asymptotic expansions in the problem of the longest head run for Markov chain with two states

Novak, S. 1989. Asymptotic expansions in the problem of the longest head run for Markov chain with two states.*Trudy Inst. Math. (Novosibirsk).*13, pp. 136-147.

##### Asymptotics of the distribution of the ratio of sums of random variables

Novak, S. and Utev, S. 1990. Asymptotics of the distribution of the ratio of sums of random variables.*Siberian Mathematical Journal.*31 (5), pp. 781-788. https://doi.org/10.1007/BF00974491

##### Rate of convergence in the limit theorem for the length of the longest head run

Novak, S. 1991. Rate of convergence in the limit theorem for the length of the longest head run.*Siberian Mathematical Journal.*32 (3), pp. 444-448. https://doi.org/10.1007/BF00970481

##### On the distribution of the maximum of random number of random variables

Novak, S. 1991. On the distribution of the maximum of random number of random variables.*Theory Probab. Appl..*36 (4), pp. 714-721.

##### Longest runs in a sequence of m-dependent random variables

Novak, S. 1992. Longest runs in a sequence of m-dependent random variables.*Probability Theory and Related Fields.*91 (3-4), pp. 269-281. https://doi.org/10.1007/BF01192057

##### On the asymptotic distribution of the number of random variables exceeding a given level

Novak, S. 1993. On the asymptotic distribution of the number of random variables exceeding a given level.*Siberian advances in mathematics.*3 (4), pp. 108-122.

##### Asymptotic expansions for the maximum of random number of random variables

Novak, S. 1994. Asymptotic expansions for the maximum of random number of random variables.*Stochastic Processes and their Applications.*51 (2), pp. 297-305. https://doi.org/10.1016/0304-4149(94)90047-7

##### Poisson approximation for the number of long match patterns in random sequences

Novak, S. 1994. Poisson approximation for the number of long match patterns in random sequences.*Theory of Probability and Its Applications.*39 (4), pp. 593-603. https://doi.org/10.1137/1139045

##### Long match patterns in random sequences

Novak, S. 1995. Long match patterns in random sequences.*Siberian Adv. Math..*5 (3), pp. 128-140.

##### On extreme values in stationary sequences

Novak, S. 1996. On extreme values in stationary sequences.*Siberian Adv. Math..*6 (3), pp. 68-80.

##### On the distribution of the ratio of sums of random variables

Novak, S. 1996. On the distribution of the ratio of sums of random variables.*Theory of Probability and Its Applications.*41 (3), pp. 479-503. https://doi.org/10.1137/S0040585X97975228

##### Statistical estimation of the maximal eigenvalue of a matrix

Novak, S. 1996. Statistical estimation of the maximal eigenvalue of a matrix.*Russian Math. (Izvestia Vys. Ucheb. Zaved.).*41 (5), pp. 46-49.

##### On the Erdös-Rènyi maximum of partial sums

Novak, S. 1998. On the Erdös-Rènyi maximum of partial sums.*Theory of Probability and Its Applications.*42 (2), pp. 254-270. https://doi.org/10.1137/S0040585X97976118

##### Limit theorems and estimates of rates of convergence in extreme value theory. – DSc thesis

Novak, S. 2013.*Limit theorems and estimates of rates of convergence in extreme value theory. – DSc thesis.*Thesis St. Petersburg branch of Steklov Institute of Mathematics, Russian Academy of Sciences, and St. Petersburg University St. Petersburg Department of Steklov Institute of Mathematics

##### On the limiting distribution of extremes

Novak, S. 1998. On the limiting distribution of extremes.*Siberian Adv. Math..*8 (2), pp. 70-95.

##### Generalised kernel density estimator

Novak, S. 1999. Generalised kernel density estimator.*Theory of Probability and Its Applications.*44 (3), pp. 570-583. https://doi.org/10.1137/S0040585X97977781

##### On the mode of an unknown probability distribution

Novak, S. 2000. On the mode of an unknown probability distribution.*Theory of Probability and Its Applications.*44 (1), pp. 109-113. https://doi.org/10.1137/s0040585x97977392

##### Measures of financial risk

Novak, S. 2016. Measures of financial risk. in: Longin, F. (ed.) Extreme Events in Finance: A Handbook of Extreme Value Theory and its Applications Wiley. pp. 215-237##### On measures of financial risk

Novak, S. 2015. On measures of financial risk.*International Conference on Risk Analysis ICRA 6 / RISK 2015.*Barcelona, Spain 26 - 29 May 2015 FUNDACIÓN MAPFRE. pp. 541-550

##### On the accuracy of inference on heavy-tailed distributions

Novak, S. 2013. On the accuracy of inference on heavy-tailed distributions.*Theory of Probability and Its Applications.*58 (3), pp. 509-518. https://doi.org/10.1137/S0040585X97986710

##### Lower bounds to the accuracy of inference on heavy tails

Novak, S. 2014. Lower bounds to the accuracy of inference on heavy tails.*Bernoulli.*20 (2), pp. 979-989. https://doi.org/10.3150/13-BEJ512

##### On exceedances of high levels

Novak, S. and Xia, A. 2012. On exceedances of high levels.*Stochastic Processes and their Applications.*122 (2), pp. 582-599. https://doi.org/10.1016/j.spa.2011.09.003

##### On limiting cluster size distributions for processes of exceedances for stationary sequences.

Borovkov, K. and Novak, S. 2010. On limiting cluster size distributions for processes of exceedances for stationary sequences.*Statistics & Probability Letters.*80 (23-24), pp. 1814-1818. https://doi.org/10.1016/j.spl.2010.08.006

##### Extreme value methods with applications to finance.

Novak, S. 2011.*Extreme value methods with applications to finance.*Chapman & Hall / CRC Press.

##### Lower bounds to the accuracy of sample maximum estimation.

Novak, S. 2009. Lower bounds to the accuracy of sample maximum estimation.*Theory of stochastic processes.*15(31) (2), pp. 156-161.

##### Impossibility of consistent estimation of the distribution function of a sample maximum.

Novak, S. 2010. Impossibility of consistent estimation of the distribution function of a sample maximum.*Statistics.*44 (1), pp. 25-30. https://doi.org/10.1080/02331880902986497

##### A remark concerning value-at-risk

Novak, S. 2010. A remark concerning value-at-risk.*International Journal of Theoretical and Applied Finance.*13 (4), pp. 507-515. https://doi.org/10.1142/S0219024910005917

##### On self-normalised sums.

Novak, S. 2000. On self-normalised sums.*Mathematical methods of statistics..*9 (4), pp. 415-436.

##### Inference on heavy tails from dependent data.

Novak, S. 2002. Inference on heavy tails from dependent data.*Siberian advances in mathematics.*12 (2), pp. 73-96.

##### On self-normalised sums [supplement]

Novak, S. 2002. On self-normalised sums [supplement].*Mathematical methods of statistics..*11 (2), pp. 256-258.

##### Evaluating currency risk in emerging markets.

Novak, S., Dalla, V. and Giraitis, L. 2007. Evaluating currency risk in emerging markets.*Acta applicandae mathematicae..*97 (1-3), pp. 163-175.

##### Advances in extreme value theory with applications to finance.

Novak, S. 2009. Advances in extreme value theory with applications to finance. in: Keene, J. (ed.) New business and finance research developments. New York Nova Science Publishers. pp. 199-251##### Measures of financial risks and market crashes.

Novak, S. 2007. Measures of financial risks and market crashes.*Theory of stochastic processes.*13 (1-2), pp. 182-193.

##### A new characterization of the normal law

Novak, S. 2006. A new characterization of the normal law.*Statistics & Probability Letters.*77 (1), pp. 95-98.

##### On Gebelein's correlation coefficient

Novak, S. 2004. On Gebelein's correlation coefficient.*Statistics & Probability Letters.*69 (3), pp. 299-303.

##### Confidence intervals for a tail index estimator

Novak, S. 2000. Confidence intervals for a tail index estimator. in: Franke, J., Stahl, G. and Hardle, W. (ed.) Measuring risk in complex stochastic systems London Springer.##### Long head runs and long match patterns.

Novak, S. and Embrechts, P. 2002. Long head runs and long match patterns. in: Sandmann, K. and Schönbucher, P. (ed.) Advances in finance and stochastics: essays in honour of Dieter Sondermann. London Springer. pp. 57-69##### Compound poisson approximation for the distribution of extremes

Novak, S., Barbour, A. and Xia, A. 2002. Compound poisson approximation for the distribution of extremes.*Advances in applied probability.*34 (1), pp. 223-240. https://doi.org/10.1239/aap/1019160958

##### Multilevel clustering of extremes

Novak, S. 2002. Multilevel clustering of extremes.*Stochastic Processes and their Applications.*97 (1), pp. 59-75. https://doi.org/10.1016/S0304-4149(01)00123-5

##### On the accuracy of multivariate compound Poisson approximation

Novak, S. 2003. On the accuracy of multivariate compound Poisson approximation.*Statistics & Probability Letters.*62 (1), pp. 35-43. https://doi.org/10.1016/S0167-7152(02)00422-4

##### On self-normalized sums and student's statistic

Novak, S. 2005. On self-normalized sums and student's statistic.*Theory of Probability and Its Applications.*49 (2), pp. 336-344. https://doi.org/10.1137/S0040585X97981081

##### The magnitude of a market crash can be predicted

Novak, S. and Beirlant, J. 2006. The magnitude of a market crash can be predicted.*Journal of Banking and Finance.*30 (2), pp. 453-462.