Estimation for misspecification when theoretical model for signal is smooth but real signal is of cusp-type and driven by a fractional Brownian motion

We study the problem of misspecification when the model proposed by the statistician (theoretical model) through a stochastic differential equation is smooth in the drift but the real model has a cusp-type singularity in the drift function and the driving force is a fractional Brownian motion.

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Published inStochastic analysis and applications Vol. 41; no. 6; pp. 1119 - 1135
Main Authors Mishra, M. N., Prakasa Rao, B. L. S.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.11.2023
Taylor & Francis Ltd
Subjects
Brownian motion
cusp-type signal
Cusps
Differential equations
Drift
fractional Brownian motion
maximum likelihood estimation
Misspecified model
Primary 60G22
Secondary 62M09
stochastic differential equation
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Abstract We study the problem of misspecification when the model proposed by the statistician (theoretical model) through a stochastic differential equation is smooth in the drift but the real model has a cusp-type singularity in the drift function and the driving force is a fractional Brownian motion.
AbstractList We study the problem of misspecification when the model proposed by the statistician (theoretical model) through a stochastic differential equation is smooth in the drift but the real model has a cusp-type singularity in the drift function and the driving force is a fractional Brownian motion.
Author Mishra, M. N.
Prakasa Rao, B. L. S.
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Cites_doi 10.1080/17442508.2013.802791
10.1177/00080683221139081
10.1016/0167-7152(85)90004-5
10.1007/978-1-4899-0027-2
10.2307/3318691
10.1007/978-3-540-75873-0
10.1214/aoms/1177698506
10.1016/S0047-259X(03)00102-7
10.1163/156939703771378581
10.1080/07362994.2019.1646140
10.1016/B978-1-4832-0022-4.50006-5
10.1007/s10463-016-0581-x
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References e_1_3_2_16_1
e_1_3_2_9_1
e_1_3_2_7_1
e_1_3_2_19_1
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Prakasa Rao B. L. S. (e_1_3_2_8_1) 1999
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Kleptsyna M. L. (e_1_3_2_15_1) 2000; 3
Prakasa Rao B. L. S. (e_1_3_2_5_1) 1987
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  year: 1968
  ident: e_1_3_2_18_1
  contributor:
    fullname: Billingsley P.
– ident: e_1_3_2_20_1
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  doi: 10.1177/00080683221139081
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    fullname: Prakasa Rao B. L. S.
– volume-title: Statistical Inference for Fractional Diffusion Processes
  year: 2010
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    fullname: Prakasa Rao B. L. S.
– ident: e_1_3_2_6_1
  doi: 10.1016/0167-7152(85)90004-5
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  doi: 10.1007/978-1-4899-0027-2
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  doi: 10.1007/978-3-540-75873-0
– ident: e_1_3_2_3_1
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– ident: e_1_3_2_7_1
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– volume-title: Fractional Integrals and Derivatives
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    fullname: Samko S. G.
– ident: e_1_3_2_9_1
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  article-title: Parameter estimation and optimal filtering for fractional type stochastic systems
  publication-title: Ann. Inst. Stat. Math
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  doi: 10.1016/B978-1-4832-0022-4.50006-5
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Snippet We study the problem of misspecification when the model proposed by the statistician (theoretical model) through a stochastic differential equation is smooth...
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StartPage 1119
SubjectTerms Brownian motion
cusp-type signal
Cusps
Differential equations
Drift
fractional Brownian motion
maximum likelihood estimation
Misspecified model
Primary 60G22
Secondary 62M09
stochastic differential equation
Title Estimation for misspecification when theoretical model for signal is smooth but real signal is of cusp-type and driven by a fractional Brownian motion
URI https://www.tandfonline.com/doi/abs/10.1080/07362994.2022.2140677
https://www.proquest.com/docview/2878928627
Volume 41
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