# Conditions of Asymptotic Normality of One-Step M-Estimators

## Abstract

In the case of independent identically distributed observations, we study the asymptotic properties of one-step M-estimators served as explicit approximations of consistent M-estimators. We find rather general conditions for the asymptotic normality of one-step M-estimators. We consider Fisher’s approximations of consistent maximum likelihood estimators and find general conditions guaranteeing the asymptotic normality of the Fisher estimators even in the case where maximum likelihood estimators do not necessarily exist or are not necessarily consistent.

- Authors:

- Sobolev Institute of Mathematics SB RAS (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771401

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; ASYMPTOTIC SOLUTIONS; MAXIMUM-LIKELIHOOD FIT

### Citation Formats

```
Linke, Yu. Yu., E-mail: linke@math.nsc.ru, and Sakhanenko, A. I., E-mail: aisakh@mail.ru.
```*Conditions of Asymptotic Normality of One-Step M-Estimators*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3730-3.

```
Linke, Yu. Yu., E-mail: linke@math.nsc.ru, & Sakhanenko, A. I., E-mail: aisakh@mail.ru.
```*Conditions of Asymptotic Normality of One-Step M-Estimators*. United States. doi:10.1007/S10958-018-3730-3.

```
Linke, Yu. Yu., E-mail: linke@math.nsc.ru, and Sakhanenko, A. I., E-mail: aisakh@mail.ru. Sun .
"Conditions of Asymptotic Normality of One-Step M-Estimators". United States. doi:10.1007/S10958-018-3730-3.
```

```
@article{osti_22771401,
```

title = {Conditions of Asymptotic Normality of One-Step M-Estimators},

author = {Linke, Yu. Yu., E-mail: linke@math.nsc.ru and Sakhanenko, A. I., E-mail: aisakh@mail.ru},

abstractNote = {In the case of independent identically distributed observations, we study the asymptotic properties of one-step M-estimators served as explicit approximations of consistent M-estimators. We find rather general conditions for the asymptotic normality of one-step M-estimators. We consider Fisher’s approximations of consistent maximum likelihood estimators and find general conditions guaranteeing the asymptotic normality of the Fisher estimators even in the case where maximum likelihood estimators do not necessarily exist or are not necessarily consistent.},

doi = {10.1007/S10958-018-3730-3},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 1,

volume = 230,

place = {United States},

year = {2018},

month = {4}

}

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