# Statistical Approaches to Aerosol Dynamics for Climate Simulation

## Abstract

In this work, we introduce two general non-parametric regression analysis methods for errors-in-variable (EIV) models: the compound regression, and the constrained regression. It is shown that these approaches are equivalent to each other and, to the general parametric structural modeling approach. The advantages of these methods lie in their intuitive geometric representations, their distribution free nature, and their ability to offer a practical solution when the ratio of the error variances is unknown. Each includes the classic non-parametric regression methods of ordinary least squares, geometric mean regression, and orthogonal regression as special cases. Both methods can be readily generalized to multiple linear regression with two or more random regressors.

- Authors:

- Publication Date:

- Research Org.:
- The Research Foundation of State University of New York

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1128424

- Report Number(s):
- DOE-STONYBROOK-25817

- DOE Contract Number:
- FC02-07ER25817

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Compound regression; Constrained regression; Geometric mean regression; Maximum likelihood method; Ordinary least squares regression; Orthogonal regression

### Citation Formats

```
Zhu, Wei.
```*Statistical Approaches to Aerosol Dynamics for Climate Simulation*. United States: N. p., 2014.
Web. doi:10.2172/1128424.

```
Zhu, Wei.
```*Statistical Approaches to Aerosol Dynamics for Climate Simulation*. United States. doi:10.2172/1128424.

```
Zhu, Wei. Tue .
"Statistical Approaches to Aerosol Dynamics for Climate Simulation". United States.
doi:10.2172/1128424. https://www.osti.gov/servlets/purl/1128424.
```

```
@article{osti_1128424,
```

title = {Statistical Approaches to Aerosol Dynamics for Climate Simulation},

author = {Zhu, Wei},

abstractNote = {In this work, we introduce two general non-parametric regression analysis methods for errors-in-variable (EIV) models: the compound regression, and the constrained regression. It is shown that these approaches are equivalent to each other and, to the general parametric structural modeling approach. The advantages of these methods lie in their intuitive geometric representations, their distribution free nature, and their ability to offer a practical solution when the ratio of the error variances is unknown. Each includes the classic non-parametric regression methods of ordinary least squares, geometric mean regression, and orthogonal regression as special cases. Both methods can be readily generalized to multiple linear regression with two or more random regressors.},

doi = {10.2172/1128424},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Sep 02 00:00:00 EDT 2014},

month = {Tue Sep 02 00:00:00 EDT 2014}

}