Nonlinear Estimation

In the most general terms, Nonlinear Estimation involves finding the best fitting relationship between the values of a dependent variable and the values of a set of one or more independent variables (it is used as either a hypothesis testing or exploratory method). For example, we may want to compute the relationship between the dose of a drug and its effectiveness, the relationship between training and subsequent performance on a task, the relationship between the price of a house and the time it takes to sell it, etc. Research issues in these examples are commonly addressed by such techniques as multiple regression (see, Multiple Regression) or analysis of variance (see, ANOVA/MANOVA). In fact, one may think of Nonlinear Estimation as a generalization of those methods. Specifically, multiple regression (and ANOVA) assumes that the relationship between the independent variable(s) and the dependent variable is linear in nature. Nonlinear Estimation leaves it up to you to specify the nature of the relationship; for example, you may specify the dependent variable to be a logarithmic function of the independent variable(s), an exponential function, a function of some complex ratio of independent measures, etc. (However, if all variables of interest are categorical in nature, or can be converted into categorical variables, you may also consider Correspondence Analysis as an alternative analysis technique.)

For more information on Nonlinear Estimation methods, see the Nonlinear Estimation Introductory Overview.