# Empirical Likelihood `emplike`¶

## Introduction¶

Empirical likelihood is a method of nonparametric inference and estimation that lifts the obligation of having to specify a family of underlying distributions. Moreover, empirical likelihood methods do not require re-sampling but still uniquely determine confidence regions whose shape mirrors the shape of the data. In essence, empirical likelihood attempts to combine the benefits of parametric and nonparametric methods while limiting their shortcomings. The main difficulties of empirical likelihood is the computationally intensive methods required to conduct inference. `statsmodels.emplike` attempts to provide a user-friendly interface that allows the end user to effectively conduct empirical likelihood analysis without having to concern themselves with the computational burdens.

Currently, `emplike` provides methods to conduct hypothesis tests and form confidence intervals for descriptive statistics. Empirical likelihood estimation and inference in a regression, accelerated failure time and instrumental variable model are currently under development.

### References¶

The main reference for empirical likelihood is:

```Owen, A.B. "Empirical Likelihood." Chapman and Hall, 2001.
```

## Examples¶

```import numpy as np
import statsmodels.api as sm

# Generate Data
x = np.random.standard_normal(50)

# initiate EL
el = sm.emplike.DescStat(x)

# confidence interval for the mean
el.ci_mean()

# test variance is 1
el.test_var(1)
```

## Module Reference¶

 `descriptive.DescStat`(endog) Returns an instance to conduct inference on descriptive statistics via empirical likelihood. `descriptive.DescStatUV`(endog) A class to compute confidence intervals and hypothesis tests involving mean, variance, kurtosis and skewness of a univariate random variable. `descriptive.DescStatMV`(endog) A class for conducting inference on multivariate means and correlation.