# 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¶

```
In [1]: import numpy as np
In [2]: import statsmodels.api as sm
# Generate Data
In [3]: x = np.random.standard_normal(50)
# initiate EL
In [4]: el = sm.emplike.DescStat(x)
# confidence interval for the mean
In [5]: el.ci_mean()
Out[5]: (0.0058122860211228256, 0.5016745943913815)
# test variance is 1
In [6]: el.test_var(1)
Out[6]: (1.3620110655131956, 0.24318925027902907)
```

## 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. |