multiple_inference.rank_condition#

Inference after ranking.

References

@techreport{andrews2019inference,
    title={ Inference on winners },
    author={ Andrews, Isaiah and Kitagawa, Toru and McCloskey, Adam },
    year={ 2019 },
    institution={ National Bureau of Economic Research }
}

@article{andrews2022inference,
    Author = {Andrews, Isaiah and Bowen, Dillon and Kitagawa, Toru and McCloskey, Adam},
    Title = {Inference for Losers},
    Journal = {AEA Papers and Proceedings},
    Volume = {112},
    Year = {2022},
    Month = {May},
    Pages = {635-42},
    DOI = {10.1257/pandp.20221065},
    URL = {https://www.aeaweb.org/articles?id=10.1257/pandp.20221065}
}

Classes

RankCondition(*args[, xmean, xycov])

Rank condition quantile-unbiased estimator.

RankConditionResults(*args[, beta, ...])

Quantile-unbiased results.
class multiple_inference.rank_condition.RankCondition(*args: Any, xmean: Optional[Sequence[float]] = None, xycov: Optional[ndarray] = None, **kwargs: Any)[source]#

Rank condition quantile-unbiased estimator.

Provides utilities for obtaining quantile-unbiased estimates conditional on the rank-ordering of conventional estimates of policy effects.

Subclasses multiple_inference.base.ModelBase.

Parameters

  • *args (Any) – Passed to multiple_inference.base.ModelBase.

  • xmean (Numeric1DArray, optional) – (# params,) array of conventional estimates to use for ranking. If None, ranking conditions are based on mean. Defaults to None.

  • xycov (np.ndarray, optional) – (# params, # params) covariance matrix between mean and xmean. Defaults to None.

  • **kwargs (Any) – Passed to multiple_inference.base.ModelBase.

Raises

ValueError – Either all or none of xmean, xcov and xycov must be specified.

Additional attributes:
xmean (np.ndarray): (# params,) array of conventional estimates to use for

ranking.

xycov (np.ndarray): (# params, # params) covariance matrix between self.mean

and self.xmean.

Examples

Compute a quantile-unbiased distribution of the x4 parameter given that it was the top-ranked parameter.

import numpy as np
from multiple_inference.rank_condition import RankCondition

model = RankCondition(np.arange(5), np.identity(5))
dist = model.get_marginal_distribution("x4")
print(dist.ppf([.025, .5, .975]))

[0.06742731 3.68627552 5.93267239]

Compute an “almost” quantile-unbiased hybrid distribution.

dist = model.get_marginal_distribution("x4", beta=.005)
print(dist.ppf([.025, .5, .975]))

[0.89034671 3.68742998 5.93290012]

Summarize the quantile-unbiased results.

results = model.fit()
print(results.summary())

Rank condition quantile-unbiased estimates
===============================================
   coef (median) pvalue (1-sided) [0.025 0.975]
-----------------------------------------------
x0         0.314            0.406 -1.933  3.933
x1         1.000            0.285 -2.922  4.922
x2         2.000            0.136 -1.922  5.922
x3         3.000            0.058 -0.922  6.922
x4         3.686            0.023  0.067  5.933
===============
Dep. Variable y
---------------

Summarize the “almost” quantile-unbiased hybrid results.

results = model.fit(beta=.005)
print(results.summary())

Rank condition quantile-unbiased estimates
===============================================
   coef (median) pvalue (1-sided) [0.025 0.975]
-----------------------------------------------
x0         0.313            0.409 -1.977  3.129
x1         1.000            0.288 -2.129  4.129
x2         2.000            0.140 -1.129  5.129
x3         3.000            0.042 -0.129  6.129
x4         3.687            0.005  0.871  5.977
===============
Dep. Variable y
---------------
get_marginal_distribution(column: Union[str, int], ranks: Optional[Sequence[float]] = None, beta: float = 0, **kwargs: Any) → quantile_unbiased[source]#

Compute a quantile-unbiased distribution for a given ranking condition.

Parameters

  • column (ColumnType) – Name or index of the parameter of interest. Defaults to None.

  • ranks (Numeric1DArray, optional) – Ranking conditions for the parameter of interest. This method returns a quantile-unbiased distribution given that the estimated rank of the parameter of interest is in ranks. If None, the estimated rank of the parameter is used as the ranking condition. Defaults to None.

  • beta (float, optional) – Used to compute the projection quantile for hybrid estimation. Defaults to 0.

  • **kwargs (Any) – Passed to quantile_unbiased.

Returns

Quantile-unbiased distribution.

Return type

quantile_unbiased

class multiple_inference.rank_condition.RankConditionResults(*args: Any, beta: float = 0, marginal_distribution_kwargs: Optional[Mapping[str, Any]] = None, **kwargs: Any)[source]#

Quantile-unbiased results.

Inherits from multiple_inference.base.ResultsBase.

Parameters