### Arun Kumar Kuchibhotla - An approach to valid post selection inference in assumption-lean linear regression analysis

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Kuchibhotla Slides (click here)

Community: WHOA-PSI 2017

Thanks for the talk. I was wondering what statisticians mean by "assumption-lean". Is it one where we do not assume that the conditional expectation of the error term (given regressors) is zero?

written
11 months ago by
Dalia Ghanem

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Usually in statistics, linear regression model (or analysis) is used to mean the classical assumptions of conditional linear mean and conditional constant variance. In the talk (or in other related paper), assumption-lean is added to emphasize the fact that we are not assuming anything about the true data generating distribution than independent observations. In my talk, the setting is more general than this assumption-lean framework.

written
11 months ago by
Arun Kuchibhotla

### 2 Answers

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Can you explain the 4th moment condition for your asymptotic normality? Can you get by with just expectation of XTX Y^2? Or maybe to some small power greater than 1?

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The asymptotic variance has the K term that is E[XX^t(Y - X^t\beta_0)^2] which by expansion of (Y - X^t\beta_0)^2 gives product of four coordinates of X. Also, it was given to be safe sufficient conditions. I am not sure what the minimal sufficient conditions are.

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