Jelena Markovic

Jelena Markovic
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Jelena Markovic
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Statistics - Methodology (4)
 
Statistics - Theory (1)
 
Mathematics - Statistics (1)

Publications Authored By Jelena Markovic

We describe a way to construct hypothesis tests and confidence intervals after having used the Lasso for feature selection, allowing the regularization parameter to be chosen via an estimate of prediction error. Our estimate of prediction error is a slight variation on cross-validation. Using this variation, we are able to describe an appropriate selection event for choosing a parameter by cross-validation. Read More

The current work proposes a Monte Carlo free alternative to inference post randomized selection algorithms with a convex loss and a convex penalty. The pivots based on the selective law that is truncated to all selected realizations, typically lack closed form expressions in randomized settings. Inference in these settings relies upon standard Monte Carlo sampling techniques, which can be prove to be unstable for parameters far off from the chosen reference distribution. Read More

Recently, Tian Harris and Taylor (2015) proposed an asymptotically pivotal test statistic valid post selection with a randomized response. In this work, we relax the more restrictive local alternatives assumption, thereby allowing for rare selection events, to improve upon their selective CLT result for heavier tailed randomizations. We also show that under the local alternatives assumption on the parameter, selective CLT holds for Gaussian randomization as well. Read More

We consider the problem of selective inference after solving a (randomized) convex statistical learning program in the form of a penalized or constrained loss function. Our first main result is a change-of-measure formula that describes many conditional sampling problems of interest in selective inference. Our approach is model-agnostic in the sense that users may provide their own statistical model for inference, we simply provide the modification of each distribution in the model after the selection. Read More

Due to measurement noise, a common problem in in various fields is how to estimate the ratio of two functions. We consider this problem of estimating the ratio of two functions in a nonparametric regression model. Assuming the noise is normally distributed, this is equivalent to estimating the ratio of the means of two normally distributed random variables. Read More