Małgorzata Bogdan

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We introduce a new estimator for the vector of coefficients β in the linear model y = Xβ + z, where X has dimensions n × p with p possibly larger than n. SLOPE, short for Sorted L-One Penalized Estimation, is the solution to [Formula: see text]where λ1 ≥ λ2 ≥ … ≥ λ p ≥ 0 and [Formula: see text] are the decreasing absolute values of the entries of b. This is(More)
A modified version (mBIC) of the Bayesian Information Criterion (BIC) has been previously proposed for backcross designs to locate multiple interacting quantitative trait loci. In this article, we extend the method to intercross designs. We also propose two modifications of the mBIC. First we investigate a two-stage procedure in the spirit of empirical(More)
We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model y = Xβ + z, then we suggest estimating the regression coefficients by means of a new estimator called the ordered lasso, which is the solution to minimize b 1 2 y − Xb 2 2 + λ 1(More)
In this note we give a proof showing that even though the number of false discoveries and the total number of discoveries are not continuous functions of the parameters, the formulas we obtain for the false discovery proportion (FDP) and the power, namely, (B.3) and (B.4) in the paper Statistical Estimation and Testing via the Sorted 1 Norm are(More)
In regression settings where explanatory variables have very low correlations and where there are relatively few effects each of large magnitude, it is commonly believed that the Lasso shall be able to find the important variables with few errors—if any. In contrast, this paper shows that this is not the case even when the design variables are(More)
To locate multiple interacting quantitative trait loci (QTL) influencing a trait of interest within experimental populations, usually methods as the Cockerham's model are applied. Within this framework, interactions are understood as the part of the joined effect of several genes which cannot be explained as the sum of their additive effects. However, if a(More)
The general aim of genetic association studies is to find among a large set of genetic markers those markers which are associated with some trait. Two prominent special cases are the problem of locating quantitative trait loci for experimental populations (QTL mapping), and genome wide association studies for natural populations (GWAS). Association can be(More)
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