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)
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 many empirical studies, it has been observed that genome scans yield biased estimates of heritability, as well as genetic effects. It is widely accepted that quantitative trait locus (QTL) mapping is a model selection procedure, and that the overestimation of genetic effects is the result of using the same data for model selection as estimation of(More)
In previous work, a modified version of the Bayesian information criterion (mBIC) was proposed to locate multiple interacting quantitative trait loci (QTL). Simulation studies and real data analysis demonstrate good properties of the mBIC in situations where the error distribution is approximately normal. However, as with other standard techniques of QTL(More)
SUMMARY The modified version of Bayesian Information Criterion (mBIC) is a relatively simple model selection procedure that can be used when locating multiple interacting quantitative trait loci (QTL). Our earlier work demonstrated the statistical properties of mBIC for situations where the average genetic map interval is at least 5 cM. In this work mBIC is(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 +(More)
<lb>In regression settings where explanatory variables have very low correlations and where there<lb>are relatively few effects each of large magnitude, it is commonly believed that the Lasso shall be<lb>able to find the important variables with few errors—if any. In contrast, this paper shows that<lb>this is not the case even when the design variables are(More)