@article{BlanchardCarpentierGutzeit2018,
  author    = {Blanchard, Gilles and Carpentier, Alexandra and Gutzeit, Maurilio},
  title     = {Minimax Euclidean separation rates for testing convex hypotheses in R-d},
  series = {Electronic journal of statistics},
  volume    = {12},
  journal   = {Electronic journal of statistics},
  number    = {2},
  publisher = {Institute of Mathematical Statistics},
  address   = {Cleveland},
  issn      = {1935-7524},
  doi       = {10.1214/18-EJS1472},
  pages     = {3713 -- 3735},
  year      = {2018},
  abstract  = {We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a closed convex subset C of R-d. We adopt a minimax point of view and our primary objective is to describe the smallest Euclidean distance between the null and alternative hypotheses such that there is a test with small total error probability. In particular, we focus on the dependence of this distance on the dimension d and variance 1/n giving rise to the minimax separation rate. In this paper we discuss lower and upper bounds on this rate for different smooth and non-smooth choices for C.},
  language  = {en}
}
@article{CarpentierKim2018,
  author    = {Carpentier, Alexandra and Kim, Arlene K. H.},
  title     = {An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution},
  series = {Statistica Sinica},
  volume    = {28},
  journal   = {Statistica Sinica},
  number    = {3},
  publisher = {Statistica Sinica, Institute of Statistical Science, Academia Sinica},
  address   = {Taipei},
  issn      = {1017-0405},
  doi       = {10.5705/ss.202016.0103},
  pages     = {1371 -- 1393},
  year      = {2018},
  abstract  = {We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix.},
  language  = {en}
}
@article{CarpentierKloppLoeffleretal.2018,
  author    = {Carpentier, Alexandra and Klopp, Olga and L{\"o}ffler, Matthias and Nickl, Richard},
  title     = {Adaptive confidence sets for matrix completion},
  series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  volume    = {24},
  journal   = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  number    = {4A},
  publisher = {International Statistical Institute},
  address   = {Voorburg},
  issn      = {1350-7265},
  doi       = {10.3150/17-BEJ933},
  pages     = {2429 -- 2460},
  year      = {2018},
  abstract  = {In the present paper, we study the problem of existence of honest and adaptive confidence sets for matrix completion. We consider two statistical models: the trace regression model and the Bernoulli model. In the trace regression model, we show that honest confidence sets that adapt to the unknown rank of the matrix exist even when the error variance is unknown. Contrary to this, we prove that in the Bernoulli model, honest and adaptive confidence sets exist only when the error variance is known a priori. In the course of our proofs, we obtain bounds for the minimax rates of certain composite hypothesis testing problems arising in low rank inference.},
  language  = {en}
}
@article{CarpentierNickl2015,
  author    = {Carpentier, Alexandra and Nickl, Richard},
  title     = {On signal detection and confidence sets for low rank inference problems},
  series = {Electronic journal of statistics},
  volume    = {9},
  journal   = {Electronic journal of statistics},
  number    = {2},
  publisher = {Institute of Mathematical Statistics},
  address   = {Cleveland},
  issn      = {1935-7524},
  doi       = {10.1214/15-EJS1087},
  pages     = {2675 -- 2688},
  year      = {2015},
  abstract  = {We consider the signal detection problem in the Gaussian design trace regression model with low rank alternative hypotheses. We derive the precise (Ingster-type) detection boundary for the Frobenius and the nuclear norm. We then apply these results to show that honest confidence sets for the unknown matrix parameter that adapt to all low rank sub-models in nuclear norm do not exist. This shows that recently obtained positive results in [5] for confidence sets in low rank recovery problems are essentially optimal.},
  language  = {en}
}