Miracle-dz/UniFAR-FTUs huggingface dataset:
Adaptive wavelet estimation of a compound Poisson process

We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as $T\rightarrow\infty$. We propose an adaptive wavelet threshold density estimator and study its performance for the $L_p$ loss, $p\geq 1$, over Besov spaces. The main novelty is that we achieve minimax rates of convergence for sampling rates $\Delta_T$ that vanish with $T$ at arbitrary polynomial rates. More precicely, our estimator attains minimax rates of convergence provided there exists a constant $K\geq 1$ such that the sampling rate $\Delta_T$ satisfies $T\Delta_T^{2K+2}\leq 1. $ If this condition cannot be satisfied we still provide an upper bound for our estimator. The estimating procedure is based on the inversion of the compounding operator in the same spirit as Buchmann and Grubel (2003).
Restricted Eigenvalue Conditions on Subgaussian Random Matrices

It is natural to ask: what kinds of matrices satisfy the Restr icted Eigenvalue (RE) condition? In this paper, we associate the RE condition (Bickel-Ritov-Tsybakov 09) with the complexity of a subset of the sphere in R p , where p is the dimensionality of the data, and show that a class of random matrices with independent rows, but not necessarily independent columns, satisfy the RE condition, when the sample size is above a certain lower bound. Here we explicitly introduce an additional covariance structure to the class of random matrices that we have known by now that satisfy the Restricted Isometry Property
Fast rate of convergence in high-dimensional linear discriminant analysis

This paper gives a theoretical analysis of high-dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis the poor performances of standard procedures in the case when dimension p is larger than sample size n. The corresponding theoretical results are non-asymptotic lower bounds. On the other hand, we propose two discrimination procedures based on dimensionality reduction and provide associated rates of convergence which can be O(log(p)/n) under sparsity assumptions. Finally, all our results rely on a theorem that provides simple sharp relations between the excess risk and an estimation error associated with the geometric parameters defining the used discrimination rule.
Sparse Group Selection Through Co-Adaptive Penalties

Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well approximated by a fit involving only a small number of covariates -- a so called sparsity assumption, which leads to the Lasso and other methods. In many situations, however, the covariates can be considered to be structured, in that the selection of some variables favours the selection of others -- with variables organised into groups entering or leaving the model simultaneously as a special case. This structure creates a different form of sparsity. In this paper, we suggest the Co-adaptive Lasso to fit models accommodating this form of `group sparsity'. The Co-adaptive Lasso is fast and simple to calculate, and we show that it holds theoretical advantages over the Lasso, performs well under a broad set of conclusions, and is very competitive in empirical simulations in comparison with previously suggested algorithms like the Group Lasso and the Adaptive Lasso.
Nonparametric inference on Lévy measures and copulas

In this paper nonparametric methods to assess the multivariate L evy measure are introduced. Starting from high-frequency observations of a L evy process X, we construct estimators for its tail integrals and the Pareto L evy copula and prove weak convergence of these estimators in certain function spaces. Given n observations of increments over intervals of length n, the rate of convergence is k 1=2 n for kn = n n which is natural concerning inference on the L
Is There Statistical Evidence that the Oregon Payday-Loan Rate Cap Hurts Consumers?

1. A recent unpublished manuscript whose conclusions were widely circulated in the electronic media (Zinman, 2009) claimed that Oregon 2007 payday loan (PL) rate-limiting regulations (hereafter, "Cap") have hurt borrowers. 2. The report's main conclusion, phrased in cause-and-effect language in the abstract - ". restricting access caused deterioration in the overall financial condition of the Oregon households. " - relies on a single, small-sample survey funded by the payday-lending industry (PLI). The survey is fraught with methodological flaws. 3. Moreover, survey results do not support the claim that Oregon borrowers fared worse than Washington borrowers, on any variable that can be plausibly attributed to the Cap. 4. In fact, Oregon respondents fared better than Washington respondents on two key variables: on-time bill payment rate and avoiding phone-line disconnects. On all other relevant variables they fared similarly to Washington respondents. In short, the reported claim is baseless.
Fast-rate and optimistic-rate error bounds for L1-regularized regression

We consider the prediction error of linear regression with L1 regularization when the number of covariates p is large relative to the sample size n. When the model is k-sparse and well-specified, and restricted isometry or similar conditions hold, the excess squared-error in prediction can be bounded on the order of sigma^2*(k*log(p)/n), where sigma^2 is the noise variance. Although these conditions are close to necessary for accurate recovery of the true coefficient vector, it is possible to guarantee good predictive accuracy under much milder conditions, avoiding the restricted isometry condition, but only ensuring an excess error bound of order (k*log(p)/n)+sigma*\surd(k*log(p)/n). Here we show that this is indeed the best bound possible (up to logarithmic factors) without introducing stronger assumptions similar to restricted isometry.
Selection of a model of cerebral activity for fMRI Group Data analysis

This thesis is dedicated to the statistical analysis of multi-sub ject fMRI data, with the purpose of identifying bain structures involved in certain cognitive or sensori-motor tasks, in a reproducible way across sub jects. To overcome certain limitations of standard voxel-based testing methods, as implemented in the Statistical Parametric Mapping (SPM) software, we introduce a Bayesian model selection approach to this problem, meaning that the most probable model of cerebral activity given the data is selected from a pre-defined collection of possible models. Based on a parcellation of the brain volume into functionally homogeneous regions, each model corresponds to a partition of the regions into those involved in the task under study and those inactive. This allows to incorporate prior information, and avoids the dependence of the SPM-like approach on an arbitrary threshold, called the clusterforming threshold, to define active regions. By controlling a Bayesian risk, our approach balances false positive and false negative risk control. Urthermore, it is based on a generative model that accounts for the spatial uncertainty on the localization of individual effects, due to spatial normalization errors. On both simulated and real fMRI datasets, we show that this new paradigm corrects several biases of the SPM-like approach, which either swells or misses the different active regions, depending on the choice of a cluster-forming threshold.
Adaptive Gaussian Inverse Regression with Partially Unknown Operator

This work deals with the ill-posed inverse problem of reconstructing a function f given implicitly as the solution of g = Af, where A is a compact linear operator with unknown singular values and known eigenfunctions. We observe the function g and the singular values of the operator subject to Gaussian white noise with respective noise levels ϵ and σ. We develop a minimax theory in terms of both noise levels and propose an orthogonal series estimator attaining the minimax rates. This estimator requires the optimal choice of a dimension parameter depending on certain characteristics of f and A. This work addresses the fully data-driven choice of the dimension parameter combining model selection with Lepski's method. We show that the fully data-driven estimator preserves minimax optimality over a wide range of classes for f and A and noise levels ϵ and σ. The results are illustrated considering Sobolev spaces and mildly and severely ill-posed inverse problems.
Stochastic Approximation and Newton’s Estimate of a Mixing Distribution

Many statistical problems involve mixture models and the need for computationally efficient methods to estimate the mixing distribution has increased dramatically in recent years. Newton [Sankhya Ser. A 64 (2002) 306--322] proposed a fast recursive algorithm for estimating the mixing distribution, which we study as a special case of stochastic approximation (SA). We begin with a review of SA, some recent statistical applications, and the theory necessary for analysis of a SA algorithm, which includes Lyapunov functions and ODE stability theory. Then standard SA results are used to prove consistency of Newton's estimate in the case of a finite mixture. We also propose a modification of Newton's algorithm that allows for estimation of an additional unknown parameter in the model, and prove its consistency.
Approximations of fractional Brownian motion

Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.
A Sub-1V Bandgap Voltage Reference with Improved PSRR Scheme

: A High performance sub-1V bandgap voltage reference (BGVR) with high power supply rejection ratio (PSRR) and low temperature coefficient (TC) is proposed in this paper. An improved PSRR scheme is inserted to isolate the supply voltage of the error amplifier and the supply voltage of BGVR core from a power supply source in order to achieve a high PSRR. The proposed circuit is designed and simulated in 0.18 μ m CMOS 1.8V/3.3V technology. The proposed BGVR deliver an output voltage of 0.6346V at 27°C and the measurement temperature coefficient is 22,3ppm/°C over temperature range -40°C to 140°C, the DC value of PSRR is -93dB at 10kHz and -71dB of PSRR is achieved at 1MHz and a line regulation of 104 μ V/V is achieve over supply voltage range 1.2V to 1.8V. The area of layout is 0.0337 mm 2 . The proposed sub-1V bandgap voltage reference is suitable for low power LDO regulators and switching regulators.
Concentration inequalities of the cross-validation estimate for stable predictors

In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for stable predictors in the context of risk assessment. The notion of stability has been first introduced by \cite{DEWA79} and extended by \cite{KEA95}, \cite{BE01} and \cite{KUNIY02} to characterize class of predictors with infinite VC dimension. In particular, this covers $k$-nearest neighbors rules, bayesian algorithm (\cite{KEA95}), boosting,. General loss functions and class of predictors are considered. We use the formalism introduced by \cite{DUD03} to cover a large variety of cross-validation procedures including leave-one-out cross-validation, $k$-fold cross-validation, hold-out cross-validation (or split sample), and the leave-$\upsilon$-out cross-validation. In particular, we give a simple rule on how to choose the cross-validation, depending on the stability of the class of predictors. In the special case of uniform stability, an interesting consequence is that the number of elements in the test set is not required to grow to infinity for the consistency of the cross-validation procedure. In this special case, the particular interest of leave-one-out cross-validation is emphasized.
Stochastic Lipschitz continuity for high dimensional Lasso with multiple linear covariate structures or hidden linear covariates

AbstractTwo extensions of generalized linear models are considered. In the ﬁrst one, response variablesdepend on multiple linear combinations of covariates. In the second one, only response variablesare observed while the linear covariates are missing. We derive stochastic Lipschitz continuityresults for the loss functions involved in the regression problems and apply them to get boundson estimation error for Lasso. Multivariate comparison results on Rademacher complexity areobtained as tools to establish the stochastic Lipschitz continuity results.AMS 2010 subject classiﬁcation. 62G08; 60E15.Key words and phrases. stochastic Lipschitz, Lasso, measure concentration, generalized linearmodels, hidden variable, multilinear.Acknowledgement. Research partially supported by NSF grant DMS-07-06048. 1 Introduction In recent years, much attention has been paid to regularized regression for high dimensional linearmodels [4, 5, 7, 8, 19, 21, 23]. Meanwhile, a much smaller body of works has been devoted to suchregression for high dimensional generalized linear models [20]. Despite the impressive progress, thefull potential of regularized regression for models with underlying linear structures seems far frombeing fully explored.Regression is a type of optimization. In current literature on high dimensional generalized linearmodels, the target, or loss, functions being optimized have the form γ
Local degeneracy of Markov chain Monte Carlo methods

We study asymptotic behavior of Markov chain Monte Carlo (MCMC) procedures. Sometimes the performances of MCMC procedures are poor and there are great importance for the study of such behavior. In this paper we call degeneracy for a particular type of poor performances. We show some equivalent conditions for degeneracy. As an application, we consider the cumulative probit model. It is well known that the natural data augmentation (DA) procedure does not work well for this model and the so-called parameter-expanded data augmentation (PX-DA) procedure is considered to be a remedy for it. In the sense of degeneracy, the PX-DA procedure is better than the DA procedure. However, when the number of categories is large, both procedures are degenerate and so the PX-DA procedure may not provide good estimate for the posterior distribution.
Estimating principal components of covariance matrices using the Nystr\"{o}m method

Covariance matrix estimates are an essential part of many signal processing algorithms, and are often used to determine a low-dimensional principal subspace via their spectral decomposition. However, exact eigenanalysis is computationally intractable for sufficiently high-dimensional matrices, and in the case of small sample sizes, sample eigenvalues and eigenvectors are known to be poor estimators of their population counterparts. To address these issues, we propose a covariance estimator that is computationally efficient while also performing shrinkage on the sample eigenvalues. Our approach is based on the Nystr\"{o}m method, which uses a data-dependent orthogonal projection to obtain a fast low-rank approximation of a large positive semidefinite matrix. We provide a theoretical analysis of the error properties of our estimator as well as empirical results, including examples of its application to adaptive beamforming and image denoising.
The Consistency of Modeled and Observed Temperature Trends in the Tropical Troposphere: A Comment on Santer et al (2008)

Santer et al (2008) (S08) compared climate models and observations in the tropical troposphere and reported that "there is no longer a serious discrepancy between modeled and observed trends in tropical lapse rates. " They found no statistically significant differences between modeled (ensemble mean) trends and observed trends at the T2LT and T2 layers, and they found no significant difference between observed and modeled surface-minus-troposphere lapse rates. However they only used data over the 1979-1999 period. Using the S08 methodology on up-to-date data, we find a statistically significant discrepancy between observations and models with respect to trends in the UAH data, as well as lapse rate trends comparing either RSS or UAH to the HADCRUT3v land-ocean surface trend.
Binary models for marginal independence

Summary. Log‐linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log‐linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach that is taken is graphical and draws on analogies with multivariate Gaussian models for marginal independence. For the graphical model representation we use bidirected graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed by using a version of the iterated conditional fitting algorithm. Finally we consider combining these models with symmetry restrictions.
Parameter and Structure Learning in Nested Markov Models

The constraints arising from DAG models with latent variables can be naturally represented by means of acyclic directed mixed graphs (ADMGs). Such graphs contain directed and bidirected arrows, and contain no directed cycles. DAGs with latent variables imply independence constraints in the distribution resulting from a 'fixing' operation, in which a joint distribution is divided by a conditional. This operation generalizes marginalizing and conditioning. Some of these constraints correspond to identifiable 'dormant' independence constraints, with the well known 'Verma constraint' as one example. Recently, models defined by a set of the constraints arising after fixing from a DAG with latents, were characterized via a recursive factorization and a nested Markov property. In addition, a parameterization was given in the discrete case. In this paper we use this parameterization to describe a parameter fitting algorithm, and a search and score structure learning algorithm for these nested Markov models. We apply our algorithms to a variety of datasets.
Two-step estimation of high dimensional additive models

This paper investigates the two-step estimation of a high dimensional additive regression model, in which the number of nonparametric additive components is potentially larger than the sample size but the number of significant additive components is sufficiently small. The approach investigated consists of two steps. The first step implements the variable selection, typically by the group Lasso, and the second step applies the penalized least squares estimation with Sobolev penalties to the selected additive components. Such a procedure is computationally simple to implement and, in our numerical experiments, works reasonably well. Despite its intuitive nature, the theoretical properties of this two-step procedure have to be carefully analyzed, since the effect of the first step variable selection is random, and generally it may contain redundant additive components and at the same time miss significant additive components. This paper derives a generic performance bound on the two-step estimation procedure allowing for these situations, and studies in detail the overall performance when the first step variable selection is implemented by the group Lasso.
Consistent distribution-free tests of association between univariate random variables

We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that are consistent, distribution free, and have excellent power properties. The tests have simple form, and are surprisingly computationally efficient thanks to accompanying innovative algorithms we develop. Moreover, we show that one of the test statistics is a consistent estimator of the mutual information. We demonstrate the good power properties in simulations, and apply the tests to a microarray study where many pairs of genes are examined simultaneously for co-dependence.
Evaluation des Präventionsprogramms "cool and clean" bei Jugendlichen - Breitensport und Talents

1 Zusammenfassung (Deutsch) . 3 Summary (English) . 13 1. Das Programm «cool and clean» . 23 1.1 Beschreibung des Programms im Bereich Jugendlicher . 23 1.1.1 Kerngedanken und Strategien von «cool and clean» . 23 1.1.2 Die fünf Commitments . 24 1.1.3 Ziele des Programms «cool and clean» . 25 1.2 Theoretischer Hintergrund des Programms . 25 1.2.1 Situierung von «cool and clean» innerhalb unterschiedlicher Präventionsansätze . 25 1.2.2 Der Lebenskompetenzmodell-Ansatz . 26 1.2.3 Wieso «cool and clean» bei Jugendlichen etwas bewirken sollte . 26 1.3 Wissenschaftliche Evaluation des Programms . 29 2. Programmziele und Forschungshypothesen . 30 2.1 Bekanntheit, Verbreitung und Befolgung des Programms . 30 2.2 Unterschiede zwischen an «cool and clean» teilnehmenden und nichtteilnehmenden Jugendlichen des Breitensports. 31 2.2.1 Unterschiede zwischen teilnehmenden und nicht teilnehmenden Jugendlichen im Breitensport 2009 und 2011 (Querschnittanalysen) . 32 2.2.2 Unterschiede zwischen der Experimentalund der Kontrollgruppe über die Zeit (Längsschnitt 2009-2011) . 32 2.2.3 Einstiegsalter . 32 2.3 Dauer und Intensität der im Rahmen von «cool and clean» durchgeführten Intervention . 33 2.4 Einstellung zu den Commitments . 33 2.5 Subjektive Einschätzung der Wirkung von «cool and clean» . 34 2.6 Zusammenhang zwischen dem Substanzkonsum und den anderen Zieldimensionen . 34 2.7 Einvs. mehrdimensionale Ansätze in der Suchtprävention . 34 2.8 Vorbildfunktion von Sportstars und Trainer/Trainerinnen . 35 2.9 Rauchfreie Sportanlagen und -veranstaltungen . 35 2.10 Ergebnisse der offenen Fragen im Breitensport. 35 2.11 Ergebnisse der Interviews mit den Talents . 35 3. Methodik . 36 3.1 Analysestrategie . 36 3.2 Breitensport . 38 3.1.1 Konstruktion des Fragebogen für den Breitensport . 38 3.1.2 Population und Stichprobe . 38
ON SIZE AND POWER OF HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS

Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well as negative finite-sample results concerning the size and power properties of a large class of heteroskedasticity and autocorrelation robust tests. Using these results we show that nonparametrically as well as parametrically corrected F-type tests in time series regression models with stationary disturbances have either size equal to one or nuisance-infimal power equal to zero under very weak assumptions on the covariance model and under generic conditions on the design matrix. In addition we suggest an adjustment procedure based on artificial regressors. This adjustment resolves the problem in many cases in that the so-adjusted tests do not suffer from size distortions. At the same time their power function is bounded away from zero. As a second application we discuss the case of heteroskedastic disturbances.