Ya'acov Ritov

Simultaneous analysis of Lasso and Dantzig selector

We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. For both methods, we derive, in parallel, oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the l p estimation loss for 1 ≤ p ≤ 2 in the linear model when the number of variables can be much larger than the sample size.

Efficient and adaptive estimation for semiparametric models

Introduction.- Asymptotic Inference for (Finite-Dimensional) Parametric Models.- Information Bounds for Euclidean Parameters in Infinite-Dimensional Models.- Euclidean Parameters: Further Examples.- Information Bounds for Infinite-Dimensional Parameters.- Infinite-Dimensional Parameters: Further Examples: Construction of Examples.

ON ASYMPTOTICALLY OPTIMAL CONFIDENCE REGIONS AND TESTS FOR HIGH-DIMENSIONAL MODELS

We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking dependence among tests into account. For linear models, our method is essentially the same as in Zhang and Zhang [J. R. Stat. Soc. Ser. B Stat. Methodol. 76 (2014) 217-242]: we analyze its asymptotic properties and establish its asymptotic optimality in terms of semiparametric efficiency. Our method naturally extends to generalized linear models with convex loss functions. We develop the corresponding theory which includes a careful analysis for Gaussian, sub-Gaussian and bounded correlated designs.

Accurate estimation of travel times from single-loop detectors

As advanced traveler information systems become increasingly prevalent the importance of accurately estimating link travel times grows. Unfortunately, the predominant source of highway traffic information comes from single-loop loop detectors which do not directly measure vehicle speed. The conventional method of estimating speed, and hence travel time, from the single-loop data is to make a common vehicle length assumption and to use a resulting identity relating density, flow, and speed. Hall and Persaud (Transportation Research Record 1232, 9-16, 1989) and Pushkar et al. (Transportation Research Record 1457, 149-157, 1994) show that these speed estimates are flawed. In this paper we present a methodology to estimate link travl times directly from the single-loop loop detector flow and occupancy data without heavy reliance on the flawed speed calculations. Our methods arise naturally from an intuitive stochastic model of traffic flow. We demonstrate by example on data collected on I-880 data (Skabardonis et al. Technical Report UCB-ITS-PRR-95-S, Institute of Transportation Studies, University of California, 1994) that when the loop detector data has a fine resolution (about one second), the single-loop based estimates of travel time can accurately track the true travel time through many degrees of congestion. Probe vehicle data and double-loop based travel time estimates corroborate the accuracy of our methods in our examples.

Tailor-made tests for goodness of fit to semiparametric hypotheses

1. Introduction. The practice of statistical testing plays several roles inempirical research. These roles range from the careful assessment of theevidence against specific scientific hypotheses to the judgment of whetheran estimated model displays decent goodness of fit to the empirical data.The paradigmatic situation we consider is one where the investigator viewssome departures from the hypothesized model as being of primary impor-tance, with others of interest if sufficiently gross, but otherwise secondary.For instance, low-frequency departures from a signal hypothesized to beconstant might be considered of interest, even if of low amplitude; whilehigh-frequency departures are less so, unless they are of high amplitude.The optimal testing of a simple hypothesis against a simple alternativeis the cornerstone of modern statistical theory. However, there is no clearnotion of optimality for more complicated situations. The H´ajek–Le Camasymptotic theory proved that there exist strong concepts of asymptotic ef-ficiency in parametric estimation. These ideas have been extended to semi-parametric models—see [3, 14, 22]. However, there is no compelling sense ofan asymptotically optimum test, in either the parametric or the semipara-metric asymptotic theories, save for some simple one-parameter hypotheses.

Analysis of Contingency Tables by Correspondence Models Subject to Order Constraints

Abstract Inferential correspondence analysis, which has gained much attention in recent years, is applied here to contingency tables with ordered categories. To reflect such order, the parameters of the underlying correspondence models are constrained to follow the order induced by the categories of the analyzed table. A reparameterization of the correspondence model in terms of a latent variable model is presented. This allows a simple and straightforward use of the EM algorithm to obtain efficient order-restricted estimates. A goodness-of-fit test is also discussed, and an example is analyzed. A small Monte Carlo example is presented.

The neuronal refractory period causes a short-term peak in the autocorrelation function

Autocorrelation functions are a major tool for the understanding of single-cell firing patterns. Short-term peaks in autocorrelation functions have previously been interpreted as a tendency towards bursting activity or elevated probability to emit spikes in a short time-scale. These peaks can actually be a result of the firing of a neuron with a refractory period followed by a period of constant firing probability. Analytic studies and simulations of such neurons replicate the autocorrelation functions of real-world neurons. The relative size of the peak increases with the refractory period and with the firing rate of the cell. This phenomenon is therefore more notable in areas such as the globus pallidus and cerebellum and less clear in the cerebral cortex. We describe here a compensation factor that can be calculated from the neurons hazard function. This factor can be removed from the original autocorrelation function to reveal the underlying firing pattern of the cell.

Trial to trial variability in either stimulus or action causes apparent correlation and synchrony in neuronal activity

In this report we show that the observed inter-neuronal correlation reflects a superposition of correlations associated with the intrinsic correlation between neurons, and correlations associated with variability in the stimuli presented to, or the actions performed by, the subject. We argue that the effects of either stimulus or action variability on the observed correlation, though generally ignored, can be substantial. Specifically, we demonstrate how observed correlations are effected by trial to trial variability in either stimulus or action. In addition, assuming that all relevant stimuli and actions are known, we outline a method for eliminating their effects on the observed correlation. It is also shown that tuning of correlations to a stimulus or an action might be a direct consequence of variability in that stimulus or action, even in the absence of any modulation of direct inter-neuronal interaction. The effects of stimulus and action variability should therefore be carefully considered when designing and interpreting experiments involving multi-neuronal recordings.

Minimizing flow-time on a single machine with integer batch sizes

We address a classical minimum flow-time, single-machine, batch-scheduling problem. Processing times and setups are assumed to be identical for all jobs and batches, respectively. Santos and Magazine (Oper. Res. Lett. 4(1985) 99) introduced an efficient solution for the relaxed (non-integer) problem. We introduce a simple rounding procedure for Santos and Magazines solution, which guarantees optimal integer batches.

Hierarchical selection of variables in sparse high-dimensional regression

We study a regression model with a huge number of interacting variables. We consider a specific approximation of the regression function under two assumptions: (i) there exists a sparse representation of the regression function in a suggested basis, (ii) there are no interactions outside of the set of the corresponding main effects. We suggest an hierarchical randomized search procedure for selection of variables and of their interactions. We show that given an initial estimator, an estimator with a similar prediction loss but with a smaller number of non-zero coordinates can be found.