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This paper presents finite‐sample efficiency bounds for the core econometric problem of estimation of linear regression coefficients. We show that the classical Gauss–Markov theorem can be restated omitting the unnatural restriction to linear estimators, without adding any extra conditions. Our results are lower bounds on the variances of unbiased estimators. These lower bounds correspond to the variances of the the least squares estimator and the generalized least squares estimator, depending on the assumption on the error covariances. These results show that we can drop the label “linear estimator” from the pedagogy of the Gauss–Markov theorem. Instead of referring to these estimators as BLUE, they can legitimately be called BUE (best unbiased estimators). 

A number of neuroimaging techniques have been employed to understand how visual information is transformed along the visual pathway. Although each technique has spatial and temporal limitations, they can each provide important insights into the visual code. While the BOLD signal of fMRI can be quite informative, the visual code is not static and this can be obscured by fMRI’s poor temporal resolution. In this study, we leveraged the high temporal resolution of EEG to develop an encoding technique based on the distribution of responses generated by a population of real-world scenes. This approach maps neural signals to each pixel within a given image and reveals location-specific transformations of the visual code, providing a spatiotemporal signature for the image at each electrode. Our analyses of the mapping results revealed that scenes undergo a series of nonuniform transformations that prioritize different spatial frequencies at different regions of scenes over time. This mapping technique offers a potential avenue for future studies to explore how dynamic feedforward and recurrent processes inform and refine high-level representations of our visual world. 

This paper develops inference methods for the iterated overidentified Generalized Method of Moments (GMM) estimator. We provide conditions for the existence of the iterated estimator and an asymptotic distribution theory, which allows for mild misspecification. Moment misspecification causes bias in conventional GMM variance estimators, which can lead to severely oversized hypothesis tests. We show how to consistently estimate the correct asymptotic variance matrix. Our simulation results show that our methods are properly sized under both correct specification and mild to moderate misspecification. We illustrate the method with an application to the model of Acemoglu, Johnson, Robinson, and Yared (2008). 

Human scene categorization is characterized by its remarkable speed. While many visual and conceptual features have been linked to this ability, significant correlations exist between feature spaces, impeding our ability to determine their relative contributions to scene categorization. Here, we used a whitening transformation to decorrelate a variety of visual and conceptual features and assess the time course of their unique contributions to scene categorization. Participants (both sexes) viewed 2250 full-color scene images drawn from 30 different scene categories while having their brain activity measured through 256-channel EEG. We examined the variance explained at each electrode and time point of visual event-related potential (vERP) data from nine different whitened encoding models. These ranged from low-level features obtained from filter outputs to high-level conceptual features requiring human annotation. The amount of category information in the vERPs was assessed through multivariate decoding methods. Behavioral similarity measures were obtained in separate crowdsourced experiments. We found that all nine models together contributed 78% of the variance of human scene similarity assessments and were within the noise ceiling of the vERP data. Low-level models explained earlier vERP variability (88 ms after image onset), whereas high-level models explained later variance (169 ms). Critically, only high-level models shared vERP variability with behavior. Together, these results suggest that scene categorization is primarily a high-level process, but reliant on previously extracted low-level features. 

Visual scene category representations emerge very rapidly, yet the computational transformations that enable such invariant categorizations remain elusive. Deep convolutional neural networks (CNNs) perform visual categorization at near human-level accuracy using a feedforward architecture, providing neuroscientists with the opportunity to assess one successful series of representational transformations that enable categorization in silico. The goal of the current study is to assess the extent to which sequential scene category representations built by a CNN map onto those built in the human brain as assessed by high-density, time-resolved event-related potentials (ERPs). We found correspondence both over time and across the scalp: earlier (0–200 ms) ERP activity was best explained by early CNN layers at all electrodes. Although later activity at most electrode sites corresponded to earlier CNN layers, activity in right occipito-temporal electrodes was best explained by the later, fully-connected layers of the CNN around 225 ms post-stimulus, along with similar patterns in frontal electrodes. Taken together, these results suggest that the emergence of scene category representations develop through a dynamic interplay between early activity over occipital electrodes as well as later activity over temporal and frontal electrodes. 

Human scene categorization is rapid and robust, but we have little understanding of how individual features contribute to categorization, nor the time scale of their contribution. This issue is compounded by the non- independence of the many candidate features. Here, we used singular value decomposition to orthogonalize 11 different scene descriptors that included both visual and semantic features. Using high-density EEG and regression analyses, we observed that most explained variability was carried by a late layer of a deep convolutional neural network, as well as a model of a scene’s functions given by the American Time Use Survey. Furthermore, features that explained more variance also tended to explain earlier variance. These results extend previous large-scale behavioral results showing the importance of functional features for scene categorization. Furthermore, these results fail to support models of visual perception that are encapsulated from higher-level cognitive attributes.