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We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is potentially present. We develop a method and discuss its capability to distinguish between covariates that are confounded with the response by latent variables and those that are not. Thus, we provide a test and methodology for partial goodness of fit. The test is based on comparing a novel higher-order least squares principle with ordinary least squares. In spite of its simplicity, the proposed method is extremely general and is also proven to be valid for high-dimensional settings. for this article are available online. [ABSTRACT FROM AUTHOR]

In particular, the Graph HT ht condition is not required in this chain of arguments as it does not rely on consistent variable selection. In particular, we simulate from the linear model Graph HT ht and follow the simulation settings from their Figures 5 and 6. Let Graph HT ht be the design matrix whose columns are indexed by Graph HT ht . [Extracted from the article]

We propose estimation methods for change points in high-dimensional covariance structures with an emphasis on challenging scenarios with missing values. We advocate three imputation like methods and investigate their implications on common losses used for change-point detection. We also discuss how model selection methods have to be adapted to the setting of incomplete data. The methods are compared in a simulation study and applied to a time series from an environmental monitoring system. An implementation of our proposals within the R-package hdcd is available via the online . [ABSTRACT FROM AUTHOR]

We investigate the problem of inferring the causal predictors of a response Y from a set of d explanatory variables (X1, ..., Xd). Classical ordinary least-square regression includes all predictors that reduce the variance of Y. Using only the causal predictors instead leads to models that have the advantage of remaining invariant under interventions; loosely speaking they lead to invariance across different "environments" or "heterogeneity patterns." More precisely, the conditional distribution of Y given its causal predictors is the same for all observations, provided that there are no interventions on Y. Recent work exploits such a stability to infer causal relations from data with different but known environments. We show that even without having knowledge of the environments or heterogeneity pattern, inferring causal relations is possible for time-ordered (or any other type of sequentially ordered) data. In particular, this allows detecting instantaneous causal relations in multivariate linear time series, which is usually not the case for Granger causality. Besides novel methodology, we provide statistical confidence bounds and asymptotic detection results for inferring causal predictors, and present an application to monetary policy in macroeconomics. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Given data sampled from a number of variables, one is often interested in the underlying causal relationships in the form of a directed acyclic graph. In the general case, without interventions on some of the variables it is only possible to identify the graph up to its Markov equivalence class. However, in some situations one can find the true causal graph just from observational data, for example, in structural equation models with additive noise and nonlinear edge functions. Most current methods for achieving this rely on nonparametric independence tests. One of the problems there is that the null hypothesis is independence, which is what one would like to get evidence for. We take a different approach in our work by using a penalized likelihood as a score for model selection. This is practically feasible in many settings and has the advantage of yielding a natural ranking of the candidate models. When making smoothness assumptions on the probability density space, we prove consistency of the penalized maximum likelihood estimator. We also present empirical results for simulated scenarios and real two-dimensional data sets (cause–effect pairs) where we obtain similar results as other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model. In presence of highly correlated variables, as is very common in high-dimensional data, it seems indispensable to go beyond an approach of inferring individual regression coefficients, and we show that detecting smallest groups of variables (MTDs: minimal true detections) is realistic. Thanks to the hierarchy among the groups of variables, powerful multiple testing adjustment is possible which leads to a data-driven choice of the resolution level for the groups. Our procedure, based on repeated sample splitting, is shown to asymptotically control the familywise error rate and we provide empirical results for simulated and real data which complement the theoretical analysis. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We propose an ℓ1-penalized algorithm for fitting high-dimensional generalized linear mixed models (GLMMs). GLMMs can be viewed as an extension of generalized linear models for clustered observations. Our Lasso-type approach for GLMMs should be mainly used as variable screening method to reduce the number of variables below the sample size. We then suggest a refitting by maximum likelihood based on the selected variables only. This is an effective correction to overcome problems stemming from the variable screening procedure that are more severe with GLMMs than for generalized linear models. We illustrate the performance of our algorithm on simulated as well as on real data examples. Supplementary materials are available online and the algorithm is implemented in the R packageglmmixedlasso. [ABSTRACT FROM PUBLISHER]

Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a recent proposal by Wasserman and Roeder that splits the data into two parts. The number of variables is then reduced to a manageable size using the first split, while classical variable selection techniques can be applied to the remaining variables, using the data from the second split. This yields asymptotic error control under minimal conditions. This involves a one-time random split of the data, however. Results are sensitive to this arbitrary choice, which amounts to a "p-value lottery" and makes it difficult to reproduce results. Here we show that inference across multiple random splits can be aggregated while maintaining asymptotic control over the inclusion of noise variables. We show that the resulting p-values can be used for control of both family-wise error and false discovery rate. In addition, the proposed aggregation is shown to improve power while reducing the number of falsely selected variables substantially. [ABSTRACT FROM AUTHOR]

The PC-algorithm was shown to be a powerful method for estimating the equivalence class of a potentially very high-dimensional acyclic directed graph (DAG) with the corresponding Gaussian distribution. Here we propose a computationally efficient robustification of the PC-algorithm and prove its consistency. Furthermore, we compare the robustified and standard version of the PC-algorithm on simulated data using the new corresponding R package pcalg. [ABSTRACT FROM AUTHOR]

Accurate volatility predictions are crucial for the successful implementation of risk management. The use of high frequency data approximately renders volatility from a latent to an observable quantity, and opens new directions to forecast future volatilities. The goals in this paper are: (i) to select an accurate forecasting procedure for predicting volatilities based on high frequency data from various standard models and modern prediction tools; (ii) to evaluate the predictive potential of those volatility forecasts for both the realized and the true latent volatility; and (iii) to quantify the differences using volatility forecasts based on high frequency data and using a GARCH model for low frequency (e.g. daily) data, and study its implication in risk management for two widely used risk measures. The pay-off using high frequency data for the true latent volatility is empirically found to be still present, but magnitudes smaller than suggested by simple analysis. [ABSTRACT FROM AUTHOR]

This article presents a tutorial and new, publicly available computational tools for variable length Markov chains (VLMC). VLMCs are Markov chains with the additional attractive structure that their memories depend on a variable number of lagged values, depending on what the actual past (the lagged values) looks like. They build a very flexible class of tree-structured models for categorical time series. Fitting VLMCs from data is a nontrivial computational task. We provide an efficient implementation of the so-called context algorithm which requires only O(n log(n)) operations. The implementation, which is publicly available, includes additional important new features and options: diagnostics, goodness of fit, simulation and bootstrap, residuals, and tuning the context algorithm. Our tutorial is presented with a version in R which is available from the Comprehensive R Archive Network (CRAN). The exposition is self-contained, gives rigorous and partly new mathematical descriptions, and is illustrated by analyzing a DNA sequence from the Epstein-Barr virus. [ABSTRACT FROM AUTHOR]

The article presents a rejoinder by the author on his article "Sieve Bootstrap With Variable-Length Markov Chains (VLMC) for Stationary Categorical Time Series." Scholar D.N. Politis suggests that we should compare the VLMC sieve bootstrap with a full Markov sieve bootstrap that resamples from an estimated full Markov model of suitable order p. This is a natural first idea in the setting of categorical time series and it is certainly easier to implement than its VLMC cousin. Some problems should he pointed out, however. The full Markov sieve bootstrap will often be faced with the problem of how to estimate transition probabilities for states that never occurred in the data. The implementation derived in an equation puts some parsimony on estimating never-occurring states, using an ad hoc rule. VLMCs deal in a formalized way not only with never-occurring states, but also with putting parsimony on rarely occurring states. Then why should we prefer ad hoc rules over the much better-formalized VLMC fitting technique, except that the latter requires much more sophisticated computation.

A bootstrap for stationary categorical time series based on the method of sieves is studied here. The data generating process is approximated by the so-called variable length Markov chain (VLMC), a flexible class of Markov models that allows for parsimonious structure. Then the resampling is given by simulating from the fitted model. It is shown that for a whole class of stationary categorical time series that is more general than VLMC, the VLMC sieve has faster rate of convergence for variance estimation than the more general block bootstrap. Results are illustrated from a theoretical and empirical perspective. Foe the latter, a real data application about (in-) homogeneity classification of a DNA stand is also presented. Finally, the VLMC sieve scheme enjoys an implementational advantage of using the plug-in rule for bootstrapping a statistical procedure, which generally is not the case for the block method. [ABSTRACT FROM AUTHOR]

In this article, the author discusses the article by Eric B. Laber and Susan A. Murphy regarding practical and nonstandard mathematical aspects of interference. He is critical on the construction of confidence intervals by the authors for the test set error. Also investigated is the potential of subsampling in the stabilization of the indicator or decision function.