Naive Estimates Research Articles

Error Variance Estimation in Ultrahigh-Dimensional Additive Models

ABSTRACTError variance estimation plays an important role in statistical inference for high-dimensional regression models. This article concerns with error variance estimation in high-dimensional sparse additive model. We study the asymptotic behavior of the traditional mean squared errors, the naive estimate of error variance, and show that it may significantly underestimate the error variance due to spurious correlations that are even higher in nonparametric models than linear models. We further propose an accurate estimate for error variance in ultrahigh-dimensional sparse additive model by effectively integrating sure independence screening and refitted cross-validation techniques. The root n consistency and the asymptotic normality of the resulting estimate are established. We conduct Monte Carlo simulation study to examine the finite sample performance of the newly proposed estimate. A real data example is used to illustrate the proposed methodology. Supplementary materials for this article are available online.

Comparison of dimensionally split and multi‐dimensional atmospheric transport schemes for long time steps

Dimensionally split advection schemes are attractive for atmospheric modelling due to their efficiency and accuracy in each spatial dimension. Accurate long time steps can be achieved without significant cost using the flux‐form semi‐Lagrangian technique. The dimensionally split scheme used in this paper is constructed from the one‐dimensional Piecewise Parabolic Method and extended to two dimensions using COSMIC splitting. The dimensionally split scheme is compared with a genuinely multi‐dimensional, method‐of‐lines scheme which, with implicit time‐stepping, is stable for Courant numbers significantly larger than 1.Two‐dimensional advection test cases on Cartesian planes are proposed which avoid the complexities of a spherical domain or multi‐panel meshes. These are solid‐body rotation, horizontal advection over orography and deformational flow. The test cases use distorted non‐orthogonal meshes either to represent sloping terrain or to mimic the distortions near cubed‐sphere edges.Mesh distortions are expected to accentuate the errors associated with dimension splitting, however the accuracy of the dimensionally split scheme decreases only a little in the presence of mesh distortions. The dimensionally split scheme also loses some accuracy when long time steps are used. The multi‐dimensional scheme is almost entirely insensitive to mesh distortions and asymptotes to second‐order accuracy at high resolution. As is expected for implicit time‐stepping, phase errors occur when using long time steps but the spatially well‐resolved features are advected at the correct speed and the multi‐dimensional scheme is always stable.A naive estimate of computational cost (number of multiplies) reveals that the implicit scheme is the most expensive, particularly for large Courant numbers. If the multi‐dimensional scheme is used instead with explicit time‐stepping, the Courant number is restricted to less than 1, the accuracy is maintained, and the cost becomes similar to the dimensionally split scheme.

Cosmic microwave background constraints for global strings and global monopoles

We present the first cosmic microwave background (CMB) power spectra from numerical simulations of the global O(N) linear σ-model, with N=2,3, which have global strings and monopoles as topological defects. In order to compute the CMB power spectra we compute the unequal time correlators (UETCs) of the energy-momentum tensor, showing that they fall off at high wave number faster than naive estimates based on the geometry of the defects, indicating non-trivial (anti-)correlations between the defects and the surrounding Goldstone boson field. We obtain source functions for Einstein-Boltzmann solvers from the UETCs, using a recently developed method that improves the modelling at the radiation-matter transition. We show that the interpolation function that mimics the transition is similar to other defect models, but not identical, confirming the non-universality of the interpolation function. The CMB power spectra for global strings and global monopoles have the same overall shape as those obtained using the non-linear σ-model approximation, which is well captured by a large-N calculation. However, the amplitudes are larger than the large-N calculation would naively predict, and in the case of global strings much larger: a factor of 20 at the peak. Finally we compare the CMB power spectra with the latest CMB data in other to put limits on the allowed contribution to the temperature power spectrum at multipole l = 10 of 1.7% for global strings and 2.4% for global monopoles. These limits correspond to symmetry-breaking scales of 2.9× 1015 GeV (6.3× 1014 GeV with the expected logarithmic scaling of the effective string tension between the simulation time and decoupling) and 6.4× 1015 GeV respectively. The bound on global strings is a significant one for the ultra-light axion scenario with axion masses ma ≲ 10−28 eV . These upper limits indicate that gravitational waves from global topological defects will not be observable at the gravitational wave observatory LISA.

Using Statistical Estimators to Gain Much Improved Convergence of Nested Monte-Carlo Simulations

The problem of estimating expectations of functions of conditional expectations using nested Monte Carlo simulation is studied. It is shown that typically the bias arising from non-linearity is in leading order inversely proportional to the number of sub-simulation paths when using a naive estimate. Various improved statistical estimators are introduced for the inner simulation. Applications to pricing of VIX derivatives, the computation of credit valuation adjustments and computation of Value-At-Risk are presented. It is shown that only small numbers of sub-paths are necessary for high accuracy.

An Improved GLRT for Image-Based Point Source Detection and Estimation

This work revisits the problem of detecting and localizing point sources in a scene using an imaging array and suggests two improvements over traditional approaches. First, the importance of covariance matrix estimation is discussed and several estimators are compared. In particular, the so-called shrinkage estimator is shown to produce better estimates of the covariance matrix and consequently provides improved detection performance over the commonly used naive estimator. We also develop an iterative algorithm for obtaining maximum likelihood estimates of the point source parameters. By using these estimates in forming the detection statistic, further improvements are demonstrated over previously used estimators.

Comparing Approaches to Treatment Effect Estimation for Subgroups in Clinical Trials

ABSTRACTIdentifying subgroups, which respond differently to a treatment, both in terms of efficacy and safety, is an important part of drug development. A well-known challenge in exploratory subgroup analyses is the small sample size in the considered subgroups, which is usually too low to allow for definite comparisons. In early phase trials, this problem is further exaggerated, because limited or no clinical prior information on the drug and plausible subgroups is available. We evaluate novel strategies for treatment effect estimation in these settings in a simulation study motivated by real clinical trial situations. We compare several approaches to estimate treatment effects for selected subgroups, employing model averaging, resampling, and Lasso regression methods. Two subgroup identification approaches are employed, one based on categorization of covariates and the other based on splines. Our results show that naive estimation of the treatment effect, which ignores that a selection has taken place, leads to bias and overoptimistic conclusions. For the considered simulation scenarios, virtually all evaluated novel methods provide more adequate estimates of the treatment effect for selected subgroups, in terms of bias, mean squared error (MSE), and confidence interval coverage. Supplementary materials for this article are available online.

Neutron-antineutron oscillations beyond the quasifree limit

Prompted by plans to conduct a new neutron oscillation experiment at the European Spallation Source (ESS), we consider issues associated with the magnetic field that must be present, some of which are potentially exacerbated by the significantly larger length $l$ contemplated for the neutron propagation region. To this end, we introduce a stochastic model of the residual magnetic field within the propagation region which draws on features of magnetic profiles measured during the last free neutron oscillation experiment [conducted at the Institut Laue-Langevin (ILL) in the 1990's]. We average over both fluctuations in the magnetic field sampled by neutrons, and representative spectra of neutron speeds. We find that deviations from the quasi-free result for the antineutron probability do not depend quadratically on $l$ (as a naive perturbative estimate would suggest) but increase only linearly with $l$. As regards the large spikes in the magnetic field which can be expected at, for example, joints in the magnetic shielding of the propagation region (despite compensating currents and magnetic idealization of the shield), we demonstrate that their effect scales as $l/D^{3/2}$, where $D$ is the diameter of the cylindrical magnetic shielding. Our arguments suggest that, provided the dimensions of the propagation region are such that the ratio $l/D^{3/2}$ does not exceed the value pertinent to the ILL experiment, and these spikes occur close to either end of the propagation region, they can be neglected. We also establish that any large magnetic field encountered after the propagation region is exited will not diminish the probability for antineutron detection. For the range of values of $l$ of most interest to the ESS experiment, it should suffice to improve on the level of magnetic suppression achieved at the ILL by a factor of two.

Improving bald eagle nest monitoring with a second spring survey

Failure to account for observation error can cause bias in estimators of variables important for wildlife management and conservation, such as abundance, occupancy, and species composition. Therefore, long-term monitoring programs need to evaluate sources of bias to ensure that objectives of the program can be met. Although trend estimation is possible using biased estimators, population status, and management decisions can be sensitive to random and systematic heterogeneity in the observation process. For example, standard methods used to monitor reproductive attempts at bald eagle (Haliaeetus leucocephalus) nests fail to quantify observation error. We used bald eagle nest surveys from 3 national parks in Alaska, USA, to examine their ability to accurately estimate nesting attempts and hypothesized that our ability to perfectly observe nesting activity was related to the timing of the survey relative to peak nest attendance by eagles. We therefore, developed 3 scenarios that evaluated our ability to correctly identify nesting status metrics: peak nesting remained unchanged (observed variation scenario), reduced ability to predict peak nest attendance (high heterogeneity scenario), and peak nest attendance occurred earlier than the survey window (low detection scenario). Eagle nest attendance was consistently underestimated using naive estimators, but productivity (predicted no. chicks/nesting attempt) was not affected by imperfect detection. All scenarios showed that using replicate observations to model imperfect detection corrected estimator bias for nest attendance and improved the estimator precision for both metrics. Our study demonstrates that imperfect observation of bald eagle nesting activity using standard methods results in estimator bias and reduced precision if not corrected. Further, our simulations show that changes in observation conditions can affect estimator bias and precision, which is an important consideration for long-term monitoring programs. Therefore, formally modeling imperfect detection should be completed for monitoring programs designed to use nesting status to inform management or conservation decisions. © 2017 The Wildlife Society.

Macroeconomic Factors Strike Back: A Bayesian Change-Point Model of Time-Varying Risk Exposures and Premia in the U.S. Cross-Section

This article proposes a Bayesian estimation framework for a typical multi-factor model with time-varying risk exposures to macroeconomic risk factors and corresponding premia to price U.S. publicly traded assets. The model assumes that risk exposures and idiosyncratic volatility follow a break-point latent process, allowing for changes at any point on time but not restricting them to change at all points. The empirical application to 40 years of U.S. data and 23 portfolios shows that the approach yields sensible results compared to previous two-step methods based on naive recursive estimation schemes, as well as a set of alternative model restrictions. A variance decomposition test shows that although most of the predictable variation comes from the market risk premium, a number of additional macroeconomic risks, including real output and inflation shocks, are significantly priced in the cross-section. A Bayes factor analysis massively favors the proposed change-point model. Supplementary materials for this article are available online.

On several estimates to the precision parameter of Dirichlet process prior

ABSTRACTThe article presents careful comparisons among several empirical Bayes estimates to the precision parameter of Dirichlet process prior, with the setup of univariate observations and multigroup data. Specifically, the data are equipped with a two-stage compound sampling model, where the prior is assumed as a Dirichlet process that follows within a Bayesian nonparametric framework. The precision parameter α measures the strength of the prior belief and kinds of estimates are generated on the basis of observations, including the naive estimate, two calibrated naive estimates, and two different types of maximum likelihood estimates stemming from distinct distributions. We explore some theoretical properties and provide explicitly detailed comparisons among these estimates, in the perspectives of bias, variance, and mean squared error. Besides, we further present the corresponding calculation algorithms and numerical simulations to illustrate our theoretical achievements.

Framework for making better predictions by directly estimating variables’ predictivity

We propose approaching prediction from a framework grounded in the theoretical correct prediction rate of a variable set as a parameter of interest. This framework allows us to define a measure of predictivity that enables assessing variable sets for, preferably high, predictivity. We first define the prediction rate for a variable set and consider, and ultimately reject, the naive estimator, a statistic based on the observed sample data, due to its inflated bias for moderate sample size and its sensitivity to noisy useless variables. We demonstrate that the [Formula: see text]-score of the PR method of VS yields a relatively unbiased estimate of a parameter that is not sensitive to noisy variables and is a lower bound to the parameter of interest. Thus, the PR method using the [Formula: see text]-score provides an effective approach to selecting highly predictive variables. We offer simulations and an application of the [Formula: see text]-score on real data to demonstrate the statistic's predictive performance on sample data. We conjecture that using the partition retention and [Formula: see text]-score can aid in finding variable sets with promising prediction rates; however, further research in the avenue of sample-based measures of predictivity is much desired.

Estimation of the Case Fatality Ratio of Middle East Respiratory Syndrome based on Patients' Comorbidities with Application to the MERS-CoV Epidemics in the Republic of Korea, 2015

In an early stage of the course of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) outbreak in Korea in 2015, the Centers for Disease Control and Prevention of Korea and several studies reported estimated Case Fatality Ratios (CFRs) that were significantly different. Here, we propose an estimation method based on the commonly quoted naive estimator of CFR utilizing the number of in-hospital patients with comorbidities, as well as the numbers of cumulative confirmed and dead patients up to a certain date. We compared the proposed estimator with two naive and an integral method estimator by simulation experiments under the individual based susceptible-exposed-infected-recovered model and analysis of data from the 2015 epidemic of MERS-CoV in Korea. The proposed estimator better simulated and analyzed the Korean MERS data.

Grammage of cosmic rays around Galactic supernova remnants

The residence time of cosmic rays (CRs) in the Galaxy is usually inferred from the measurement of the ratio of secondary-to-primary nuclei, such as the boron (B)/carbon (C) ratio, which provides an estimate of the amount of matter traversed by CRs during their propagation, the so called CR grammage. However, after being released by their parent sources, for instance supernova remnants (SNRs), CRs must cross the disc of the Galaxy, before entering the much lower density halo, in which they are believed to spend most of the time before eventually escaping the Galaxy. In the near-source region, the CR propagation is shown to be dominated by the non-linear self-generation of waves. Here we show that due to this effect, the time that CRs with energies up to $\sim$ 10 TeV spend within a distance $L_{c}\sim 100$ pc from the sources is much larger than naive estimates would suggest. The corresponding grammage is close to current estimates of the total grammage traversed throughout the whole Galaxy. Moreover, there is an irreducible grammage that CRs traverse while trapped downstream of the shock that accelerated them, though this contribution is rather uncertain. We conclude that at energies $\lesssim 1$ TeV, the observed grammage is heavily affected by the near-source non-linear trapping of CRs, and at energies $\gtrsim 1$ TeV it is affected by the source grammage. As a result, the measurement of the B/C ratio should be used very cautiously as an indicator of the propagation of CRs on large Galactic scales.

The Effect of Income on Mortality—new Evidence for the Absence of a Causal Link

Summary We analyse the effect of income on mortality in Austria by using administrative social security data. To tackle potential endogeneity concerns arising in this context, we estimate time invariant firm-specific wage components and use them as instruments for actual wages. Although we find quantitatively small yet statistically significant effects in our naive least squares estimations, instrumental variables regressions reveal a robust zero effect of income on 10-year death rates for workers aged 40–60 years, both in terms of coefficient magnitude and narrow width of confidence intervals. These results are robust to various sample specifications and both linear and non-linear estimation methods.

Exact inference for the risk ratio with an imperfect diagnostic test.

The risk ratio quantifies the risk of disease in a study population relative to a reference population. Standard methods of estimation and testing assume a perfect diagnostic test having sensitivity and specificity of 100%. However, this assumption typically does not hold, and this may invalidate naive estimation and testing for the risk ratio. We propose procedures that control for sensitivity and specificity of the diagnostic test, given the risks are measured by proportions, as it is in cross-sectional studies or studies with fixed follow-up times. These procedures provide an exact unconditional test and confidence interval for the true risk ratio. The methods also cover the case when sensitivity and specificity differ in the two groups (differential misclassification). The resulting test and confidence interval may be useful in epidemiological studies as well as in clinical and vaccine trials. We illustrate the method with real-life examples which demonstrate that ignoring sensitivity and specificity of the diagnostic test may lead to considerable bias in the estimated risk ratio.

Variance estimation when using inverse probability of treatment weighting (IPTW) with survival analysis

Propensity score methods are used to reduce the effects of observed confounding when using observational data to estimate the effects of treatments or exposures. A popular method of using the propensity score is inverse probability of treatment weighting (IPTW). When using this method, a weight is calculated for each subject that is equal to the inverse of the probability of receiving the treatment that was actually received. These weights are then incorporated into the analyses to minimize the effects of observed confounding. Previous research has found that these methods result in unbiased estimation when estimating the effect of treatment on survival outcomes. However, conventional methods of variance estimation were shown to result in biased estimates of standard error. In this study, we conducted an extensive set of Monte Carlo simulations to examine different methods of variance estimation when using a weighted Cox proportional hazards model to estimate the effect of treatment. We considered three variance estimation methods: (i) a naïve model‐based variance estimator; (ii) a robust sandwich‐type variance estimator; and (iii) a bootstrap variance estimator. We considered estimation of both the average treatment effect and the average treatment effect in the treated. We found that the use of a bootstrap estimator resulted in approximately correct estimates of standard errors and confidence intervals with the correct coverage rates. The other estimators resulted in biased estimates of standard errors and confidence intervals with incorrect coverage rates. Our simulations were informed by a case study examining the effect of statin prescribing on mortality. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Robust best linear estimator for Cox regression with instrumental variables in whole cohort and surrogates with additive measurement error in calibration sample

Biomedical researchers are often interested in estimating the effect of an environmental exposure in relation to a chronic disease endpoint. However, the exposure variable of interest may be measured with errors. In a subset of the whole cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies an additive measurement error model, but it may not have repeated measurements. The subset in which the surrogate variables are available is called a calibration sample. In addition to the surrogate variables that are available among the subjects in the calibration sample, we consider the situation when there is an instrumental variable available for all study subjects. An instrumental variable is correlated with the unobserved true exposure variable, and hence can be useful in the estimation of the regression coefficients. In this paper, we propose a nonparametric method for Cox regression using the observed data from the whole cohort. The nonparametric estimator is the best linear combination of a nonparametric correction estimator from the calibration sample and the difference of the naive estimators from the calibration sample and the whole cohort. The asymptotic distribution is derived, and the finite sample performance of the proposed estimator is examined via intensive simulation studies. The methods are applied to the Nutritional Biomarkers Study of the Women's Health Initiative.

LHC benchmarks from flavored gauge mediation

We present benchmark points for LHC searches from flavored gauge mediation models, in which messenger-matter couplings give flavor-dependent squark masses. Our examples include spectra in which a single squark - stop, scharm, or sup - is much lighter than all other colored superpartners, motivating improved quark flavor tagging at the LHC. Many examples feature flavor mixing; in particular, large stop-scharm mixing is possible. The correct Higgs mass is obtained in some examples by virtue of the large stop A-term. We also revisit the general flavor and CP structure of the models. Even though the A-terms can be substantial, their contributions to EDM's are very suppressed, because of the particular dependence of the A-terms on the messenger coupling. This holds regardless of the messenger-coupling texture. More generally, the special structure of the soft terms often leads to stronger suppression of flavor- and CP-violating processes, compared to naive estimates.

Inference on quantile residual life function under right-censored data

The quantile residual lifetime function is a comprehensive quantitative description of a residual lifetime. Under the assumption of independent censoring, a naive estimator for the quantile residual lifetime function can be obtained by inverting the Kaplan–Meier estimator. However, this naive estimator is biased when survival and censoring times are dependent. In this paper, we propose a method for estimating the quantile residual lifetime function, taking into account the covariates and relaxing the assumption of independent censoring. To compare two quantile residual lifetime functions at fixed time points, we construct two test statistics which are easy to implement. We also derive the asymptotic properties for the proposed estimator and test statistics. A re-sampling method for estimating the asymptotic variance of the proposed estimator is provided. Simulation studies are conducted to assess the finite sample properties of the estimator and the performance of the test statistics. We also apply the proposed method to the real data and report some interesting results.

Brane realization of q-theory and the cosmological constant problem

We discuss the cosmological constant problem using the properties of a freely-suspended two-dimensional condensed-matter film, i.e., an explicit realization of a 2D brane. The large contributions of vacuum fluctuations to the surface tension of this film are cancelled in equilibrium by the thermodynamic potential arising from the conservation law for particle number. In short, the surface tension of the film vanishes in equilibrium due to a thermodynamic identity. This 2D brane can be generalized to a 4D brane with gravity. For the 4D brane, the analogue of the 2D surface tension is the 4D cosmological constant, which is also nullified in full equilibrium. The 4D brane theory provides an alternative description of the phenomenological $q$-theory of the quantum vacuum. As for other realizations of the vacuum variable $q$, such as the 4-form field-strength realization, the main ingredient is the conservation law for the variable $q$, which makes the vacuum a self-sustained system. For a vacuum within this class, the nullification of the cosmological constant takes place automatically in equilibrium. Out of equilibrium, the cosmological constant can be as large as suggested by naive estimates based on the summation of zero-point energies. In this brane description, $q$-theory also corresponds to a generalization of unimodular gravity.