Inference on a distribution from noisy draws

In many applications, data are imperfectly collected. Variables are often measured with error and data are missing for various reasons. Regression calibration is often a simple solution to correct measurement error bias for mean regressions. The measurement error-induced bias could be corrected by solving the corrected estimating equations, as in, or, equivalently, by minimizing a corrected quantile regression loss function. As for the mean regression calibration approach designed to correct measurement errors, simple conditional mean imputation is only valid when the estimation equations are linear, but that is not the case for quantile regression. Likewise, ignoring missing observations in the data can lead to efficiency loss or biased estimation. While there is an abundant literature on measurement errors and missing data, there have been little attention devoted to quantile methods directly, primarily due to the lack of parametric likelihood in quantile regression. Ignoring the missing data will undermine study efficiency and sometimes introduce substantial bias.

To generate random variates from an unknown continuous distribution via the inverse transform method, we present a flexible, computationally tractable procedure for estimating the associated inverse distribution function based on sample data. Previously proposed methods for estimating inverse distribution functions can fail in either the distribution-fitting or variate-generation stages of application. To avoid these difficulties, we have developed the procedure IDPF for estimating an Inverse Distribution with a Polynomial Filter. After a first-cut or reference distribution has been obtained by some standard technique, a front-end polynomial filter for the inverse of the reference distribution is estimated by constrained nonlinear regression so that the resulting inverse distribution has minimum distance from the empirical inverse distribution. The constraints on the regression ensure that the fitted inverse distribution function is nondefective and monotonically nondecreasing. A specific implementation of this procedure is based on well-known techniques for obtaining a reference fit from the Johnson translation system of distributions. We present the results of a Monte Carlo study to demonstrate the effectiveness of the method. Compared to the reference fit, procedure IDPF yields significantly better approximations not only to the empirical inverse distribution function but also to the underlying theoretical inverse distribution function.

FORTRAN 77 program for constructing and plotting confidence bands for the distribution and quantile functions for truncated data

This paper provides a method to construct simultaneous confidence bands for quantile functions and quantile effects in nonlinear network and panel models with unobserved two-way effects, strictly exogenous covariates, and possibly discrete outcome variables. The method is based upon projection of simultaneous confidence bands for distribution functions constructed from fixed effects distribution regression estimators. These fixed effects estimators are bias corrected to deal with the incidental parameter problem. Under asymptotic sequences where both dimensions of the data set grow at the same rate, the confidence bands for the quantile functions and effects have correct joint coverage in large samples. An empirical application to gravity models of trade illustrates the applicability of the methods to network data.

This article develops an adaptive group lasso estimator for factor models with both global and group-specific factors. The global factors can affect all variables, whereas the group-specific factors are only allowed to affect the variables within a certain group. We propose a new method to separately identify the spaces spanned by global and group-specific factors, and we develop a new shrinkage estimator that can consistently estimate the factor loadings and determine the number of factors simultaneously. The asymptotic result shows that the proposed estimator can select the true model specification with a probability approaching one. An information criterion is developed to select the optimal tuning parameters in the shrinkage estimation. Monte Carlo simulations confirm our asymptotic theory, and the proposed estimator performs well in finite samples. In an empirical application, we implement the proposed method to a dataset consisting of Eurozone, United States, and United Kingdom macroeconomic variables, and we detect one global factor, one U.S.-specific factor, and one Eurozone-specific factor.

In this article, we improve parameter estimation in the zero-inflated Poisson regression model using shrinkage strategies when it is suspected that the regression parameter vector may be restricted to a linear subspace. We consider a situation where the response variable is subject to right-censoring. We develop the asymptotic distributional biases and risks of the shrinkage estimators. We conduct an extensive Monte Carlo simulation for various combinations of the inactive predictors and censoring constants to compare the performance of the proposed estimators in terms of their simulated relative efficiencies. The results demonstrate that the shrinkage estimators outperform the classical estimator in certain parts of the parameter space. When there are many inactive predictors in the model, as well as when the censoring percentage is low, the proposed estimators perform better. The performance of the positive Stein-type estimator is superior to the Stein-type estimator in certain parts of the parameter space. We evaluated the estimators’ performance using wildlife fish data.

Shrinkage estimators modify classical statistical estimators by scaling them towards zero in order to decrease their prediction error. We propose shrinkage estimators for linear regression models which explicitly take into account the presence of the intercept term, shrinking it independently from other coefficients. This is different from current shrinkage estimators, which treat the intercept just as an ordinary regression coefficient. We demonstrate that the proposed approach brings systematic improvements in prediction accuracy if the true intercept term differs in magnitude from other coefficients, which is often the case in practice. We then generalize the approach to uplift regression which aims to predict the causal effect of a specific action on an individual with given characteristics. In this case the proposed estimators improve prediction accuracy over previously proposed shrinkage estimators and achieve impressive performance gains over original models.

Road safety modelers frequently use average annual daily traffic (AADT) as a measure of exposure in regression models of expected crash frequency for road segments and intersections. Recorded AADT values at most locations are estimated by state and local transportation agencies with significant uncertainty, often by extrapolating short-term traffic counts over time and space. This uncertainty in the traffic volume estimates, often termed in a modeling context as measurement error in right-hand-side variables, can have serious effects on model estimation, including: 1) biased regression coefficient estimates; and 2) increases in dispersion. The structure and magnitude of measurement error in AADT estimates are not clearly understood by researchers or practitioners, leading to difficulties in explicitly accounting for this error in statistical road safety models, and ultimately in finding solutions for its correction. This study explores the impacts of measurement error in traffic volume estimates on statistical road safety models by employing measurement error correction approaches, including regression calibration and simulation extrapolation. The concept is demonstrated using crash, traffic, and roadway data from rural, two-lane horizontal curves in the State of Washington. The overall results show that the regression coefficient estimates with a positive coefficient were larger and those with a negative coefficient were smaller (i.e., more negative) when the measurement error correction methods were applied to the regression models of expected crash frequency. Future directions in applications of measurement error correction approaches to road safety research are provided.

In this article, we introduce a new one-parameter model, which is named sine inverted exponential (SIE) distribution. The SIE distribution is a new extension of the inverse exponential (IE) distribution. The SIE distribution aims to provide the SIE model for data-fitting purposes. The SIE distribution is more flexible than the inverted exponential (IE) model, and it has many applications in physics, medicine, engineering, nanophysics, and nanoscience. The density function (PDFu) of SIE distribution can be unimodel shape and right skewed shape. The hazard rate function (HRFu) of SIE distribution can be J-shaped and increasing shaped. We investigated some fundamental statistical properties such as quantile function (QFu), moments (Mo), moment generating function (MGFu), incomplete moments (ICMo), conditional moments (CMo), and the SIE distribution parameters were estimated using the maximum likelihood (ML) method for estimation under censored samples (CS). Finally, the numerical results were investigated to evaluate the flexibility of the new model. The SIE distribution and the IE distribution are compared using two real datasets. The numerical results show the superiority of the SIE distribution.

This paper focuses on the accelerated failure time model which is often suggested as an alternative to the Cox proportional hazards model. We propose pretest and shrinkage estimation methods for estimating the regression parameters in the accelerated failure time model for right-censored data when some of the parameters shrink to a restricted subspace. Shrinkage estimators take information from the unrestricted model and provide an efficient estimate of the regression parameters by shrinking the unrestricted estimate toward the restricted model estimate. This technique increases the bias in the estimation process but reduces the overall mean-squared error, which offsets the bias. We show that if the shrinkage dimension exceeds two, the risk of the shrinkage estimator is strictly less than that of the maximum-likelihood estimator. Extensive numerical studies are conducted to evaluate the performance of the pretest and shrinkage estimators. An empirical application is provided to illustrate the practical usefulness of the proposed estimators.

The impact of covariate measurement error on quantile regression functions is investigated using a small variance approximation. The approximation shows how the error contaminated and error free quantile regression functions are related, a key factor being the distribution of the error free covariate. Exact calculations probe the accuracy of the approximation. The order of the approxiamtion error is unchanged if the error free covariate density is replaced by the error contaminated density. It is then possible to use the approximation to investigate the sensitivity of estimates to varying amounts of measurement error.

Satellite radar altimetry is presently the only method that has provided the spatial coverage and density of observations needed to reduce the present uncertainty in the mass balance of the Greenland Ice Sheet and its contribution to change in eustatic sea level. The only such measurement reported, however, estimated that southern Greenland was thickening at 23±6 cm a-1 which is larger than was thought hitherto. This value is reconsidered given more recent information concerning the errors in the measurement. A survey of measurements of specific mass balance of the Greenland Ice Sheet is given, together with estimates of its sensitivity to temperature change. The expected behaviour is described of errors in the satellite position and errors in the range measurement to the ice sheet surface. The treatment of biases and the number of independent observations of random errors is described. It is found in particular that a higher degree of independence was given to the random errors than should have been the case. The total error is recalculated with this accounted for, and is found to remain dominated by the bias estimate and therefore largely unaffected by this change; the estimate is 23 ± 7 cm a-1. It is concluded that the observation does support a recent thickening of the southern Greenland Ice Sheet.

In this paper, we propose a method for monitoring the evolution of data described by histograms of values. Our proposal consists to define new order statistics on the quantile functions associated with the empirical distributions, represented by the histogram-data. We introduce the Median, the First and the Third Quartile quantile functions, as well as a generalized representation of the box and whiskers plot. For example, the proposed representations and indices are useful for identifying and classifying outliers, arriving along the time in a data stream environment.

Threshold autoregressive models have a wide range of applications in the field of econometrics. This paper considers the Bayesian empirical likelihood (BEL) shrinkage estimation and order selection for a class of sparse threshold autoregressive models. With the help of Taylor explanation, a “normally distributed” nonparametric likelihood is obtained. Based on this likelihood, the BEL estimation is well addressed. By using the Markov Chain Monte Carlo (MCMC) techniques under a Bayesian hierarchical model, the order and the non-zero autoregressive coefficients of the model can be accurately determined. Some simulation studies are conducted to show the performances of the proposed methods. Finally, an application to the US gross national product data set is provided.

This study presents a simplified multivariate bias correction scheme that is sequentially implemented in the GEOS5 data assimilation system and compared against a control experiment without model bias correction. The results show considerable improvement in terms of the mean biases of rawinsonde observation-minus-background (OmB) residuals for observed water vapor, wind and temperature variables. The time series spectral analysis shows whitening of bias-corrected OmB residuals, and mean biases for rawinsonde observation-minus-analysis (OmA) are also improved. Some wind and temperature biases in the control experiment near the equatorial tropopause nearly vanish from the bias-corrected experiment. Despite the analysis improvement, the bias correction scheme has only a moderate impact on forecast skill. Significant interaction is also found among quality-control, satellite observation bias correction, and background bias correction, and the latter positively impacts satellite bias correction.