1,721,120 research outputs found
Parametric estimation of non-crossing quantile functions
Full text linkQuantile regression (QR) has gained popularity during the last decades, and is now considered a standard method by applied statisticians and practitioners in various fields. In this work, we applied QR to investigate climate change by analysing historical temperatures in the Arctic Circle. This approach proved very flexible and allowed to investigate the tails of the distribution, that correspond to extreme events. The presence of quantile crossing, however, prevented using the fitted model for prediction and extrapolation. In search of a possible solution, we first considered a different version of QR, in which the QR coefficients were described by parametric functions. This alleviated the crossing problem, but did not eliminate it completely. Finally, we exploited the imposed parametric structure to formulate a constrained optimization algorithm that enforced monotonicity. The proposed example showed how the relatively unexplored field of parametric quantile functions could offer new solutions to the long-standing problem of quantile crossing. Our approach is particularly convenient in situations, like the analysis of time series, in which the fitted model may be used to predict extreme quantiles or to perform extrapolation. The described estimator has been implemented in the R package qrcm
Robust estimation and regression with parametric quantile functions
No full textA new, broad family of quantile-based estimators is described, and theoretical and empirical evidence is provided for their robustness to outliers in the response. The proposed method can be used to estimate all types of parameters, including location, scale, rate and shape parameters, extremes, regression coefficients and hazard ratios, and can be extended to censored and truncated data. The described estimator can be utilized to construct robust versions of common parametric and semiparametric methods, such as linear (Normal) regression, generalized linear models, and proportional hazards models. A variety of significant results and applications is presented to show the flexibility of the proposed approach. The R package Qest implements the estimator and provides the necessary functions for model building, prediction, and inference
Parametric modeling of quantile regression coefficient functions with count data
No full textApplying quantile regression to count data presents logical and practical complications which are usually solved by artificially smoothing the discrete response variable through jittering. In this paper, we present an alternative approach in which the quantile regression coefficients are modeled by means of (flexible) parametric functions. The proposed method avoids jittering and presents numerous advantages over standard quantile regression in terms of computation, smoothness, efficiency, and ease of interpretation. Estimation is carried out by minimizing a “simultaneous” version of the loss function of ordinary quantile regression. Simulation results show that the described estimators are similar to those obtained with jittering, but are often preferable in terms of bias and efficiency. To exemplify our approach and provide guidelines for model building, we analyze data from the US National Medical Expenditure Survey. All the necessary software is implemented in the existing R package qrcm
Parametric modelling of M-quantile regression coefficient functions with application to small area estimation
Full text linkSmall area estimation methods can be used to obtain reliable estimates of a parameter of interest within an unplanned domain or subgroup of the population for which only a limited sample size is available. A standard approach to small area estimation is to use a linear mixed model in which the heterogeneity between areas is accounted for by area level effects. An alternative solution, which has gained popularity in recent years, is to use M-quantile regression models. This approach requires much weaker assumptions than the standard linear mixed model and enables computing outlier robust estimators of the area means. We introduce a new framework for M-quantile regression, in which the model coefficients, β(τ), are described by (flexible) parametric functions of τ. We illustrate the advantages of this approach and its application to small area estimation. Using the European Union Survey on Income and Living Conditions data, we estimate the average equivalized household income in three Italian regions. The paper is accompanied by an R package Mqrcm that implements the necessary procedures for estimation, inference and prediction
An estimating equation for censored and truncated quantile regression
No full textAn estimation equation for censored, truncated quantile regression is introduced. The asymptotic covariance matrix has a relatively simple expression and can be estimated from the data. Simulation results are presented, and the described estimator is used to evaluate the effects of birth weight on percentiles of survival time after age 65 with a population-based cohort of Swedish men. The proposed method is efficiently implemented in the R package ctqr
L'approccio biografico come strumento di analisi dei cambiamenti familiari e residenziali
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