arXiv subjects

Ingrid Van Keilegom

Publications and source records attributed to Ingrid Van Keilegom.

At least 37 records · Page 2Linked to original sources

arXiv2023

Testing for homogeneous treatment effects in linear and nonparametric instrumental variable models

The hypothesis of homogeneous treatment effects is central to the instrumental variables literature. This assumption signifies that treatment effects are constant across all subjects. It allows to interpret instrumental variable estimates as average treatment effects over the whole population of the study. When this assumption does not hold, the bias of instrumental variable estimators can be larger than that of naive estimators ignoring endogeneity. This paper develops two tests for the assumption of homogeneous treatment effects when the treatment is endogenous and an instrumental variable is available. The tests leverage a covariable that is (jointly with the error terms) independent of a coordinate of the instrument. This covariate does not need to be exogenous. The first test assumes that the potential outcomes are linear in the regressors and is computationally simple. The second test is nonparametric and relies on Tikhonov regularization. The treatment can be either discrete or continuous. We show that the tests have asymptotically correct level and asymptotic power equal to one against a range of alternatives. Simulations demonstrate that the proposed tests attain excellent finite sample performances. The methodology is also applied to the evaluation of returns to schooling and the effect of price on demand in a fish market.

econ.EM↗

arXiv2023

Comparison of Quantile Regression Curves with Censored Data

This paper proposes a new test for the comparison of conditional quantile curves when the outcome of interest, typically a duration, is subject to right censoring. The test can be applied both in the case of two independent samples and for paired data, and can be used for the comparison of quantiles at a fixed quantile level, a finite set of levels or a range of quantile levels. The asymptotic distribution of the proposed test statistics is obtained both under the null hypothesis and under local alternatives. We describe a bootstrap procedure in order to approximate the critical values, and present the results of a simulation study, in which the performance of the tests for small and moderate sample sizes is studied and compared with the behavior of alternative tests. Finally, we apply the proposed tests on a data set concerning diabetic retinopathy.

stat.ME↗

arXiv2023

Instrumental variable quantile regression under random right censoring

This paper studies a semiparametric quantile regression model with endogenous variables and random right censoring. The endogeneity issue is solved using instrumental variables. It is assumed that the structural quantile of the logarithm of the outcome variable is linear in the covariates and censoring is independent. The regressors and instruments can be either continuous or discrete. The specification generates a continuum of equations of which the quantile regression coefficients are a solution. Identification is obtained when this system of equations has a unique solution. Our estimation procedure solves an empirical analogue of the system of equations. We derive conditions under which the estimator is asymptotically normal and prove the validity of a bootstrap procedure for inference. The finite sample performance of the approach is evaluated through numerical simulations. An application to the national Job Training Partnership Act study illustrates the method.

econ.EM↗

arXiv2023

Density estimation and regression analysis on S^d in the presence of measurement error

This paper studies density estimation and regression analysis with contaminated data observed on the unit hypersphere S^d. Our methodology and theory are based on harmonic analysis on general S^d. We establish novel nonparametric density and regression estimators, and study their asymptotic properties including the rates of convergence and asymptotic distributions. We also provide asymptotic confidence intervals based on the asymptotic distributions of the estimators and on the empirical likelihood technique. We present practical details on implementation as well as the results of numerical studies.

math.ST↗

arXiv2023

An instrumental variable approach under dependent censoring

This paper considers the problem of inferring the causal effect of a variable $Z$ on a dependently censored survival time $T$. We allow for unobserved confounding variables, such that the error term of the regression model for $T$ is correlated with the confounded variable $Z$. Moreover, $T$ is subject to dependent censoring. This means that $T$ is right censored by a censoring time $C$, which is dependent on $T$ (even after conditioning out the effects of the measured covariates). A control function approach, relying on an instrumental variable, is leveraged to tackle the confounding issue. Further, it is assumed that $T$ and $C$ follow a joint regression model with bivariate Gaussian error terms and an unspecified covariance matrix such that the dependent censoring can be handled in a flexible manner. Conditions under which the model is identifiable are given, a two-step estimation procedure is proposed, and it is shown that the resulting estimator is consistent and asymptotically normal. Simulations are used to confirm the validity and finite-sample performance of the estimation procedure. Finally, the proposed method is used to estimate the causal effect of job training programs on unemployment duration.

math.ST↗

arXiv2022

Instrumental variable estimation of dynamic treatment effects on a duration outcome

This paper considers identification and estimation of the causal effect of the time Z until a subject is treated on a survival outcome T. The treatment is not randomly assigned, T is randomly right censored by a random variable C and the time to treatment Z is right censored by min(T,C). The endogeneity issue is treated using an instrumental variable explaining Z and independent of the error term of the model. We study identification in a fully nonparametric framework. We show that our specification generates an integral equation, of which the regression function of interest is a solution. We provide identification conditions that rely on this identification equation. For estimation purposes, we assume that the regression function follows a parametric model. We propose an estimation procedure and give conditions under which the estimator is asymptotically normal. The estimators exhibit good finite sample properties in simulations. Our methodology is applied to find evidence supporting the efficacy of a therapy for burn-out.

math.ST↗

arXiv2022

A 2-step estimation procedure for semiparametric mixture cure models

Cure models have been developed as an alternative modelling approach to conventional survival analysis in order to account for the presence of cured subjects that will never experience the event of interest. Mixture cure models, which model separately the cure probability and the survival of uncured subjects depending on a set of covariates, are particularly useful for distinguishing curative from life-prolonging effects. In practice, it is common to assume a parametric model for the cure probability and a semiparametric model for the survival of the susceptibles. Because of the latent cure status, maximum likelihood estimation is performed by means of the iterative EM algorithm. Here, we focus on the cure probabilities and propose a two-step procedure to improve upon the performance of the maximum likelihood estimator when the sample size is not large. The new method is based on the idea of presmoothing by first constructing a nonparametric estimator and then projecting it into the desired parametric class. We investigate the theoretical properties of the resulting estimator and show through an extensive simulation study for the logistic-Cox model that it outperforms the existing method. Practical use of the method is illustrated through two melanoma datasets.

stat.ME↗

arXiv2021

Semi-Parametric Estimation of Incubation and Generation Times by Means of Laguerre Polynomials

In epidemics many interesting quantities, like the reproduction number, depend on the incubation period (time from infection to symptom onset) and/or the generation time (time until a new person is infected from another infected person). Therefore, estimation of the distribution of these two quantities is of distinct interest. However, this is a challenging problem since it is normally not possible to obtain precise observations of these two variables. Instead, in the beginning of a pandemic, it is possible to observe for infection pairs the time of symptom onset for both people as well as a window for infection of the first person (e.g. because of travel to a risk area). In this paper we suggest a simple semi-parametric sieve-estimation method based on Laguerre-Polynomials for estimation of these distributions. We provide detailed theory for consistency and illustrate the finite sample performance for small datasets via a simulation study.

math.ST↗

arXiv2021

Robust censored regression with l1-norm regularization

This paper considers inference in a linear regression model with random right censoring and outliers. The number of outliers can grow with the sample size while their proportion goes to zero. The model is semiparametric and we make only very mild assumptions on the distribution of the error term, contrary to most other existing approaches in the literature. We propose to penalize the estimator proposed by Stute for censored linear regression by the l1-norm. We derive rates of convergence and establish asymptotic normality of the estimator of the regression coefficients. Our estimator has the same asymptotic variance as Stute's estimator in the censored linear model without outliers. Hence, there is no loss of efficiency as a result of robustness. Tests and confidence sets can therefore rely on the theory developed by Stute. The outlined procedure is also computationally advantageous, since it amounts to solving a convex optimization program. We also propose a second estimator which uses the proposed penalized Stute estimator as a first step to detect outliers. It has similar theoretical properties but better performance in finite samples as assessed by simulations.

math.ST↗

arXiv2021

A presmoothing approach for estimation in semiparametric mixture cure models

A challenge when dealing with survival analysis data is accounting for a cure fraction, meaning that some subjects will never experience the event of interest. Mixture cure models have been frequently used to estimate both the probability of being cured and the time to event for the susceptible subjects, by usually assuming a parametric (logistic) form of the incidence. We propose a new estimation procedure for a parametric cure rate that relies on a preliminary smooth estimator and is independent of the model assumed for the latency. We investigate the theoretical properties of the estimators and show through simulations that, in the logistic/Cox model, presmoothing leads to more accurate results compared to the maximum likelihood estimator. To illustrate the practical use, we apply the new estimation procedure to two studies of melanoma survival data.

stat.ME↗

arXiv2021

A nonparametric instrumental approach to endogeneity in competing risks models

This paper discusses endogenous treatment models with duration outcomes, competing risks and random right censoring. The endogeneity issue is solved using a discrete instrumental variable. We show that the competing risks model generates a non-parametric quantile instrumental regression problem. The cause-specific cumulative incidence, the cause-specific hazard and the subdistribution hazard can be recovered from the regression function. A distinguishing feature of the model is that censoring and competing risks prevent identification at some quantiles. We characterize the set of quantiles for which exact identification is possible and give partial identification results for other quantiles. We outline an estimation procedure and discuss its properties. The finite sample performance of the estimator is evaluated through simulations. We apply the proposed method to the Health Insurance Plan of Greater New York experiment.

stat.ME↗

arXiv2021

Dependent censoring based on copulas

Consider a survival time T that is subject to random right censoring, and suppose that T is stochastically dependent on the censoring time C. We are interested in the marginal distribution of T. This situation is often encountered in practice. Consider for instance the case where T is the time to death of a patient suffering from a certain disease. Then, the censoring time C is for instance the time until the person leaves the study or the time until he/she dies from another disease. If the reason for leaving the study is related to the health condition of the patient or if he/she dies from a disease that has similar risk factors as the disease of interest, then T and C are likely dependent. In this paper we propose a new model that takes this dependence into account. The model is based on a parametric copula for the relationship between T and C, and on parametric marginal distributions for T and C. Unlike most other papers in the literature, we do not assume that the parameter defining the copula function is known. We give sufficient conditions on these parametric copula and marginals under which the bivariate distribution of (T;C) is identifed. These sufficient conditions are then checked for a wide range of common copulas and marginal distributions. We also study the estimation of the model, and carry out extensive simulations and the analysis of data on pancreas cancer to illustrate the proposed model and estimation procedure.

stat.ME↗

arXiv2021

A test for comparing conditional ROC curves with multidimensional covariates

The comparison of Receiver Operating Characteristic (ROC) curves is frequently used in the literature to compare the discriminatory capability of different classification procedures based on diagnostic variables. The performance of these variables can be sometimes influenced by the presence of other covariates, and thus they should be taken into account when making the comparison. A new non-parametric test is proposed here for testing the equality of two or more dependent ROC curves conditioned to the value of a multidimensional covariate. Projections are used for transforming the problem into a one-dimensional approach easier to handle. Simulations are carried out to study the practical performance of the new methodology. A real data set of patients with Pleural Effusion is analysed to illustrate this procedure.

stat.ME↗

arXiv2020

Nonparametric instrumental regression with right censored duration outcomes

This paper analyzes the effect of a discrete treatment Z on a duration T. The treatment is not randomly assigned. The confounding issue is treated using a discrete instrumental variable explaining the treatment and independent of the error term of the model. Our framework is nonparametric and allows for random right censoring. This specification generates a nonlinear inverse problem and the average treatment effect is derived from its solution. We provide local and global identification properties that rely on a nonlinear system of equations. We propose an estimation procedure to solve this system and derive rates of convergence and conditions under which the estimator is asymptotically normal. When censoring makes identification fail, we develop partial identification results. Our estimators exhibit good finite sample properties in simulations. We also apply our methodology to the Illinois Reemployment Bonus Experiment.

math.ST↗

arXiv2020

Testing parametric models in linear-directional regression

This paper presents a goodness-of-fit test for parametric regression models with scalar response and directional predictor, that is, a vector on a sphere of arbitrary dimension. The testing procedure is based on the weighted squared distance between a smooth and a parametric regression estimator, where the smooth regression estimator is obtained by a projected local approach. Asymptotic behavior of the test statistic under the null hypothesis and local alternatives is provided, jointly with a consistent bootstrap algorithm for application in practice. A simulation study illustrates the performance of the test in finite samples. The procedure is applied to test a linear model in text mining.

stat.ME↗

arXiv2020

A simulation-extrapolation approach for the mixture cure model with mismeasured covariates

We consider survival data from a population with cured subjects in the presence of mismeasured covariates. We use the mixture cure model to account for the individuals that will never experience the event and at the same time distinguish between the effect of the covariates on the cure probabilities and on survival times. In particular, for practical applications, it seems of interest to assume a logistic form of the incidence and a Cox proportional hazards model for the latency. To correct the estimators for the bias introduced by the measurement error, we use the simex algorithm, which is a very general simulation based method. It essentially estimates this bias by introducing additional error to the data and then recovers bias corrected estimators through an extrapolation approach. The estimators are shown to be consistent and asymptotically normally distributed when the true extrapolation function is known. We investigate their finite sample performance through a simulation study and apply the proposed method to analyse the effect of the prostate specific antigen (PSA) on patients with prostate cancer.

stat.ME↗

arXiv2020

Specification testing in semi-parametric transformation models

In transformation regression models the response is transformed before fitting a regression model to covariates and transformed response. We assume such a model where the errors are independent from the covariates and the regression function is modeled nonparametrically. We suggest a test for goodness-of-fit of a parametric transformation class based on a distance between a nonparametric transformation estimator and the parametric class. We present asymptotic theory under the null hypothesis of validity of the semi-parametric model and under local alternatives. A bootstrap algorithm is suggested in order to apply the test. We also consider relevant hypotheses to distinguish between large and small distances of the parametric transformation class to the `true' transformation.

math.ST↗

arXiv2019

Nonparametric estimation of conditional cure models for heavy-tailed distributions and under insufficient follow-up

When analyzing time-to-event data, it often happens that some subjects do not experience the event of interest. Survival models that take this feature into account (called `cure models') have been developed in the presence of covariates. However, the current literature on nonparametric cure models with covariates cannot be applied when the follow-up is insufficient, i.e., when the right endpoint of the support of the censoring time is strictly smaller than that of the survival time of the susceptible subjects. In this paper we attempt to fill this gap in the literature by proposing new estimators of the conditional cure rate and the conditional survival function using extrapolation techniques coming from extreme value theory. We establish the asymptotic normality of the proposed estimators, and show how the estimators work for small samples by means of a simulation study. We also illustrate their practical applicability through the analysis of data on the survival of colon cancer patients.

math.ST↗