arXiv subjects

Cindy Feng

Publications and source records attributed to Cindy Feng.

7 recordsLinked to original sources

arXiv2026

Tweedie-based nonparametric estimation for semicontinuous mixed densities

Semicontinuous outcomes occur frequently in health services, insurance, and cost studies. Standard nonparametric density estimators are not well suited to such data because they do not naturally accommodate the mixed structure, the nonnegative support, or the pronounced boundary effects near zero. To address these limitations, we introduce an asymmetric kernel estimator for mixed densities on $[0,\infty)$ based on the Tweedie distribution. For a power parameter $p\in(1,2)$, the Tweedie kernel itself has a point mass at zero and an absolutely continuous component on $(0,\infty)$, yielding a unified smoothing construction that preserves the atom at zero and smooths the positive component using the full semicontinuous sample. We establish pointwise bias and variance expansions, derive asymptotic formulae for the mean squared error and mean integrated squared error, obtain optimal bandwidth rates, and prove asymptotic normality. We propose a profile least-squares cross-validation procedure to jointly select the bandwidth and the power parameter. Simulation results show competitive performance, particularly in challenging boundary-spike and heavy-tailed settings, and an application to emergency department length-of-stay data illustrates the practical value of the method.

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arXiv2026

Asymptotic properties of the multivariate Sz\'{a}sz-Mirakyan estimator for cumulative distribution functions on the nonnegative orthant

The asymptotic properties of multivariate Sz\'{a}sz-Mirakyan estimators for cumulative distribution functions (cdf) supported on the nonnegative orthant are investigated. Explicit bias and variance expansions are derived on compact subsets of the interior, yielding sharp mean squared error characterizations and optimal smoothing rates. The analysis shows that the proposed Poisson smoothing yields a non-negligible variance reduction relative to the empirical cdf, leading to asymptotic efficiency gains that can be quantified through local and global deficiency measures. The behavior of the estimator near the boundary of its support is examined separately. Under a boundary-layer scaling that preserves nondegenerate Poisson smoothing as the evaluation point approaches the boundary of $[0,\infty)^d$, bias and variance expansions are obtained that differ fundamentally from those in the interior region. In particular, the variance reduction mechanism disappears at leading order, implying that no asymptotically optimal smoothing parameter exists in the boundary regime. Central limit theorems and almost sure uniform consistency are also established. Together, these results provide a unified asymptotic theory for multivariate Sz\'{a}sz-Mirakyan cdf estimation and clarify the distinct roles of smoothing in the interior and boundary regions.

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arXiv2023

A Comparison of Parameter Estimation Methods for Shared Frailty Models

This paper compares six different parameter estimation methods for shared frailty models via a series of simulation studies. A shared frailty model is a survival model that incorporates a random effect term, where the frailties are common or shared among individuals within specific groups. Several parameter estimation methods are available for fitting shared frailty models, such as penalized partial likelihood (PPL), expectation-maximization (EM), pseudo full likelihood (PFL), hierarchical likelihood (HL), maximum marginal likelihood (MML), and maximization penalized likelihood (MPL) algorithms. These estimation methods are implemented in various R packages, providing researchers with various options for analyzing clustered survival data using shared frailty models. However, there is a limited amount of research comparing the performance of these parameter estimation methods for fitting shared frailty models. Consequently, it can be challenging for users to determine the most appropriate method for analyzing clustered survival data. To address this gap, this paper aims to conduct a series of simulation studies to compare the performance of different parameter estimation methods implemented in R packages. We will evaluate several key aspects, including parameter estimation, bias and variance of the parameter estimates, rate of convergence, and computational time required by each package. Through this systematic evaluation, our goal is to provide a comprehensive understanding of the advantages and limitations associated with each estimation method.

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arXiv2023

Cross-validatory Z-Residual for Diagnosing Shared Frailty Models

Residual diagnostic methods play a critical role in assessing model assumptions and detecting outliers in statistical modelling. In the context of survival models with censored observations, Li et al. (2021) introduced the Z-residual, which follows an approximately normal distribution under the true model. This property makes it possible to use Z-residuals for diagnosing survival models in a way similar to how Pearson residuals are used in normal regression. However, computing residuals based on the full dataset can result in a conservative bias that reduces the power of detecting model mis-specification, as the same dataset is used for both model fitting and validation. Although cross-validation is a potential solution to this problem, it has not been commonly used in residual diagnostics due to computational challenges. In this paper, we propose a cross-validation approach for computing Z-residuals in the context of shared frailty models. Specifically, we develop a general function that calculates cross-validatory Z-residuals using the output from the \texttt{coxph} function in the \texttt{survival} package in R.Our simulation studies demonstrate that, for goodness-of-fit tests and outlier detection, cross-validatory Z-residuals are significantly more powerful and more discriminative than Z-residuals without cross-validation. We also compare the performance of Z-residuals with and without cross-validation in identifying outliers in a real application that models the recurrence time of kidney infection patients. Our findings suggest that cross-validatory Z-residuals can identify outliers that are missed by Z-residuals without cross-validation.

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arXiv2023

Z-residual diagnostics for detecting misspecification of the functional form of covariates for shared frailty models

In survival analysis, the hazard function often depends on a set of covariates. Martingale and deviance residual are most widely used for examining the validity of the function form of covariates by checking whether there is a discernible trend in their scatterplot against continuous covariates. However, visual inspection of martingale and deviance residuals is often subjective. In addition, these residuals lack a reference distribution due to censoring. It is therefore challenging to derive numerical statistical tests based on martingale or deviance residuals. In this paper, we extend the idea of randomized survival probability (Li et al. 2021) and develop a residual diagnostic tool that can provide both graphical and numerical tests for checking the covariate functional form in semi-parametric shared frailty models. We develop a general function that calculates Z-residuals for semi-parametric shared frailty models based on the output from the \texttt{coxph} function in the \texttt{survival} package in R. Our extensive simulation studies indicate that the derived numerical test based on Z-residuals has great power for checking the functional form of covariates. In a real data application on modelling the survival time of acute myeloid leukemia patients, the Z-residual diagnosis results show that a model with log-transformation is inappropriate for modelling the survival time, which could not be detected by other diagnostic methods.

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arXiv2019

Model diagnostics for censored regression via randomized survival probabilities

Residuals in normal regression are used to assess a model's goodness-of-fit (GOF) and discover directions for improving the model. However, there is a lack of residuals with a characterized reference distribution for censored regression. In this paper, we propose to diagnose censored regression with normalized randomized survival probabilities (RSP). The key idea of RSP is to replace the survival probability of a censored failure time with a uniform random number between 0 and the survival probability of the censored time. We prove that RSPs always have the uniform distribution on $(0,1)$ under the true model with the true generating parameters. Therefore, we can transform RSPs into normally-distributed residuals with the normal quantile function. We call such residuals by normalized RSP (NRSP residuals). We conduct simulation studies to investigate the sizes and powers of statistical tests based on NRSP residuals in detecting the incorrect choice of distribution family and non-linear effect in covariates. Our simulation studies show that, although the GOF tests with NRSP residuals are not as powerful as a traditional GOF test method, a non-linear test based on NRSP residuals has significantly higher power in detecting non-linearity. We also compared these model diagnostics methods with a breast-cancer recurrent-free time dataset. The results show that the NRSP residual diagnostics successfully captures a subtle non-linear relationship in the dataset, which is not detected by the graphical diagnostics with CS residuals and existing GOF tests.

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arXiv2019

Randomized Predictive P-values: A Versatile Model Diagnostic Tool with Unified Reference Distribution

Examining residuals such as Pearson and deviance residuals, is a standard tool for assessing normal regression. However, for discrete response, these residuals cluster on lines corresponding to distinct response values. Their distributions are far from normality; graphical and quantitative inspection of these residuals provides little information for model diagnosis. Marshall and Spiegelhalter (2003) defined a cross-validatory predictive p-value for identifying outliers. Predictive p-values are uniformly distributed for continuous response but not for discrete response. We propose to use randomized predictive p-values (RPP) for diagnosing models with discrete responses. RPPs can be transformed to "residuals" with normal distribution, called NRPPs by us. NRPPs can be used to diagnose all regression models with scalar response using the same way for diagnosing normal regression. The NRPPs are nearly the same as the randomized quantile residuals (RQR), which are previously proposed by Dunn and Smyth (1996) but remain little known by statisticians. This paper provides an exposition of RQR using the RPP perspective. The contributions of this exposition include: (1) we give a rigorous proof of uniformity of RPP and illustrative examples to explain the uniformity under the true model; (2) we conduct extensive simulation studies to demonstrate the normality of NRPPs under the true model; (3) our simulation studies also show that the NRPP method is a versatile diagnostic tool for detecting many kinds of model inadequacies due to lack of complexity. The effectiveness of NRPP is further demonstrated with a health utilization dataset.

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