Semiparametric Framework Research Articles

Poisson PCA: Poisson measurement error corrected PCA, with application to microbiome data.

In this paper, we study the problem of computing a principal component analysis of data affected by Poisson noise. We assume samples are drawn from independent Poisson distributions. We want to estimate principal components of a fixed transformation of the latent Poisson means. Our motivating example is microbiome data, though the methods apply to many other situations. We develop a semiparametric approach to correct the bias of variance estimators, both for untransformed and transformed (with particular attention to log-transformation) Poisson means. Furthermore, we incorporate methods for correcting different exposure or sequencing depth in the data. In addition to identifying the principal components, we also address the nontrivial problem of computing the principal scores in this semiparametric framework. Most previous approaches tend to take a more parametric line: for example, fitting a log-normal Poisson (PLN) model. We compare our method with the PLN approach and find that in many cases our method is better at identifying the main principal components of the latent log-transformed Poisson means, and as a further major advantage, takes far less time to compute. Comparing methods on real and simulated data, we see that our method also appears to be more robust to outliers than the parametricmethod.

A Semiparametric Approach to Model Effect Modification

One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for identifying such effect modification. Instead of using the traditional outcome models, we directly posit semiparametric models on contrasts, or expected differences of the outcome under different treatment choices or exposures. Through semiparametric estimation theory, all valid estimating equations, including the efficient scores, are derived. Besides doubly robust loss functions, our approach also enables dimension reduction in presence of many covariates. The asymptotic and non-asymptotic properties of the proposed methods are explored via a unified statistical and algorithmic analysis. Comparison with existing methods in both simulation and real data analysis demonstrates the superiority of our estimators especially for an efficiency improved version. Supplementary materials for this article are available online.

Flexible weighted dirichlet process mixture modelling and evaluation to address the problem of forecasting return distribution

ABSTRACT Forecasting volatility has been widely addressed in the fields of finance, environmetrics, and other areas involving massive time series. The important part of addressing this problem is how to specify the error term's distribution. With a weaker distribution assumption, we achieve greater model flexibility. In this paper, we present a flexible semiparametric Bayesian framework to address the problem of forecasting volatility in time series data by introducing the weighted Dirichlet process mixture (WDPM). We illustrate the advantages of WDPM using simulation data and stock return data.

Modeling COVID-19 pandemic using Bayesian analysis with application to Slovene data

In the paper, we propose a semiparametric framework for modeling the COVID-19 pandemic. The stochastic part of the framework is based on Bayesian inference. The model is informed by the actual COVID-19 data and the current epidemiological findings about the disease.The framework combines many available data sources (number of positive cases, number of patients in hospitals and in intensive care, etc.) to make outputs as accurate as possible and incorporates the times of non-pharmaceutical governmental interventions which were adopted worldwide to slow-down the pandemic. The model estimates the reproduction number of SARS-CoV-2, the number of infected individuals and the number of patients in different disease progression states in time. It can be used for estimating current infection fatality rate, proportion of individuals not detected and short term forecasting of important indicators for monitoring the state of the healthcare system. With the prediction of the number of patients in hospitals and intensive care units, policy makers could make data driven decisions to potentially avoid overloading the capacities of the healthcare system. The model is applied to Slovene COVID-19 data showing the effectiveness of the adopted interventions for controlling the epidemic by reducing the reproduction number of SARS-CoV-2. It is estimated that the proportion of infected people in Slovenia was among the lowest in Europe (0.350%, 90% CI [0.245–0.573]%), that infection fatality rate in Slovenia until the end of first wave was 1.56% (90% CI [0.94–2.21]%) and the proportion of unidentified cases was 88% (90% CI [83–93]%).The proposed framework can be extended to more countries/regions, thus allowing for comparison between them. One such modification is exhibited on data for Slovene hospitals.

Reliability Prediction of Battery Management System for Electric Vehicles Based on Accelerated Degradation Test: A Semi-Parametric Approach

The Li-ion battery has emerged as the most prominent energy storage device and been widely applied in electric vehicles (EVs). To ensure the safety and performance of batteries, a battery management system (BMS) is incorporated in the EVs. However, how to predict and verify the BMS reliability remains an issue. We conduct the accelerated degradation test on the BMS and develop a semi-parametric framework to predict the reliability. A new measure based on similarity is further proposed for model comparison. A real data set of the BMS is used to verify the validity of the proposed method. A comparison with the other four models shows that our approach can generate a more similar trend to the original data, with 39.23% improvement compared with the best-performed model based on the proposed measure. Besides, the proposed model gives a prediction of lower bound of the reliable lifetime as 10.8 years, which is more reasonable compared with the results (i.e., around one year) given by the conventional models.

A multiple robust propensity score method for longitudinal analysis with intermittent missing data

Longitudinal data are very popular in practice, but they are often missing in either outcomes or time-dependent risk factors, making them highly unbalanced and complex. Missing data may contain various missing patterns or mechanisms, and how to properly handle it for unbiased and valid inference still presents a significant challenge. Here, we propose a novel semiparametric framework for analyzing longitudinal data with both missing responses and covariates that are missing at random and intermittent, a general and widely encountered situation in observational studies. Within this framework, we consider multiple robust estimation procedures based on innovative calibrated propensity scores, which offers additional relaxation of the misspecification of missing data mechanisms and shows more satisfactory numerical performance. Also, the corresponding robust information criterion on consistent variable selection for our proposed model is developed based on empirical likelihood-based methods. These advocated methods are evaluated in both theory and extensive simulation studies in a variety of situations, showing competing properties and advantages compared to the existing approaches. We illustrate the utility of our approach by analyzing the data from the HIV Epidemiology ResearchStudy.

Quantile structural treatment effects: application to smoking wage penalty and its determinants

We propose a new treatment effect parameter called the quantile structural treatment effect (QSTE) to distinguish between observed and unobserved treatment heterogeneity in the semiparametric additive potential outcome framework. The QSTE is defined as the quantile treatment effect if the observed covariates were exogenously set to a fixed value while keeping unobserved heterogeneity unchanged. We show the QSTE is identified under unconfoundedness and propose a semiparametric inverse probability weighted-type estimator that converges weakly to a Gaussian process. A multiplier bootstrap procedure is also carried out to construct uniform confidence bands. Using data from the Panel Study of Income Dynamics and focusing on the female group for the plausibility of the unconfoundedness assumption, we examine observed and unobserved determinants of the adverse effects of smoking on wages known as the smoking wage penalty. Our findings suggest that different levels of observable human capital may partly explain the smoking heterogeneity on wages. However, no evidence is found to support unobservable explanations such as discrimination against smokers, especially in the upper tail of the unobserved heterogeneity distribution.

Analysis of Recurrent Events with Associated Informative Censoring: Application to HIV Data

In this study, we adapt a Cox-based model for recurrent events; the Prentice, Williams and Peterson Total -Time (PWP-TT) that has largely, been used under the assumption of non-informative censoring and evaluate it under an informative censoring setting. Empirical evaluation was undertaken with the aid of the semi-parametric framework for recurrent events suggested by Huang [1] and implemented in R Studio software. For validation we used data from a typical HIV care setting in Kenya. Of the three models under consideration; the standard Cox Model had gender hazard ratio (HR) of 0.66 (p-value=0.165), Andersen-Gill had HR 0.46 (with borderline p-value=0.054) and extended PWP TT had HR 0.22 (p-value=0.006). The PWP-TT model performed better as compared to other models under informative setting. In terms of risk factors under informative setting, LTFU due to stigma; gender [base=Male] had HR 0.544 (p-value =0.002), age [base is < 37] had HR 0.772 (p-value=0.008), ART regimen [base= First line] had HR 0.518 (p-value= 0.233) and differentiated care model (Base=not on DCM) had HR 0.77(p-value=0.036). In conclusion, in spite of the multiple interventions designed to address incidences of LTFU among HIV patients, within-person cases of LTFU are usually common and recurrent in nature, with the present likelihood of a person getting LTFU influenced by previous occurrences and therefore informative censoring should be checked

Multiply robust causal inference with double-negative control adjustment for categorical unmeasured confounding.

Unmeasured confounding is a threat to causal inference in observational studies. In recent years, the use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity. Negative controls have a long-standing tradition in laboratory sciences and epidemiology to rule out non-causal explanations, although they have been used primarily for bias detection. Recently, Miao and colleagues have described sufficient conditions under which a pair of negative control exposure and outcome variables can be used to identify non-parametrically the average treatment effect (ATE) from observational data subject to uncontrolled confounding. We establish non-parametric identification of the ATE under weaker conditions in the case of categorical unmeasured confounding and negative control variables. We also provide a general semiparametric framework for obtaining inferences about the ATE while leveraging information about a possibly large number of measured covariates. In particular, we derive the semiparametric efficiency bound in the non-parametric model, and we propose multiply robust and locally efficient estimators when non-parametric estimation may not be feasible. We assess the finite sample performance of our methods in extensive simulation studies. Finally, we illustrate our methods with an application to the post-licensure surveillance of vaccine safety among children.

Modeling Extreme Events: Time-Varying Extreme Tail Shape

A dynamic semi-parametric framework is proposed to study time variation in tail fatness of sovereign bond yield changes during the 2010--2012 euro area sovereign debt crisis measured at a high (15-minute) frequency. The framework builds on the Generalized Pareto Distribution (GPD) for modeling peaks over thresholds as in Extreme Value Theory, but casts the model in a conditional framework to allow for time-variation in the tail shape parameters. The score-driven updates used improve the expected Kullback-Leibler divergence between the model and the true data generating process on every step even if the GPD only fits approximately and the model is mis-specified, as will be the case in any finite sample. This is confirmed in simulations. Using the model, we find the ECB program had a beneficial impact on extreme upper tail quantiles, leaning against the risk of extremely adverse market outcomes while active.

Fully Modified Least Squares for Multicointegrated Systems

Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces links between these variables and partial sums of the equilibrium errors. This paper departs from the parametric model, using a semiparametric formulation that reveals the explicit role that singularity of the long run conditional covariance matrix plays in determining multicointegration. The semiparametric framework has the advantage that short run dynamics do not need to be modeled and estimation by standard techniques such as fully modified least squares (FM-OLS) on the original I(1) system is straightforward. The paper derives FM-OLS limit theory in the multicointegrated setting, showing how faster rates of convergence are achieved in the direction of singularity and that the limit distribution depends on the distribution of the conditional one-sided long run covariance estimator used in FM-OLS estimation. Wald tests of restrictions on the regression coefficients have nonstandard limit theory which depends on nuisance parameters in general. The usual tests are shown to be conservative when the restrictions are isolated to the directions of singularity and, under certain conditions, are invariant to singularity otherwise. Simulations show that approximations derived in the paper work well in finite samples. We illustrate our findings by analyzing fiscal sustainability of the US government over the post-war period.

ICBayes: a package of Bayesian semiparametric regression for intervel-censored data

Interval-censored data arise frequently in medical studies of diseases that require periodic examinations for symptoms of interest, such as disease-free survival (DFS). This paper provides an introduction to the R package ICBayes which implements a set of programs for analyzing case 1 interval-censored data and case 2 interval-censored data under Bayesian semiparametric framework. The main function ICBayes fits commonly-used survival regression models: proportional hazards, proportional odds, and probit. A simulation study is conducted to compare the performance of the package with two R packages that fit Bayesian proportional hazards, proportional odds, and accelerated failure time models. The use of the package is illustrated through analyzing a case 2 interval-censored breast cosmesis data and a case 1 interval-censored animal tumorigenicity data.

Volatility estimation for stochastic PDEs using high-frequency observations

We study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of the grid in the time variable goes to zero. Focusing on volatility estimation, we provide an explicit and easy to implement method of moments estimator based on squared increments. The estimator is consistent and admits a central limit theorem. This is established moreover for the joint estimation of the integrated volatility and parameters in the differential operator in a semi-parametric framework. Starting from a representation of the solution of the SPDE with Dirichlet boundary conditions as an infinite factor model and exploiting mixing-type properties of time series, the theory considerably differs from the statistics for semi-martingales literature. The performance of the method is illustrated in a simulation study.

Incorporating risk into technical efficiency for Vietnam’s and ASEAN banks

Purpose The purpose of this paper is to incorporate risk in technical efficiency of ASEAN banks in a panel data framework for the period 2000 to 2015. Design/methodology/approach The directional distance function and semi-parametric framework are employed to estimate efficiency scores for two scenarios, one with only good outputs and the other with a combination of good and bad outputs. Findings The findings show there is no evidence of technological progress for banks in ASEAN and concerns about the outperformance of Vietnam’s banks. In addition, performance of Vietnam’s banks tends to be distorted by low level of loan loss reserves. Practical implications To reflect the true performance and shorten the period of removing bad assets, the State Bank of Vietnam can request banks in Vietnam to book more loan loss reserves. Originality/value By examining such a new approach, this study makes an early attempt to incorporate credit risk into the banking efficiency in ASEAN region.

Simultaneous estimation for semi-parametric multi-index models

ABSTRACTEstimation of a general multi-index model comprises determining the number of linear combinations of predictors (structural dimension) that are related to the response, estimating the loadings of each index vector, selecting the active predictors and estimating the underlying link function. These objectives are often achieved sequentially at different stages of the estimation process. In this study, we propose a unified estimation approach under a semi-parametric model framework to attain these estimation goals simultaneously. The proposed estimation method is more efficient and stable than many existing methods where the estimation error in the structural dimension may propagate to the estimation of the index vectors and variable selection stages. A detailed algorithm is provided to implement the proposed method. Comprehensive simulations and a real data analysis illustrate the effectiveness of the proposed method.

A hybrid omnibus test for generalized semiparametric single-index models with high-dimensional covariate sets.

Numerous statistical methods have been developed for analyzing high-dimensional data. These methods often focus on variable selection approaches but are limited for the purpose of testing with high-dimensional data. They are often required to have explicit-likelihood functions. In this article, we propose a "hybrid omnibus test" for high-dicmensional data testing purpose with much weaker requirements. Our hybrid omnibus test is developed under a semiparametric framework where a likelihood function is no longer necessary. Our test is a version of a frequentist-Bayesian hybrid score-type test for a generalized partially linear single-index model, which has a link function being a function of a set of variables through a generalized partially linear single index. We propose an efficient score based on estimating equations, define local tests, and then construct our hybrid omnibus test using local tests. We compare our approach with an empirical-likelihood ratio test and Bayesian inference based on Bayes factors, using simulation studies. Our simulation results suggest that our approach outperforms the others, in terms of type I error, power, and computational cost in both the low- and high-dimensional cases. The advantage of our approach is demonstrated by applying it to genetic pathway data for type II diabetes mellitus.

Semiparametric Dose Finding Methods: Special Cases

SummaryA broad structure for the design and analysis of early phase clinical trials has recently been presented. The approach is described as being semiparametric in that the dose–toxicity function is modelled through a parameter of interest and a nuisance parameter. Although very general, the semiparametric method SPM allows for the possibility of specific calibration. In particular, it is shown that we can obtain identical operating characteristics of more richly parameterized designs such as the continual reassessment method. Here, we consider several other designs that have weaker parameterizations than the continual reassessment method, in particular the cumulative cohort distributions design, the modified toxicity probability interval design, the Bayesian optimal interval design and the keyboard design. We show that all of these designs are included, as special cases, in the semiparametric framework. It becomes immediately apparent how to structure any investigation into the operating characteristics of these designs as well as how to tune any design further with the purpose of improving on these characteristics. Simulations are provided to give added support to these findings.

A quantitative approach for analyzing the spatio-temporal distribution of 3D intracellular events in fluorescence microscopy.

Analysis of the spatial distribution of endomembrane trafficking is fundamental to understand the mechanisms controlling cellular dynamics, cell homeostasy, and cell interaction with its external environment in normal and pathological situations. We present a semi-parametric framework to quantitatively analyze and visualize the spatio-temporal distribution of intracellular events from different conditions. From the spatial coordinates of intracellular features such as segmented subcellular structures or vesicle trajectories, QuantEv automatically estimates weighted densities that are easy to interpret and performs a comprehensive statistical analysis from distribution distances. We apply this approach to study the spatio-temporal distribution of moving Rab6 fluorescently labeled membranes with respect to their direction of movement in crossbow- and disk-shaped cells. We also investigate the position of the generating hub of Rab11-positive membranes and the effect of actin disruption on Rab11 trafficking in coordination with cell shape.

Conditional Extremes in Asymmetric Financial Markets

ABSTRACTThe global financial crisis of 2007–2009 revealed the great extent to which systemic risk can jeopardize the stability of the entire financial system. An effective methodology to quantify systemic risk is at the heart of the process of identifying the so-called systemically important financial institutions for regulatory purposes as well as to investigate key drivers of systemic contagion. The article proposes a method for dynamic forecasting of CoVaR, a popular measure of systemic risk. As a first step, we develop a semi-parametric framework using asymptotic results in the spirit of extreme value theory (EVT) to model the conditional probability distribution of a bivariate random vector given that one of the components takes on a large value, taking into account important features of financial data such as asymmetry and heavy tails. In the second step, we embed the proposed EVT method into a dynamic framework via a bivariate GARCH process. An empirical analysis is conducted to demonstrate and compare the performance of the proposed methodology relative to a very flexible fully parametric alternative.

Bayesian Semiparametric Mixed Effects Markov Models With Application to Vocalization Syntax

ABSTRACTStudying the neurological, genetic, and evolutionary basis of human vocal communication mechanisms using animal vocalization models is an important field of neuroscience. The datasets typically comprise structured sequences of syllables or “songs” produced by animals from different genotypes under different social contexts. It has been difficult to come up with sophisticated statistical methods that appropriately model animal vocal communication syntax. We address this need by developing a novel Bayesian semiparametric framework for inference in such datasets. Our approach is built on a novel class of mixed effects Markov transition models for the songs that accommodate exogenous influences of genotype and context as well as animal-specific heterogeneity. Crucial advantages of the proposed approach include its ability to provide insights into key scientific queries related to global and local influences of the exogenous predictors on the transition dynamics via automated tests of hypotheses. The methodology is illustrated using simulation experiments and the aforementioned motivating application in neuroscience. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.