Proposed Estimation Procedure Research Articles

Linearized maximum rank correlation estimation when covariates are functional

This paper extends the linearized maximum rank correlation (LMRC) estimation proposed by Shen et al. (2023) to the setting where the covariate is a function. However, this extension is nontrivial due to the difficulty of inverting the covariance operator, which may raise the ill-posed inverse problem, for which we integrate the functional principal component analysis to the LMRC procedure. The proposed estimator is robust to outliers in response and computationally efficient. We establish the rate of convergence of the proposed estimator, which is minimax optimal under certain smoothness assumptions. Furthermore, we extend the proposed estimation procedure to handle discretely observed functional covariates, including both sparse and dense sampling designs, and establish the corresponding rate of convergence. Simulation studies demonstrate that the proposed estimators outperform the other existing methods for some examples. Finally, we apply our method to a real data to illustrate its usefulness.

A variable clustering approach for overdispersed high-dimensional count data using a copula-based mixture model

In this paper, we propose a latent variable model for the analysis and clustering of high-dimensional correlated and overdispersed count data. We use a set of random effects to capture within-group correlations and a copula to address between-group correlations. Since maximum likelihood (ML) estimation is computationally intensive for high-dimensional data, we propose a fast moment-based estimation procedure. Additionally, we implement the proposed estimation procedure into a clustering algorithm, borrowing ideas from the K-means algorithm. Based on a simulation study, we demonstrate that the estimation procedure shows good stability and precision. Furthermore, it is computationally fast, unlike the ML approach which shows serious convergence issues. In addition, the clustering algorithm with our moment-based estimation procedure can identify the simulated grouped data structure. The approach is further illustrated with a high-dimensional RNA-Seq dataset of commercial potatoes.

Semiparametric estimation for the functional additive hazards model

AbstractWe propose a new functional additive hazards model to investigate the potential effects of functional and scalar predictors on mortality risks, and develop a penalized least squares estimation method for model parameters based on a pseudoscore estimating equation. A reproducing kernel Hilbert space approach is used to establish the consistency, convergence rate, and joint asymptotic distribution of the resulting estimators for finite‐dimensional and infinite‐dimensional parameters. Our simulation studies demonstrate that the proposed estimation procedure performs well. For illustration, we apply the proposed method to the Medical Information Mart for Intensive Care III dataset.

A multivariate heavy-tailed integer-valued GARCH process with EM algorithm-based inference

A new multivariate integer-valued Generalized AutoRegressive Conditional Heteroscedastic (GARCH) process based on a multivariate Poisson generalized inverse Gaussian distribution is proposed. The estimation of parameters of the proposed multivariate heavy-tailed count time series model via maximum likelihood method is challenging since the likelihood function involves a Bessel function that depends on the multivariate counts and its dimension. As a consequence, numerical instability is often experienced in optimization procedures. To overcome this computational problem, two feasible variants of the expectation-maximization (EM) algorithm are proposed for estimating the parameters of our model under low and high-dimensional settings. These EM algorithm variants provide computational benefits and help avoid the difficult direct optimization of the likelihood function from the proposed process. Our model and proposed estimation procedures can handle multiple features such as modeling of multivariate counts, heavy-tailedness, overdispersion, accommodation of outliers, allowances for both positive and negative autocorrelations, estimation of cross/contemporaneous-correlation, and the efficient estimation of parameters from both statistical and computational points of view. Extensive Monte Carlo simulation studies are presented to assess the performance of the proposed EM algorithms. Two empirical applications of our approach are provided. The first application concerns modeling bivariate count time series data on cannabis possession-related offenses in Australia, while the second one involves modeling intraday high-frequency financial transactions data from multiple holdings in the U.S. financial market.

Multiply robust estimation for average treatment effect among treated

We propose a multiply robust estimator for the Average Treatment Effect Among the Treated (ATT). The proposed estimation procedure can simultaneously accommodate multiple working models for both the propensity score and the conditional mean of the counterfactual outcome given covariates. In addition, it can explicitly balance a set of user-specified moments of the covariate distributions between the treatment groups. The resulting estimator is consistent if any working model is correctly specified. With the data generating process typically unknown for observational studies, the proposed method provides substantial robustness against possible model misspecifications compared to existing estimators of the ATT. Simulation results show the excellent finite sample performance of the proposed estimator.

Bayesian inference with spike-and-slab priors for differential item functioning detection in a multiple-group IRT tree model

Group differences have practical implications in analysing data from achievement tests or questionnaires. In the current study, we develop a model that accounts for between-group differences, differential item functioning (DIF), latent factors, and missing item response data simultaneously. Different from most of the present DIF studies where one has to iteratively select anchor items and detect DIF items, we achieve DIF detection and parameter estimation simultaneously by properly reparameterizing model parameters and applying some spike-and-slab priors (Ishwaran & Rao, Spike and slab variable selection: frequentist and Bayesian strategies. Ann Stat. 2005a;33:730–773; Ročková & George, The spike-and-slab LASSO. J Am Stat Assoc. 2018;113:431–444) in Bayesian estimation. Simulation studies are conducted to illustrate the validation of the proposed estimation procedure and the efficiency of DIF detection. The proposed method is further applied to a real dataset for illustration.

Nonparametric estimation of a survival function in the presence of measurement errors on the failure time of interest

AbstractThis article discusses nonparametric estimation of a survival function in the presence of measurement errors on the observation of the failure time of interest. One situation where such issues arise would be clinical studies of chronic diseases where the observation on the time to the failure event of interest such as the onset of the disease relies on patient recall or chart review of electronic medical records. It is easy to see that both situations can be subject to measurement errors. To resolve this problem, we propose a simulation extrapolation approach to correct the bias induced by the measurement error. To overcome potential computational difficulties, we use spline regression to approximate the unspecified extrapolated coefficient function of time, and establish the asymptotic properties of our proposed estimator. The proposed method is applied to nonparametric estimation based on interval‐censored data. Extensive numerical experiments involving both simulated and actual study datasets demonstrate the feasibility of this proposed estimation procedure.

Statistical inference in Burr type XII lifetime model based on progressive randomly censored data

Censoring commonly occurs in real-world scenarios, either intentionally or unintentionally. Unintentional (or accidental) censoring usually happens randomly, i.e., it is out of the experimenters’ control, such as broken equipment, lack of follow-up, etc. Experimenters typically use intentional censoring to save experimental time and cost. In this article, we develop frequentist and Bayesian statistical inferential procedures for the parameters and reliability characteristics of the Burr type XII lifetime model under the Koziol-Green model based on progressive randomly censored data. For the frequentist approach, maximum likelihood methods for point and interval estimation are developed. For the Bayesian approach, the Bayes estimates under the squared error loss function (SELF) are evaluated using the Markov Chain Monte Carlo (MCMC) and Tierney-Kadane (T-K) approximation techniques. A Monte Carlo simulation study is used to assess the performance of the proposed estimation procedures. A real data analysis is performed to illustrate the proposed methods. Moreover, obtaining progressive censoring schemes for experimental planning purposes is also discussed.

Estimation of stability index for symmetric $$\alpha $$-stable distribution using quantile conditional variance ratios

AbstractThe class of $$\alpha $$ α -stable distributions is widely used in various applications, especially for modeling heavy-tailed data. Although the $$\alpha $$ α -stable distributions have been used in practice for many years, new methods for identification, testing, and estimation are still being refined and new approaches are being proposed. The constant development of new statistical methods is related to the low efficiency of existing algorithms, especially when the underlying sample is small or the distribution is close to Gaussian. In this paper, we propose a new estimation algorithm for the stability index, for samples from the symmetric $$\alpha $$ α -stable distribution. The proposed approach is based on a quantile conditional variance ratio. We study the statistical properties of the proposed estimation procedure and show empirically that our methodology often outperforms other commonly used estimation algorithms. Moreover, we show that our statistic extracts unique sample characteristics that can be combined with other methods to refine existing methodologies via ensemble methods. Although our focus is set on the symmetric $$\alpha $$ α -stable case, we demonstrate that the considered statistic is insensitive to the skewness parameter change, so our method could be also used in a more generic framework. For completeness, we also show how to apply our method to real data linked to financial market and plasma physics.

M-quantile regression shrinkage and selection via the Lasso and Elastic Net to assess the effect of meteorology and traffic on air quality.

In this work, we intersect data on size-selected particulate matter (PM) with vehicular traffic counts and a comprehensive set of meteorological covariates to study the effect of traffic on air quality. To this end, we develop an M-quantile regression model with Lasso and Elastic Net penalizations. This allows (i) to identify the best proxy for vehicular traffic via model selection, (ii) to investigate the relationship between fine PM concentration and the covariates at different M-quantiles of the conditional response distribution, and (iii) to be robust to the presence of outliers. Heterogeneity in the data is accounted by fitting a B-spline on the effect of the day of the year. Analytic and bootstrap-based variance estimates of the regression coefficients are provided, together with a numerical evaluation of the proposed estimation procedure. Empirical results show that atmospheric stability is responsible for the most significant effect on fine PM concentration: this effect changes at different levels of the conditional response distribution and is relatively weaker on the tails. On the other hand, model selection allows to identify the best proxy for vehicular traffic whose effect remains essentially the same at different levels of the conditional responsedistribution.

Blind Separation of the Measured Mixed Cyclostationary Waveforms in Transmission Lines of the PCB

Crosstalk is an undesirable factor that degrades the quality of data transmission in printed circuit boards (PCBs). The signal integrity (SI) in multiconductor transmission lines is controlled by using a large number of multiport tests and measurements, which require a lot of time and expensive laboratory equipment. Proposed signal processing methods based on blind identification allow a reduction in the measurement burden. Contrary to the traditional approach requiring knowledge of sampling time offset, input pseudorandom bit sequence (PRBS), and time delay between received data and transmitted PRBS, the proposed alternative method performs blind separation of measured data for the linear fit pulse response (LFPR) procedure. The waveform identification of the partial pulse responses is evaluated for additively mixed cyclostationary sources of the data, intersymbol interference, and crosstalk. A mixed matrix model of composed random vectors is considered. The proposed estimation procedure is based on preprocessing of measured data using principal component analysis (PCA) and following independent component analysis (ICA). It is shown that the proposed component analysis allows diagnostics of signal integrity using eye-diagram patterns and the channel operating margin (COM).

An Exponentiated Skew-Elliptic Nonlinear Extension to the Log–Linear Birnbaum–Saunders Model with Diagnostic and Residual Analysis

In this paper, we propose a nonlinear regression model with exponentiated skew-elliptical errors distributed, which can be fitted to datasets with high levels of asymmetry and kurtosis. Maximum likelihood estimation procedures in finite samples are discussed and the information matrix is deduced. We carried out a diagnosis of the influence for the nonlinear model. To analyze the sensitivity of the maximum likelihood estimators of the model’s parameters to small perturbations in distribution assumptions and parameter estimation, we studied the perturbation schemes, the case weight, and the explanatory and response variables of perturbations; we also carried out a residual analysis of the deviance components. Simulation studies were performed to assess some properties of the estimators, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a real dataset is presented.

Extrapolation estimation for nonparametric regression with measurement error

AbstractFor the nonparametric regression models with covariates contaminated with the normal measurement errors, this paper proposes an extrapolation algorithm to estimate the regression functions. By applying the conditional expectation directly to the kernel‐weighted least squares of the deviations between the local linear approximation and the observed responses, the proposed algorithm successfully bypasses the simulation step in the classical simulation extrapolation, thus significantly reducing the computational time. It is noted that the proposed method also provides an exact form of the extrapolation function, although the extrapolation estimate generally cannot be obtained by simply setting the extrapolation variable to negative one in the fitted extrapolation function, if the bandwidth is less than the SD of the measurement error. Large sample properties of the proposed estimation procedure are discussed, as well as simulation studies and a real data example being conducted to illustrate its applications.

Nonlinear kernel mode‐based regression for dependent data

Under stationary ‐mixing dependent samples, we in this article develop a novel nonlinear regression based on mode value for time series sequences to achieve robustness without sacrificing estimation efficiency. The estimation process is built on a kernel‐based objective function with a constant bandwidth (tuning parameter) that is independent of sample size and can be adjusted to maximize efficiency. The asymptotic distribution of the resultant estimator is established under suitable conditions, and the convergence rate is demonstrated to be the same as that in nonlinear mean regression. To numerically estimate the kernel mode‐based regression, we develop a modified modal‐expectation‐maximization algorithm in conjunction with Taylor expansion. A robust Wald‐type test statistic derived from the resulting estimator is also provided, along with its asymptotic distribution for the null and alternative hypotheses. The local robustness of the proposed estimation procedure is studied using influence function analysis, and the good finite sample performance of the newly suggested model is verified through Monte Carlo simulations. We finally combine the recommended kernel mode‐based regression with neural networks to develop a kernel mode‐based neural networks model, the performance of which is evidenced by an empirical examination of exchange rate prediction.

Continuous estimation of kinetic variables while walking using an accelerometer and artificial neural networks

Measuring the gait variables outside the laboratory is so important because they can be used to analyze walking in the long run and during real life situations. Wearable sensors like accelerometer show high potential in these applications. So, the aim of this study was continuous estimation of kinetic variables while walking using an accelerometer and artificial neural networks (ANNs). Seventy-three subjects (26 women and 47 men) voluntarily participated in this study. The subjects walked at the slow, moderate, and fast speeds on a walkway which covered with 10 Vicon camera. Acceleration was used as input for a feedforward neural networks to predict the lower limb moments (in sagittal, frontal, and transverse planes), power, and ground reaction force (GRF) (in medial-lateral, anterior-posterior, and vertical directions) during walking. Normalized root mean square error (nRMSE), and Pearson correlation coefficient (r) were computed between the measured and predicted variables. Statistical parametric mapping (SPM) was used to compare the measured and predicted variables. The results of this study showed approximately r values of 91–99 and nRMSE values of 4%–15% for GRF, power, and moment between the measured and predicted data. The SPM showed no significant difference between the measured and predicted variables in throughout stance phase. This work has shown the potential of predicting kinetic variables (GRF, moment, and power) in various speeds of walking using the accelerometer. The proposed estimation procedure utilizing a mixture of biomechanics and ANNs can be utilized to solve the tradeoff between richness of data and ease of measuring inherent in wearable sensors.

An autocovariance-based learning framework for high-dimensional functional time series

Many scientific and economic applications involve the statistical learning of high-dimensional functional time series, where the number of functional variables is comparable to, or even greater than, the number of serially dependent functional observations. In this paper, we model observed functional time series, which are subject to errors in the sense that each functional datum arises as the sum of two uncorrelated components, one dynamic and one white noise. Motivated from the fact that the autocovariance function of observed functional time series automatically filters out the noise term, we propose a three-step framework by first performing autocovariance-based dimension reduction, then formulating a novel autocovariance-based block regularized minimum distance estimation to produce block sparse estimates, and based on which obtaining the final functional sparse estimates. We investigate theoretical properties of the proposed estimators, and illustrate the proposed estimation procedure with the corresponding convergence analysis via three sparse high-dimensional functional time series models. We demonstrate via both simulated and real datasets that our proposed estimators significantly outperform their competitors.

Robust estimation for varying-coefficient partially linear measurement error model with auxiliary instrumental variables

<abstract><p>We study the varying-coefficient partially linear model when some linear covariates are not observed, but their auxiliary instrumental variables are available. Combining the calibrated error-prone covariates and modal regression, we present a two-stage efficient estimation procedure, which is robust against outliers or heavy-tail error distributions. Asymptotic properties of the resulting estimators are established. Performance of our proposed estimation procedure is illustrated through some numerous simulations and a real example. And the results confirm that the proposed methods are satisfactory.</p></abstract>

Robust estimation for varying-coefficient partially nonlinear model with nonignorable missing response

<abstract><p>In this paper, we studied the robust estimation for the varying-coefficient partially nonlinear model based on modal regression with nonignorable missing response. First, an instrumental variable was used to handle the identifiability issue of parameters in the propensity score function, and a generalized method of moment was combined to obtain the consistent estimators. Second, inverse probability weighting and modal regression were adopted to construct the estimators of parameters and coefficient function in the model. Under some mild conditions, the asymptotic properties of the resulting estimators were established. Furthermore, simulation studies and a real example were carried out to illustrate the effectiveness of our proposed estimation procedures.</p></abstract>

Globally Adaptive Longitudinal Quantile Regression with High Dimensional Compositional Covariates.

In this work, we propose a longitudinal quantile regression framework that enables a robust characterization of heterogeneous covariate-response associations in the presence of high-dimensional compositional covariates and repeated measurements of both response and covariates. We develop a globally adaptive penalization procedure, which can consistently identify covariate sparsity patterns across a continuum set of quantile levels. The proposed estimation procedure properly aggregates longitudinal observations over time, and ensures the satisfaction of the sum-zero coefficient constraint that is needed for proper interpretation of the effects of compositional covariates. We establish the oracle rate of uniform convergence and weak convergence of the resulting estimators, and further justify the proposed uniform selector of the tuning parameter in terms of achieving global model selection consistency. We derive an efficient algorithm by incorporating existing R packages to facilitate stable and fast computation. Our extensive simulation studies confirm the theoretical findings. We apply the proposed method to a longitudinal study of cystic fibrosis children where the association between gut microbiome and other diet-related biomarkers is of interest.

Inference for a general family of inverted exponentiated distributions under unified hybrid censoring with partially observed competing risks data

In this paper, statistical inference of a competing risks model is developed based on a unified hybrid censoring scheme when the latent failure times follow a general family of inverted exponentiated distributions, which covers a wide range of lifetime distributions. Point and interval estimation methods for estimating the model parameters based on maximum likelihood and Bayesian approaches under non-restricted and restricted parameter spaces are developed. The Bayes estimates are obtained under the squared error loss function with non-informative and informative prior distributions. The existence and uniqueness of the maximum likelihood estimates of the model parameters are proved. A Monte Carlo simulation study is carried out to evaluate the performance of the proposed estimation procedures. To illustrate the proposed inferential procedures, a real data analysis is provided. Finally, some concluding remarks and future research directions are presented.