Quantile Regression in Survival Analysis: Comparing Check-Based Modeling and the Minimum Distance Approach

This study used a quantile regression model and a non-homogeneous regression model to calibrate probabilistic forecasts of wind speed. These techniques were applied to the forecasts of wind speed over Pyeongchang area using 51-member European Centre for Medium-Range Weather Forecast (ECMWF). Reliability analysis was carried out by using rank histogram to identify the statistical consistency of ensemble forecasts and corresponding observations. The performances were evaluated by rank histogram, mean absolute error, root mean square error and continuous ranked probability score. The results showed that the forecasts of quantile regression and non-homogeneous regression models performed better than the raw ensemble forecasts. However, the differences of prediction skills between quantile regression and nonhomogeneous regression models were insignificant.

The prediction of human motion is essential for safe human-robot collaboration (HRC). For existing prediction methods based on adaptive neural network (NN) models, estimation errors (EEs) of model parameters are directly coupled with prior EEs of trajectories. This results in poor assessment of the mean square estimation error (MSEE) of model parameters, which is a potential danger to the safety HRC. In this paper, a novel “look-backward-and-forward” method is proposed to assess the EEs of model parameters. This method firstly computes EEs of model parameters in the past few time instants based on the actual error of trajectory predicted in the past. Subsequently, the EEs of model parameters are recursively updated till the current time instant. In this way, the trajectory of a single particle and its MSEE are accurately accessed. The direct coupling between the MSEE of the trajectory and that of model parameters is cut off and the mean estimation errors (MEEs) of parameters are only affected by the EEs of the past trajectory at the recent several time instants, rather than accumulating as the time propagates. This method is further extended to estimate the pose trajectory of a rigid body based on fitting of an ellipsoid’s parameters. The experimental results of predicting 3-D trajectories of human motions show the effectiveness of the proposed method.

Graphs are commonly used in various applications such as online social networks (OSNs), E-commerce systems and social recommender systems. Random walk sampling is often used to conduct statistical estimation over such graphs. This paper develops an algorithmic framework to reduce the mean square error of such statistical estimation. Our algorithmic framework is inspired by that the mean square error can be decomposed into a sum of the bias and variance of the estimator. More specifically, we apply the bootstrapping technique to design a bias reduction algorithm. A new feature of this bias reduction algorithm is that it allows the variance to increase whenever the bias can be further reduced. The increased variance may lead to a large mean square error of the estimator. We use multiple parallel random walks to reduce this variance such that it can be reduced to arbitrarily small by deploying a sufficient number of random walks. Our algorithmic framework enables one to attain different trade-offs between the sample complexity (i.e., number of parallel random walks) and the mean square error of the statistical estimation. Also, the proposed bias reduction algorithm is generic and can be applied to optimize a large class of random walk sampling algorithms. To demonstrate the versatility of the framework, we apply it to optimize the Metropolis random walk and simple random walk sampling. Extensive experiments confirm the effectiveness and efficiency of our proposed algorithmic framework.

Development and comparison of forensic interval age prediction models by statistical and machine learning methods based on the methylation rates of ELOVL2 in blood DNA

Statiscal Downscaling (SD) was a method to model the relationship between local scale data as response variable and global scale data as predictor variable. The response variable was the rainfall and the predictor variable was the global circulation model (GCM) ouput. In general, GCM output had a large dimension and multicollinearity so the principal component analysis was used to solve this problem. This study modeled the rainfall with the selected principal component using quantile regression. This functional relationship could be parametric or nonparametric relationship. In this case, nonparametric functional relationship used spline to accommodate the extreme value with the quantile regression. The result showed that the quantile spline model was better than the quantile polynomial regression model especially in predicting the extreme values in the 90 th and 95 th quantile with correlation values of 0.95 and 0.93.

Asthma is a chronic condition of great public health concern globally. The associated morbidity, mortality and healthcare utilisation place an enormous burden on healthcare infrastructure and services. This study demonstrates a multistage quantile regression approach to predicting excess demand for health care services in the form of asthma daily admissions in London, using retrospective data from the Hospital Episode Statistics, weather and air quality. Trivariate quantile regression models (QRM) of asthma daily admissions were fitted to a 14-day range of lags of environmental factors, accounting for seasonality in a hold-in sample of the data. Representative lags were pooled to form multivariate predictive models, selected through a systematic backward stepwise reduction approach. Models were cross-validated using a hold-out sample of the data, and their respective root mean square error measures, sensitivity, specificity and predictive values compared. Two of the predictive models were able to detect extreme number of daily asthma admissions at sensitivity levels of 76 % and 62 %, as well as specificities of 66 % and 76 %. Their positive predictive values were slightly higher for the hold-out sample (29 % and 28 %) than for the hold-in model development sample (16 % and 18 %). QRMs can be used in multistage to select suitable variables to forecast extreme asthma events. The associations between asthma and environmental factors, including temperature, ozone and carbon monoxide can be exploited in predicting future events using QRMs.

Co-efficient of variation is a unitless measure of dispersion and is very frequently used in scientific investigations. This has motivated several researchers to propose estimators and tests concerning the co-efficient of variation of normal distribution(s). While proposing a class of estimators for the co-efficient of variation of a finite population, Tripathi et al., (2002) suggested that the estimator of co-efficient of variation of a finite population can also be used as an estimator of C.V for any distribution when the sampling design is SRSWR. This has motivated us to propose 28 estimators of finite population co-efficient of variation as estimators of co-efficient of variation of one component of a bivariate normal distribution when prior information is available regarding the second component. Cramer Rao type lower bound is derived to the mean square error of these estimators. Extensive simulation is carried out to compare these estimators. The results indicate that out of these 28 estimators, eight estimators have larger relative efficiency compared to the sample co-efficient of variation. The asymptotic mean square errors of the best estimators are derived to the order of  for the benefit of users of co-efficient of variation.

In this paper we define a finite mixture of quantile and M-quantile regression models for heterogeneous and /or for dependent/clustered data. Components of the finite mixture represent clusters of individuals with homogeneous values of model parameters. For its flexibility and ease of estimation, the proposed approaches can be extended to random coefficients with a higher dimension than the simple random intercept case. Estimation of model parameters is obtained through maximum likelihood, by implementing an EM-type algorithm. The standard error estimates for model parameters are obtained using the inverse of the observed information matrix, derived through the Oakes (J R Stat Soc Ser B 61:479---482, 1999) formula in the M-quantile setting, and through nonparametric bootstrap in the quantile case. We present a large scale simulation study to analyse the practical behaviour of the proposed model and to evaluate the empirical performance of the proposed standard error estimates for model parameters. We considered a variety of empirical settings in both the random intercept and the random coefficient case. The proposed modelling approaches are also applied to two well-known datasets which give further insights on their empirical behaviour.

This study applies quantile regression to model the Body Mass Index (BMI) of 152 students from Delta State Polytechnic in Delta State, Nigeria. The BMI serves as the response variable, while skin fold (SK), feeding habit (FH), feeding frequency (FF), and frequency of exercising (FE) are considered as explanatory variables. A comparison is made between the results obtained from the classical linear regression model and quantile regression models at different quantiles (p = 0.1, 0.25, 0.5, 0.75, and 0.9) to examine the impact of the variables on the students' BMI and assess if the relationships differ across quantiles. The findings reveal significant differences between the classical linear regression and quantile regression models, emphasizing the importance of quantile regression in capturing the nuances of the relationship between variables at different points of the BMI distribution. The study highlights the limitations of the classical linear regression model in providing a comprehensive understanding of the data and underscores the value of quantile regression in enhancing our insights into the relationship between BMI and the considered factors. This research contributes to the broader literature on quantile regression and its applications in exploring BMI and related health issues among students

This paper study two stratified quantile regression models of the marginal and the conditional varieties. We estimate the quantile functions of these models by using two nonparametric methods of smoothing spline (B-spline) and kernel regression (Nadaraya-Watson). The estimates can be obtained by solve nonparametric quantile regression problem which means minimizing the quantile regression objective functions and using the approach of varying coefficient models. The main goal is discussing the comparison between the estimators of the two nonparametric methods and adopting the best one between them.

This paper describes the creation of a tracking system represented by a wheeled robot following a target (for example, a human). An artificial neural network (ANN) is used in the control loop of the robot to determine the range and bearing of the target, which are the tracking parameters. The main focus of the work is to develop a computer model of ANN capable of calculating near-optimal estimates of tracking parameters. In this case, the root mean square error (RMSE) of tracking parameter estimates is used as the criterion of efficiency of ANN operation. As a result, for the best ANN model the RMSE for the range was 0.009 m, and for the bearing was 1.006 degrees.

PurposeThe purpose of this paper is to develop FT‐NIR technique for determination of moisture content in bael pulp.Design/methodology/approachCalibration and validation sets were designed for the conception and evaluation of the method adequacy in the range of moisture content 70 to 95 per cent (wb). The prediction models based on partial least squares (PLS) regression, were developed in the near‐infrared region (4,000‐2,500cm‐1). Conventional criteria such as the R2, the root mean square errors of cross validation (RMSECV), root mean square errors of estimation (RMSEE) as well as the number of PLS factors were considered for the selection of three pre‐processing (vector normalization, minimum‐maximum normalization and multiplicative scatter correction) methods.FindingsThe best calibration model was developed with min‐max normalization (MMN) spectral pre‐processing (R2=99.3). The MMN pre‐processing method was found most suitable and the maximum coefficient of determination (R2) value of 0.993 was obtained for the calibration model developed. The developed results indicated that FTNIR spectroscopy could be used for rapid detection of moisture content in bael pulp samples without any sample destruction.Originality/valueThe research in this paper is useful for the quick detection of moisture content of bael fruit pulp during processing.

Quality assessment of liquorice combined with quantum fingerprint profiles and electrochemical activity

In the framework of quantile regression, local linear smoothing techniques have been studied by several authors, particularly by Yu and Jones (J Am Stat Assoc 93:228–237, 1998). The problem of bandwidth selection was addressed in the literature by the usual approaches, such as cross-validation or plug-in methods. Most of the plug-in methods rely on restrictive assumptions on the quantile regression model in relation to the mean regression, or on parametric assumptions. Here we present a plug-in bandwidth selector for nonparametric quantile regression that is defined from a completely nonparametric approach. To this end, the curvature of the quantile regression function and the integrated squared sparsity (inverse of the conditional density) are both nonparametrically estimated. The new bandwidth selector is shown to work well in different simulated scenarios, particularly when the conditions commonly assumed in the literature are not satisfied. A real data application is also given.

For fixed $\alpha \epsilon (0, 1)$, the quantile regression function gives the $\alpha$th quantile $\theta_{\alpha}(\mathbf{x})$ in the conditional distribution of a response variable Y given the value $\mathbf{X} = \mathbf{x}$ of a vector of covariates. It can be used to measure the effect of covariates not only in the center of a population, but also in the upper and lower tails. A functional that summarizes key features of the quantile specific relationship between X and Y is the vector $\beta_{\alpha}$ of weighted expected values of the vector of partial derivatives of the quantile function $\theta_{\alpha}(\mathbf{x})$. In a nonparametric setting, $\beta_{\alpha}$ can be regarded as a vector of quantile specific nonparametric regression coefficients. In survival analysis models (e.g., Cox's proportional hazard model, proportional odds rate model, accelerated failure time model) and in monotone transformation models used in regression analysis, $\beta_{\alpha}$ gives the direction of the parameter vector in the parametric part of the model. $\beta_{\alpha}$ can also be used to estimate the direction of the parameter vector in semiparametric single index models popular in econometrics. We show that, under suitable regularity conditions, the estimate of $\beta_{\alpha}$ obtained by using the locally polynomial quantile estimate of Chaudhuri (1991a) is $n^{1/2}$-consistent and asymptotically normal with asymptotic variance equal to the variance of the influence function of the functional $\beta_{\alpha}$. We discuss how the estimate of $\beta_{\alpha}$ can be used for model diagnostics and in the construction of a link function estimate in general single index models.