In this paper, we study the variable selection and parameter estimation for the semiparametric varying-coefficient partially linear models when the covariates are measured with errors. The proposed penalised empirical likelihood estimators are shown to possess the oracle property. Also, we conclude that the asymptotic distribution of penalised empirical likelihood ratio test statistic is a chi-square

In this paper, we first present the symmetric property of the extropy of record values and some characterisations of exponential distributions. Then a new test for symmetry of the continuous distribution is proposed based on a characterisation result. Our proposed test has an advantage that we do not need to estimate the centre of symmetry. Moreover, for a wide variety of alternative asymmetric distributions

In many applications, data cluster. Failing to take the cluster structure into consideration generally leads to underestimated variances of point estimators and inflated type I errors in hypothesis tests. Many circumstance-dependent approaches have been developed to handle clustered data. A working covariance matrix may be used in generalised estimating equations. One may throw out the cluster structure

ABSTRACT Non-linear aggregation strategies have recently been proposed in response to the problem of how to combine, in a non-linear way, estimators of the regression function (see for instance [Biau, G., Fischer, A., Guedj, B., and Malley, J. (2016), ‘COBRA: A Combined Regression Strategy’, Journal of Multivariate Analysis, 146, 18–28.]), classification rules (see [Cholaquidis, A., Fraiman, R., Kalemkerian

Two new properties of the kernel distribution function estimator of diverse nature are derived. Firstly, a law of the iterated logarithm is proved for both the integrated absolute error and the integrated squared error of the estimator. Secondly, the maximal smoothing principle in kernel density estimation developed by Terrell is extended to kernel distribution function estimation, which allows, among

Malaria can be diagnosed by the presence of parasites and symptoms (usually fever) due to the parasites. In endemic areas, however, an individual may have fever attributable either to malaria or to other causes. Thus the parasite level of an individual with fever follows a two-component mixture, with the two components corresponding to malaria and nonmalaria individuals. Furthermore, the parasite levels

In this paper, we consider the empirical likelihood inferences for a class of varying coefficient ARCH-M models, which is an extended version of parametric ARCH-M models. By constructing a weighted auxiliary random vector, we propose a weighted empirical likelihood method for estimating the functional-coefficients. Under some regularity conditions, the constructed empirical log-likelihood ratio is

We propose local polynomial estimators for the conditional mean of a continuous response when only pooled response data are collected under different pooling designs. Asymptotic properties of these estimators are investigated and compared. Extensive simulation studies are carried out to compare finite sample performance of the proposed estimators under various model settings and pooling strategies

This paper studies semiparametric estimation of a partially linear single index model with a monotone link function. Our estimator is an extension of the score-type estimator developed by Balabdaoui et al. (2019) for the monotone single index model, which profiles out the unknown link function by isotonic regression. An attractive feature of the proposed estimator is that it is free from tuning parameters

ABSTRACT The focus of the present paper is on the uniform in bandwidth consistency of kernel-type estimators of the regression function E ( Ψ ( Y ) ∣ X = x ) derived by modern empirical process theory, under weaker conditions on the kernel than previously used in the literature. Our theorems allow data-driven local bandwidths for these statistics. We extend existing uniform bounds on kernel regression

This paper deals with robust marginal estimation under a general regression model when missing data occur in the response and also in some covariates. The target is a marginal location parameter given through an M-functional. To obtain robust Fisher-consistent estimators, properly defined marginal distribution function estimators are considered. These estimators avoid the bias due to missing values

This paper is concerned with the estimating problem of heteroscedastic semiparametric regression model. We investigate the asymptotic normality for wavelet estimators of the slope parameter and the nonparametric component in the case of known error variance with ϕ-mixing random errors. Also, when the error variance is unknown, the asymptotic normality for the estimators of the slope parameter and the

ABSTRACT Conditional variable screening arises when researchers have prior information regarding the importance of certain predictors. It is natural to consider feature screening methods conditioning on these known important predictors. Barut, E., Fan, J., and Verhasselt, A. [(2016), ‘Conditional Sure Independence Screening’, Journal of the American Statistical Association, 111, 1266–1277] proposed

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

We consider a penalised nonparametric estimation of the relative risk function in the Cox proportional hazards model for survival data with right censoring. We derive the convergence rate, functional Bahadur representation (FBR) and local asymptotic normality of the nonparametric estimator by using reproducing kernel Hilbert space, counting process and empirical process theory. The new theoretical

ABSTRACT The mean residual life (MRL) function for a given random variable T is the expected remaining lifetime of T after a fixed time point t. It is of great interest in survival analysis, reliability, actuarial applications, duration modelling, etc. Liang, Shen, and He [‘Likelihood Ratio Inference for Mean Residual Life of Length-biased Random Variable’, Acta Mathematicae Applicatae Sinica, English

We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain on R d . Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel estimator is proposed whose bandwidths are selected by a method inspired by the works of Goldenshluger and Lepski [(2011), ‘Bandwidth Selection in Kernel Density Estimation: Oracle

This paper introduces and investigates powerful omnibus test for uniformity and compares it with some classical and recent solutions. All statistics under consideration are weighted functionals of the classical empirical process. The goal is to provide a quantitative comparison of tests under consideration and to study real possibilities of using them to detect departures from the hypothesised distribution

In this paper, we consider semiparametric efficient inferences in the generalised partially linear models. A novel bias-corrected estimating procedure and a bias-corrected empirical log-likelihood ratio are developed, respectively, for point estimation and confidence regions for parameters of interest. Under mild conditions, the resulting likelihood ratio is shown to be standard chi-squared distributed

The main purpose of this paper is to estimate, semi-parametrically, the quantiles of a conditional distribution when the response is a real-valued random variable subject to a right-censorship phenomenon and the predictor takes values in an infinite dimensional space. We assume that the explanatory and the response variables are linked through a single-index structure. First, we introduce a kernel-type

We give some asymptotic approximations for the upper tail probabilities of two nonparametric test statistics, namely the Wilcoxon signed-rank statistic and Kendall's tau coefficient. Then, we provide numerical comparisons, by comparing the exact probabilities with a normal approximation, a classical saddlepoint approximation, a Lugannani and Rice saddlepoint approximation and an Edgeworth expansion

This paper proposes to estimate possibly misspecified semiparametric estimating equations models using a two-step combined nonparametric likelihood method. The method uses in the first step the plug in principle and replaces the infinite dimensional parameter with a consistent estimator. In the second step an estimator for the finite dimensional parameter is obtained by combining exponential tilting

This paper introduces a novel hypothesis test for additivity in nonparametric regression models. Inspired by recent advances in the asymptotic theory of analysis of variance when the number of factor levels is large, we develop a test statistic that checks for possible nonlinear relations between the available predictors and the residuals from fitting the additive model. The asymptotic distribution

For testing hypothesis on the covariance operator of functional time series, we suggest to use the full functional information and to avoid dimension reduction techniques. The limit distribution follows from the central limit theorem of the weak convergence of the partial sum process in general Hilbert space applied to the product space. In order to obtain critical values for tests, we generalise bootstrap

For the data of size n from the unit or semi-infinite interval, several asymmetric kernel density estimators, having the mean integrated squared errors of order O ( n − 4 / 5 ) or O ( n − 8 / 9 ) , are available in the literature. We develop more higher-order bias-corrected estimators, achieving the order O ( n − 4 p / ( 4 p + 1 ) ) , where p ≥ 2 is a given integer. We illustrate the finite sample

We propose a kernel function for ordered categorical data that overcomes limitations present in ordered kernel functions appearing in the literature on the estimation of probability mass functions for multinomial ordered data. Some limitations arise from assumptions made about the support of the underlying random variable. Furthermore, many existing ordered kernel functions lack a particularly appealing

W. Stute [(1991), Annals of Probability, 19, 812–825] introduced a class of so-called conditional U-statistics, which may be viewed as a generalisation of the Nadaraya–Watson estimates of a regression function. Stute proved their strong pointwise consistency to m(t):=E[ϕ(Y1,…,Ym)|(X1,…,Xm)=t],for t∈Rdm. We apply the methods developed in Dony and Mason [(2008), Bernoulli, 14(4), 1108–1133] to establish

The main purpose of this paper is the development of data-driven iterative plug-in algorithms for local polynomial estimation of the trend and its derivatives under dependent errors. Furthermore, a data-driven lag-window estimator for the variance factor in the bandwidth is proposed so that the nonparametric stage is carried out without any parametric assumption on the stationary errors. Analysis of

In Pharmacokinetic (PK) and Pharmacodynamic (PD), the hazard rate functions play a central role in modelling time-to-event data. In the context of assessing the appropriateness of a given parametric hazard model, Huh, Y., and Hutmacher, M. [(2016), ‘Application of a Hazard-based Visual Predictive Check to Evaluate Parametric Hazard Models’, Journal of Pharmacokinetics and Pharmacodynamics, 43, 57–71]

In this article, we propose a two-step approach to estimate the volatility function of a jump-diffusion model in noisy data setting. The preaveraging method and threshold technique is used to remove microstructure noise and jumps, respectively. The newly proposed estimator is shown to be consistent and asymptotically normal. A simulation study and a real data application are undertaken to assess the

In this article, we consider a class of partially linear spatially varying coefficient autoregressive models for data distributed over complex domains. We propose approximating the varying coefficient functions via bivariate splines over triangulation to deal with the complex boundary of the spatial domain. Under some regularity conditions, the estimated constant coefficients are asymptotically normally

Random coefficient regression models are the regression counterparts of the classical random effects models in Analysis of Variance and panel data analysis. While several heuristic methods have been proposed for the detection of such random regression coefficients, little is known on their optimality properties. Based on a nonstandard ULAN property, we are proposing locally asymptotically optimal (in

It is well known that a neighbourhood problem exists between stationarity and random walk with correlated error for any finite sample size n. That is, any stationary process is approximated by random walk with correlated error for any finite n. Hence, one cannot distinguish between them easily. In this article, we propose a stationarity test based on nonparametric density that resolves the neighbourhood

Pretest-posttest studies are a commonly used design by social scientists, medical and health researchers to examine the effect of a treatment or an intervention. We propose an empirical likelihood based Mann-Whitney test on the equality of the response distribution functions of the treatment and control arms for non-randomised pretest-posttest studies with missing responses. The proposed test is multiply

Existing high-dimensional inferential methods for comparing multiple groups test hypotheses are formulated in terms of mean vectors or location parameters. These methods are applicable mainly for metric data. Furthermore, the mean-based methods assume that moments exist and the nonparametric (location-based) ones assume elliptical-contoured distributions for the populations. In this paper, a fully

Production frontier is an important concept in modern economics and has been widely used to measure production efficiency. Existing nonparametric frontier models often only allow one or low-dimensional input variables due to ‘curse-of-dimensionality’. In this paper we propose a flexible additive frontier model which quantifies the effects of multiple input variables on the maximum output. In addition

This paper proposes nonparametric two-sample tests for the direct comparison of the probabilities of a particular transition between states of a continuous time non-homogeneous Markov process with a finite state space. The proposed tests are a linear nonparametric test, an L 2-norm-based test and a Kolmogorov-Smirnov-type test. Significance level assessment is based on rigorous procedures, which are

In this paper, we propose a new strategy of estimation for the survival function S, associated to a survival time subject to interval censoring case 2. Our method is based on a least squares contrast of regression type with parameters corresponding to the coefficients of the development of S on an orthonormal basis. We obtain a collection of projection estimators where the dimension of the projection

Nonignorable missing data is common in studies where the outcome is relevant to the subject's behaviour. Ibrahim, Lipsitz, and Horton [(2001), ‘Using Auxiliary Data for Parameter Estimation with Non-ignorably Missing Outcomes’, Journal of the Royal Statistical Society: Series C (Applied Statistics), 50, 361–373] fitted a logistic regression for a binary outcome subject to nonignorable missing data

Panel count data frequently arise in various applications such as medical research, social sciences and so on. In this paper, a partially varying coefficient model of the panel count data with informative observation times is developed to accommodate the nonlinear interact effects between covariates. For statistical inference of the unknown parameters, quantile regression approaches are proposed, in

This paper reports on our study of a binary classifier based on B-splines and the total variation penalty. The decision boundary of the proposed classifier is obtained using a variant of the hinge loss function. We restrict our focus to a two-dimensional predictor space to analyse the theoretical behaviour of the spline decision curve estimator. Theoretical investigation shows that the proposed estimator

Improving estimation efficiency for regression coefficients is an important issue in the analysis of longitudinal data, which involves estimating the covariance matrix of errors. But challenges arise in estimating the covariance matrix of longitudinal data collected at irregular or unbalanced time points. In this paper, we develop a regularisation method for estimating the covariance function and a

The Gini index has been widely used as a measure of income (or wealth) inequality in social sciences. To construct a confidence interval for the difference of two Gini indices from the paired samples, Wang and Zhao [‘Jackknife Empirical Likelihood for Comparing Two Gini Indices’, The Canadian Journal of Statistics, 44(1), 102–119] used a profile jackknife empirical likelihood. However, the computing

This paper introduces a test for detecting moment generating function order dominance. We develop a family of scale-invariant test statistics based on the weighted integrals of the difference between the empirical moment generating function and the mgf of an appropriate exponential distribution. The asymptotic distributions of our test statistics are derived and consistency of the test is established

There has been continuing interest in Bayesian regressions in which no parametric assumptions are imposed on the error distribution. In this study, we consider semiparametric Bayesian nonlinear regression models. We do not impose a parametric form for the likelihood function. Instead, we treat the true density function of error terms as an infinite-dimensional nuisance parameter and estimate it nonparametrically

In this paper we design a test to detect the arrivals of jumps in asset prices contaminated by market microstructure noise. This test is defined by means of the truncated two-scales realised volatility estimator, recently introduced in Brownlees, Nualart, and Sun [2019, ‘On the Estimation of Integrated Volatility in the Presence of Jumps and Microstructure Noise’, https://papers.ssrn.com/sol3/papers

For linear regression and related models, a permutation inference distribution (PID) is introduced. Like the confidence distribution in the Bayesian/Fiducial/Frequentist inference framework, the PID allows the construction of both confidence intervals and p-values. For two-sample problems and pairwise comparisons in ANOVA models, a fast Fourier transformation method can be used to find the exact PID

In this note, we consider the situation where we have a functional predictor as well as some more traditional scalar predictors, which we call the partially functional problem. We propose a semiparametric model based on sufficient dimension reduction, and thus our main interest is in dimension reduction although prediction can be carried out at a second stage. We establish root-n consistency of the

We propose time-varying coefficient mixed-effects models for continuous multiple time series data and longitudinal data. The challenge is how to simultaneously display serial, clustering, and multivariate attributes of the data set, to which the routinely assumed two-level hierarchical model and univariate response models are not able to apply. Asymptotic properties of the proposed methods are established

Many distribution-free control charts have been proposed for jointly monitoring location and scale parameters of a continuous distribution when their in-control (IC) status are unknown in advance. Unfortunately, most existing methods require relatively large amount of historical observations to estimate the IC parameters or to activate the control chart, and batch observations to construct the charting

Regression analysis of interval-censored failure time data with noninformative censoring has been widely investigated and many methods have been proposed. Sometimes the mechanism behind the interval censoring may be informative and several approaches have also been developed for this latter situation. However, all of these existing methods are for single models and it is well known that in many situations

In biomedical studies, patients' reaction to the treatment can be different depending on their health condition at baseline. In this paper, we develop a bivariate varying-coefficient regression model for longitudinal data with the baseline outcome. The proposed model enables the exploration of the dynamic trend of response variables over time and to provide an effective treatment based on an individual's

We introduce two algebraic structures induced by an Archimedean n-copula: a one-parameter group of transformations and a one-parameter local group of transformations. We then study the natural functional characteristics (integral generators) of these structures. We discuss differential equations joining the integral generators and the additive generators of copulas. We show that the algebraic structures

In this paper, we develop the James–Stein improved method for the estimation problem of a nonparametric periodic function observed with Lévy noises in continuous time. An adaptive model selection procedure based on the weighted improved least squares estimates is constructed. The improvement effect for nonparametric models is studied. It turns out that in non-asymptotic setting the accuracy improvement

We look into the minimax results for the anisotropic two-dimensional functional deconvolution model with the two-parameter fractional Gaussian noise. We derive the lower bounds for the Lp-risk, 1≤p<∞, and taking advantage of the Riesz poly-potential, we apply a wavelet-vaguelette expansion to de-correlate the anisotropic fractional Gaussian noise. We construct an adaptive wavelet hard-thresholding

In this paper we propose model-based penalties for smoothing spline density estimation and inference. These model-based penalties incorporate indefinite prior knowledge that the density is close to, but not necessarily in a family of distributions. We will use the Pearson and generalisation of the generalised inverse Gaussian families to illustrate the derivation of penalties and reproducing kernels

In this paper, we consider the estimation and goodness-of-fit test of a semiparametric varying-coefficient partially linear (SVCPL) model when both responses and part of covariates are measured with error. It is assumed that the true variables are measurable functions of some auxiliary variables. The often-used assumptions on the measurement error, such as a known error variance, a known distribution

In this paper, we consider a statistical estimation problem known as atomic deconvolution. Introduced in reliability, this model has a direct application when considering biological data produced by flow cytometers. From a statistical point of view, we aim at inferring the percentage of cells expressing the selected molecule and the probability distribution function associated with its fluorescence

The present article provides a statistical inference on comparative performances of two treatments in a clinical trial under a two-stage adaptive allocation design. Suppose a fixed number (2m+n, say) of subjects are available for treatment by any of the two competing treatments, say, A and B for a particular ailment. As per the proposed allocation design, 2m incoming subjects are randomised equally

In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried