ABSTRACT This paper explores the homogeneity of coefficient functions in nonlinear models with functional coefficients and identifies the underlying semiparametric modelling structure. With initial kernel estimates, we combine the classic hierarchical clustering method with a generalised version of the information criterion to estimate the number of clusters, each of which has a common functional coefficient

This paper is devoted to the estimation of partial derivatives of multivariate density functions. In this regard, nonparametric linear wavelet-based estimators are introduced, showing their attractive properties from the theoretical point of view. In particular, we prove the strong uniform consistency properties of these estimators, over compact subsets of Rd, with the determination of the corresponding

Recursive nonparametric density estimation for nonnegative data is considered, using an asymmetric kernel with nonnegative support. It has a computational advantage in a situation where a huge number of data are sequentially collected. The recursive asymmetric kernel estimator keeps desirable asymptotic properties similar to the ordinary non-recursive asymmetric kernel estimator. Also, simulation studies

Case-1 and case-2 interval-censored failure time data commonly occur in medical research as well as other fields and many methods have been developed for their analysis under different frameworks. In this paper, we consider regression analysis of such data and present a general class of nonparametric transformation models. One major advantage of these models is their flexibility and generality as they

Estimation of a precision matrix (i.e. inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the dimensionality increases. In this work, we propose robust estimation of the inverse covariance matrix based on an l1 regularised objective function with a weighted sample

In this article, we focus on the efficient estimation in single-index models with heteroscedastic errors. We first develop a nonparametric estimator of the variance function based on a fully nonparametric function or a dimension reduction structure, and the resulting estimator is consistent. Then, we propose a reweighting estimator of the parametric component via taking the estimated variance function

Quantile treatment effects are often considered in a quantile regression framework to adjust for the effect of covariates. In this study, we focus on the problem of testing whether the treatment effect is significant at a set of quantile levels (e.g. lower quantiles). We propose a regional quantile regression rank test as a generalisation of the rank test at an individual quantile level. This test

Stute [Ann. Probab. 19 (1991) 812–825] introduced a class of estimators called conditional U-statistics of E(φ(Y1,…,Ym)∣(X1,…,Xm)=t),for t∈Rm. In the present work, we provide a new class of estimators of conditional U-statistics. More precisely, we investigate the conditional U-statistics based on copula representation. We establish the uniform-in-bandwidth consistency for the proposed estimator. Our

To ameliorate some drawbacks of Martingale Difference Correlation (MDC) such as the asymmetry in the sense that for a pair of vectors, the value of MDC may not be equal to 1, and the self-MDC of any random vector can be different from vector to vector in value, we in this paper propose a modified MDC (MMDC). Further, as the corresponding partial MDC (PMDC), with controlling another random vector, cannot

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

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

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

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

Generalised additive models (GAMs) provide flexible models for a wide array of data sources. In the past, improvements of GAM estimation have focused on the smoothers used in the local scoring algorithm used for estimation, but poor prediction for non-Gaussian data motivates the need for robust estimation of GAMs. In this paper, rank-based estimation, as a robust and efficient alternative to the likelihood-based

(2021). Estimation of shape constrained additive models with missing response at random. Journal of Nonparametric Statistics: Vol. 33, No. 1, pp. 118-133.

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

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

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

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

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

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 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

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

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

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 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

ABSTRACT The focus of the present paper is on the uniform in bandwidth consistency of kernel-type estimators of the regression function 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 estimator and making

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

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

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

ABSTRACT We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain on . 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:

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

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

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 or , are available in the literature. We develop more higher-order bias-corrected estimators, achieving the order , where is a given integer. We illustrate the finite sample performance of the estimators through the simulations.

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

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

ABSTRACT 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 We apply the methods developed in Dony and Mason [(2008), Bernoulli, 14(4), 1108–1133] to establish uniformity in and in bandwidth

ABSTRACT 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

ABSTRACT 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

ABSTRACT 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

ABSTRACT 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

ABSTRACT 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

ABSTRACT 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

ABSTRACT 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

ABSTRACT 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.

We present novel tests for the hypothesis of independence when the number of variables is larger than the number of vector observations. We show that two multivariate normal vectors are independent if and only if their interpoint distance are independent. The proposed test statistics exploit different properties of the sample interpoint distances. A simulation study compares the new tests with three

ABSTRACT Penalised likelihood methods have been a success in analysing high dimensional data. Tang and Leng [(2010), ‘Penalized High-Dimensional Empirical Likelihood’, Biometrika, 97(4), 905–920] extended the penalisation approach to the empirical likelihood scenario and showed that the penalised empirical likelihood estimator could identify the true predictors consistently in the linear regression

Recent advances have greatly facilitated the collection of high-dimensional data in many fields. Often the dimension of the data is much larger than the sample size, the so-called high dimension, low sample size setting. One important research problem is how to develop efficient change-point detection procedures for this new setting. Thanks to their simplicity of computation, interpoint distance-based

In this paper we establish the law of large numbers (LLN) and central limit theorem (CLT) for second-order kernel-weighted U-statistics of cross-sectionally dependent variables. To illustrate the usefulness of our theorems, we apply the new LLN and CLT to nonparametric model misspecification testing in spatial regression framework. Monte Carlo simulations are used to assess the finite sample performance

ABSTRACT Bivariate current status data occur in many areas and many authors have discussed their analysis and proposed many inference procedures [Jewell, N.P., van der Laan, M.J., and Lei, X. (2005), ‘Bivariate Current Status Data with Univariate Monitoring Times’, Biometrika, 92, 847–862; Wang, N., Wang, L., and McMahan, C.S. (2015), ‘Regression Analysis of Bivariate Current Status Data Under the

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

This paper investigates the estimation of parametric copula models when the data have nonignorable nonresponse. We consider the propensity follows a general semiparametric model, but the distribution of the response variable and related covariates is unspecified. To solve the identifiability problem, we use an instrumental covariate, which is related to the response variable but unrelated to the propensity

Nonparametric regression has received considerable attention in biomedical research because it allows for data-driven dependence of the response variable on covariates. In the presence of missing data, doubly robust estimators have been proposed for nonparametric regression, which allow one model for the missingness mechanism and one model for the outcome regression. We propose multiply robust kernel

The article presents, discusses, and explores incomplete variants of interdirections, lift-interdirections, and symmetrised lift-interdirections (with a few incomplete designs). Although they are easier to compute in high-dimensional spaces than the originals, they can still replace them in many optimal statistical procedures based on signs and ranks without significantly changing their properties

Confident prediction is highly relevant in machine learning; for example, in applications such as medical diagnoses, wrong prediction can be fatal. For classification, there already exist procedures that allow to not classify data when the confidence in their prediction is weak. This approach is known as classification with reject option. In this paper, we provide a new methodology for this approach

ABSTRACT The main purpose of this paper is to obtain strong laws of large numbers for arrays or weighted sums of random variables under a scenario of dependence. Namely, for triangular arrays of row-wise extended negatively dependent random variables weakly mean dominated by a random variable and sequences of positive constants, conditions are given to ensure . Our statements allow us to establish

Misclassified current status data occur when each subject under study is observed only once and the failure status at the observation time is determined by a diagnostic test with imperfect sensitivity and specificity. In this article, we provide a methodology for the analysis of such data under a wide class of flexible semiparametric transformation models. For inference, a nonparametric maximum likelihood

ABSTRACT 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