Search

The main purpose of the present paper is to investigate the problem of the nonparametric estimation of the expectile regression in which the response variable is scalar while the covariate is a random function. More precisely, an estimator is constructed by using the local linear k Nearest Neighbor procedures (kNN). The main contribution of this study is the establishment of the Uniform consistency in Number of Neighbors of the constructed estimators. These results are established under fairly general structural conditions on the classes of functions and the underlying models. The usefulness of our result for the smoothing parameter automatic selection is discussed. Some simulation studies are carried out to show the finite sample performances of the kNN estimator. The theoretical uniform consistency results, established in this paper, are (or will be) key tools for many further developments in functional data analysis. [ABSTRACT FROM AUTHOR]

Let X, Y be continuous random variables with unknown distributions. The aim of this paper is to study the problem of estimating the probability θ : = P (X < Y) based on independent random samples from the distributions of X ′ , Y ′ , ζ and η , where X ′ = X + ζ , Y ′ = Y + η and X, Y, ζ , η are mutually independent random variables. In this context, ζ , η are referred to as measurement errors. We apply the ridge-parameter regularization method to derive a nonparametric estimator for θ depending on two parameters. Our estimator is shown to be consistent with respect to mean squared error if the characteristic functions of ζ , η only vanish on Lebesgue measure zero sets. Under some further assumptions on the densities of X, Y, ζ and η , we obtain some upper and lower bounds on the convergence rate of the estimator. A numerical example is also given to illustrate the efficiency of our method. [ABSTRACT FROM AUTHOR]

Fiducial inference is applied to nonparametric g-modeling in the discrete case. We propose a computationally efficient algorithm to sample from the fiducial distribution and use the generated samples to construct point estimates and confidence intervals. We study the theoretical properties of the fiducial distribution and perform extensive simulations in various scenarios. The proposed approach gives rise to good statistical performance in terms of the mean squared error of point estimators and coverage of confidence intervals. Furthermore, we apply the proposed fiducial method to estimate the probability of each satellite site being malignant using gastric adenocarcinoma data with 844 patients. [ABSTRACT FROM AUTHOR]

In this article, we establish complete convergence for randomly weighted sums of negatively orthant-dependent random variables. We also establish complete convergence for the maximums of randomly weighted sums of negatively associated random variables. As a corollary, a Marcinkiewicz-Zygmund-type strong law for randomly weighted sums of negatively associated random variables is obtained. The results can be applied to the bootstrap sample means, and an open problem in a convergence rate of the bootstrap sample means posed by Csörgő (2004) is solved completely. [ABSTRACT FROM AUTHOR]

AbstractLet θ=P(XY are independent random variables, with known constants μX,μZ∈R, σ>0. Suppose we observe a random sample Y1′,…,Yn′ from the distribution of Y′=Y+ε. Here ε is a random error and distributed with a known continuous distribution. Our aim is to estimate θ based on the sample as well as on the complete knowledge about the distributions of X, Z and ε. We propose a nonparametric estimator of θ by applying the Fourier deconvolution method. Our estimator is shown to be mean consistent with respect to the mean squared error and strongly consistent. Under some regularity assumptions on the densities of Y and ε, some error estimates of the proposed estimator are derived. A simulation study is also conducted to illustrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

This paper reports on our study of a regularization path algorithm for a regression spline estimator based on B-splines and total variation penalty. The total variation-penalized regression spline estimation method enjoys a spatial adaptation property, since the penalty function enables data-adaptive knot selection. Although the theoretical properties of the related methods have been well established in the literature, the existing implementation algorithms are usually based on techniques with a high computational cost. In particular, the selection of the optimal complexity parameter, required to strike a balance in bias-variance tradeoff, is based on the computationally intensive grid search method. In this study, we propose an efficient path algorithm by formulating an equivalent ℓ 1 penalized optimization problem. The least angle regression algorithm is applied to the reformulated problem to obtain an entire path of the jump size of B-spline derivatives that represents the knot removal condition. Numerical studies based on real and simulated data are provided to illustrate the advantages of the proposed algorithm. The simulation result shows that the proposed algorithm is significantly faster than an existing algorithm. The proposed algorithm has an additional benefit of obtaining an entire regularization path, which can provide additional statistical insights into the given problem. [ABSTRACT FROM AUTHOR]

This paper focuses on nonparametrically estimating the probability $ \mathbb {P} \left ( X_t \lt Y_t \right ) $ P(Xt

The mean residual lifetime (MRL) of a unit is its expected additional lifetime provided that it has survived until time t. The MRL estimation problem has been frequently addressed in the literature since it has wide applications in statistics, reliability and survival analysis. In this paper, we consider the problem of estimating the MRL in ranked set sampling when actual quantifications of a concomitant variable are available. To exploit the additional information of the concomitant variable, we introduce several MRL estimators based on some regression techniques. We then compare them with the standard MRL estimator in simple random sampling using Monte Carlo simulation and a real dataset from the Surveillance, Epidemiology, and End Results Program. Our results indicate the superiority of the procedures that we have developed when the quality of ranking is fairly good. [ABSTRACT FROM AUTHOR]

In the past 20 years, model averaging has been developed as a better tool than model selection in statistical prediction. Expectile prediction is widely used for modeling data with the heterogeneous conditional distribution. In this article, we introduce a model averaging estimator for additive expectile prediction. The resulting model averaging estimator is shown to have asymptotic optimality under some regular conditions. Simulation experiments are conducted to demonstrate that the performance of our method is better than that of other common model selection and model averaging methods under the finite-sample case. Our method is also verified in the house and wage datasets. [ABSTRACT FROM AUTHOR]

This article deals with the problem of estimating the service time distribution of the M t / G / ∞ queue from observation of the departure epochs. We develop minimax optimal estimators of G and study behavior of the minimax pointwise risk over a suitable family of service time distribution functions. In addition, we address the problem of adaptive estimation and propose a data–driven estimation procedure that adapts to unknown smoothness of the service time distribution function G. Lastly, a numerical study is presented to illustrate practical performance of the developed adaptive procedure. [ABSTRACT FROM AUTHOR]

Panel count regression is often required in recurrent event studies, where the interest is to model the event rate. Existing rate models are unable to handle time-varying covariate effects due to theoretical and computational difficulties. Mean models provide a viable alternative but are subject to the constraints of the monotonicity assumption, which tends to be violated when covariates fluctuate over time. In this paper, we present a new semiparametric rate model for panel count data along with related theoretical results. For model fitting, we present an efficient EM algorithm with three different methods for variance estimation. The algorithm allows us to sidestep the challenges of numerical integration and difficulties with the iterative convex minorant algorithm. We showed that the estimators are consistent and asymptotically normally distributed. Simulation studies confirmed an excellent finite sample performance. To illustrate, we analyzed data from a real clinical study of behavioral risk factors for sexually transmitted infections. [ABSTRACT FROM AUTHOR]

Consider a diffusion process X = (X t) t ∈ [ 0 , 1 ] observed at discrete times and high frequency, solution of a stochastic differential equation whose drift and diffusion coefficients are assumed to be unknown. In this article, we focus on the nonparametric estimation of the diffusion coefficient. We propose ridge estimators of the square of the diffusion coefficient from discrete observations of X that are obtained by minimization of the least squares contrast. We prove that the estimators are consistent and derive rates of convergence as the number of observations tends to infinity. Two observation schemes are considered in this paper. The first scheme consists in one diffusion path observed at discrete times, where the discretization step of the time interval [0, 1] tends to zero. The second scheme consists in repeated observations of the diffusion process X, where the number of the observed paths tends to infinity. The theoretical results are completed with a numerical study over synthetic data. [ABSTRACT FROM AUTHOR]

A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method to optimally select this threshold. It combines the theoretical mean squared error of the estimator with a parametric estimation of the copula linking observations in the tails. Using simulations, we compare this semiparametric method with other approaches proposed in the literature, including the plateau-finding algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nonparametric regression model $ Y_{ni}= g(t_{ni})+\varepsilon _i $ Y ni = g (t ni) + ϵ i ( $ 1\leq i\leq n $ 1 ≤ i ≤ n), where $ \varepsilon _{i}=\sum _{j=-\infty }^{\infty }a_je_{i-j} $ ϵ i = ∑ j = − ∞ ∞ a j e i − j and $ e_{i} $ e i are identically distributed and asymptotically negatively associated (ANA or $ \rho ^- $ ρ − , for short) sequences. This paper obtains the Berry-Esseen bounds of the wavelet estimator of $ g(\cdot) $ g (⋅) , and the rate of the normal approximation is shown as $ O(n^{-1/4}) $ O (n − 1 / 4) under certain conditions. Finally, the simulation study is provided to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

To study the symmetry and asymmetry of the model error under multiplicative distortion measurement errors setting, we propose a correlation coefficient-based measure between the distribution function and the root of density function. The unknown distribution function and density function are estimated from four kinds of residuals: the conditional mean calibration-based residuals, the conditional absolute mean calibration-based residuals, the conditional variance calibration-based residuals, and the conditional absolute logarithmic calibration-based residuals. We study the asymptotic results of the estimators of correlation coefficient-based measure under four calibrations. Next, we consider statistical inference of the correlation coefficient-based measure by using the empirical likelihood method. The empirical likelihood statistics are shown to be an asymptotically standard chi-squared distribution. Simulation studies demonstrate the performance of the proposed estimators and test statistics. A real example is analyzed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]

In this paper, we study the complete convergence and complete moment convergence for randomly weighted sums of arrays of rowwise widely negative dependent random variables in sub-linear expectation space under some appropriate conditions, which extend and improve the corresponding ones in classical probability space to the case of sub-linear expectation space. And we obtain a strong law of large numbers for the randomly weighted sums of arrays of rowwise widely negative dependent random variables. As applications of our main results, we not only present a result on the complete consistency for the weighted estimator in a nonparametric regression model, but also obtain the complete consistency for the least squares estimators in errors-in-variables regression models based on widely negative dependent errors under sub-linear expectations. We perform some numerical simulations to verify the validity of the theoretical results and a real example is analysed for illustration. [ABSTRACT FROM AUTHOR]

Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been observed by the intriguing concept of the risk quadrangles, for example. Stochastic dominance is a binary relation for random variables to compare random outcomes. It is demonstrated that the concepts of higher order risk measures and stochastic dominance are equivalent, they can be employed to characterize the other. The paper explores these relations and connects stochastic orders, higher order risk measures and the risk quadrangle. Expectiles are employed to exemplify the relations obtained. [ABSTRACT FROM AUTHOR]

AbstractIn this article, the robust estimation for a class of semiparametric spatial autoregressive models has been investigated. By combining the QR decomposition technique for matrix and the weighted composite quantile regression method, we propose a robust estimation procedure for the parametric and non parametric components. Under certain regularity conditions, asymptotic properties of the resulting estimators are proved. Several simulation analyses have been conducted for further illustrating the performance of the proposed method, and the simulation results demonstrate that the proposed method improve the robustness of the models. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the nonparametric regression model Y i = g (x i) + ε i , 1 ≤ i ≤ n , and study the strong consistency and uniform strong consistency of the estimator of Priestley and Chao based on the martingale difference errors. These results partially extend and improve some known works. Furthermore, the moment convergency and uniform moment convergency of the estimator are established also. [ABSTRACT FROM AUTHOR]

This work introduces a new Riemannian optimization method for registering open parameterized surfaces with a constrained global optimization approach. The proposed formulation leads to a rigorous theoretic foundation and guarantees the existence and the uniqueness of a global solution. We also propose a new Bayesian clustering approach where local distributions of surfaces are modeled with spherical Gaussian processes. The maximization of the posterior density is performed with Hamiltonian dynamics which provide a natural and computationally efficient spherical Hamiltonian Monte Carlo sampling. Experimental results demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

We develop a practical and computationally efficient penalised estimation approach for partially linear additive models to zero-inflated binary outcome data. To facilitate estimation, B-splines are employed to approximate unknown nonparametric components. A two-stage iterative expectation-maximisation (EM) algorithm is proposed to calculate penalised spline estimates. The large-sample properties such as the uniform convergence and the optimal rate of convergence for functional estimators, and the asymptotic normality and efficiency for regression coefficient estimators are established. Further, two variance-covariance estimation approaches are proposed to provide reliable Wald-type inference for regression coefficients. We conducted an extensive Monte Carlo study to evaluate the numerical properties of the proposed penalised methodology and compare it to the competing spline method [Li and Lu. 'Semiparametric Zero-Inflated Bernoulli Regression with Applications', Journal of Applied Statistics, 49, 2845–2869]. The methodology is further illustrated by an egocentric network study. [ABSTRACT FROM AUTHOR]

In many studies on disease progression, biomarkers are restricted by detection limits, hence informatively missing. Current approaches ignore the problem by just filling in the value of the detection limit for the missing observations for the estimation of the mean and covariance function, which yield inaccurate estimation. Inspired by our recent work [Liu and Houwing-Duistermaat (2022), 'Fast Estimators for the Mean Function for Functional Data with Detection Limits', Stat, e467.] in which novel estimators for mean function for data subject to detection limit are proposed, in this paper, we will propose a novel estimator for the covariance function for sparse and dense data subject to a detection limit. We will derive the asymptotic properties of the estimator. We will compare our method to the standard method, which ignores the detection limit, via simulations. We will illustrate the new approach by analysing biomarker data subject to a detection limit. In contrast to the standard method, our method appeared to provide more accurate estimates of the covariance. Moreover its computation time is small. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a marginal screening method for variable screening in high-dimensional binary classification based on the Wasserstein distance accounting for the distributional difference. Many existing screening methods, such as the two-sample t-test and Kolmogorov test, have been developed under the parametric/nonparametric modeling assumptions to reduce the dimension of the predictors. However, such modeling specifications or nonparametric approaches are associated with the probability measure induced by the predictor in a Euclidean space. While many machine learning methods have successfully found the nonlinear decision boundary in the transformed space, called the reproducing kernel Hilbert space (RKHS), we consider the Wasserstein filter's capacity to detect the distributional difference between two probability measures induced by the nonlinear function of the predictor in the RKHS. Thereby, we can flexibly filter out the non-informative predictors associated with the binary classification, as well as escape the modeling assumptions required in a Euclidean space. We prove that the Wasserstein filter satisfies the sure screening property under some mild conditions. We also demonstrate the advantages of our proposed approach by comparing the finite sample performance of it with those of the existing choices through simulation studies, as well as through application to lung cancer data. [ABSTRACT FROM AUTHOR]

Consider a time series that takes values in a general topological space, and suppose that its Small-ball probability is factorised into two terms that play the role of a surrogate density and a volume term. The latter allows us to study the complexity of the underlying process. In some cases, the volume term can be analytically specified in a parametric form as a function of a complexity index. This work presents the study of an estimator for such an index whenever the volume term is monomial. Weak consistency and asymptotic Gaussianity are shown under an appropriate dependence structure, providing theoretical support for the construction of confidence intervals. A Monte Carlo simulation is performed to evaluate the performance of the approach under various conditions. Finally, the method is applied to identify the complexity of two real data sets. [ABSTRACT FROM AUTHOR]

We discuss nonparametric estimation of the trend coefficient in models governed by a stochastic differential equation driven by a Gaussian process with small noise. [ABSTRACT FROM AUTHOR]

Conjugate gradient (CG) methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems. In this paper, a new hybrid conjugate gradient (CG) method is presented and analyzed for solving unconstrained optimization problems, where the parameter β k is a convex combination of β k WYL and β k CD . Under the strong Wolfe line search, the new method possesses the sufficient descent condition and the global convergence properties. The preliminary numerical results show the efficiency of our method in comparison with other CG methods. Furthermore, the proposed algorithm HWYLCD was extended to solve the problem of a mode function. [ABSTRACT FROM AUTHOR]

Effective risk exposure descriptions can be made using continuous distributions. To illustrate the level of exposure to a certain danger, it is better to use a single number, or at the very least, a small set of numbers. These risk exposure numbers, which are commonly referred to as significant risk indicators, are unquestionably the output of a particular model. In this regard, five key indicators are utilized to define the risk exposure in the reinsurance revenues data. For this specific purpose we introduce a new distribution called odd log-logistic XGamma model. We estimated the parameters using maximum-likelihood method, least squares method and Bayesian method. Monte Carlo simulation study is performed under a set of conditions and controls. The risk exposure under the reinsurance revenue data was also described using five important risk indicators, including value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and mean excess loss function. These statistical measures were developed for the proposed new model. [ABSTRACT FROM AUTHOR]

This paper focuses on the function estimation problem in nonparametric regression model based on biased samples under strong mixing. We propose a wavelet estimator by using wavelet kernel and investigate the consistency properties of the wavelet estimator. The mean consistency, strong consistency and convergence rate are obtained and the convergence rate is similar as that of wavelet estimator in the standard nonparametric model even although with the presence of bias and strong mixing dependence. [ABSTRACT FROM AUTHOR]

Sparse clustering divides samples into distinct groups while simultaneously reducing dimensionality in ultra-high dimensional unsupervised learning. To achieve sparse clustering that can screening out noise variables, an adaptive sparse clustering framework based on sufficient variable screening, abbreviated as adaptive sufficient sparse clustering (ASSC), is developed by controlling false discovery. Without any specific model, ASSC employs a composite hypothesis testing procedure that leverages conditional marginal correlations of variables across distinct groups, aiming to pinpoint sufficient variables via sparse clustering and promoting the performance of sparse clustering in ultra-high dimensionality. To control false discoveries of the hypothesis testing procedure at a predetermined level, ASSC provides the adaptive threshold for identifying conditional marginal dependency, which ensures to accuracy of clustering with high probability. Under mild conditions, the sufficient screening properties and sufficient clustering properties of ASSC are established based on variable screening procedure by controlling false discovery. Numerical studies on synthetic data and real datasets corroborate the performance and flexibility of ASSC, and underscore its potent utility in unsupervised learning. [ABSTRACT FROM AUTHOR]

We propose a method for finding a cumulative distribution function (cdf) that minimizes the distance to a given cdf, while belonging to an ambiguity set constructed relative to another cdf and, possibly, incorporating soft information. Our method embeds the family of cdfs onto the space of upper semicontinuous functions endowed with the hypo-distance. In this setting, we present an approximation scheme based on epi-splines, defined as piecewise polynomial functions, and use bounds for estimating the hypo-distance. Under appropriate hypotheses, we guarantee that the cluster points corresponding to the sequence of minimizers of the resulting approximating problems are solutions to a limiting problem. We describe a large class of functions that satisfy these hypotheses. The approximating method produces a linear-programming-based approximation scheme, enabling us to develop an algorithm from off-the-shelf solvers. The convergence of our proposed approximation is illustrated by numerical examples for the bivariate case. [ABSTRACT FROM AUTHOR]

In this study, the strong law of large numbers and the convergence rate for weighted sums of non-identically distributed widely orthant dependent random variables are established. As applications, the strong consistency for weighted estimator in nonparametric regression model and the rate of strong consistency for least-squares estimator in multiple linear regression model are obtained. Some numerical simulations are also provided to verify the validity of the theoretical results.

We propose a nonlinear difference-in-differences (DiD) method to estimate multivariate counterfactual distributions in classical treatment and control study designs with observational data. Our approach sheds a new light on existing approaches like the changes-in-changes estimator and the classical semiparametric DiD estimator, and it also generalizes them to settings with multivariate heterogeneity in the outcomes. The main benefit of this extension is that it allows for arbitrary dependence between the coordinates of vector potential outcomes and includes higher-dimensional unobservables, something that existing methods cannot provide in general. We demonstrate its utility on both synthetic and real data. In particular, we revisit the classical Card & Krueger dataset, which reports fast food restaurant employment before and after a minimum wage increase. A reanalysis with our methodology suggests that these restaurants substitute full-time labor with part-time labor on aggregate in response to a minimum wage increase. This treatment effect requires estimation of the multivariate counterfactual distribution, an object beyond the scope of classical causal estimators previously applied to this data.

A century ago, Neyman showed how to evaluate the efficacy of treatment using a randomized experiment under a minimal set of assumptions. This classical repeated sampling framework serves as a basis of routine experimental analyses conducted by today’s scientists across disciplines. In this article, we demonstrate that Neyman’s methodology can also be used to experimentally evaluate the efficacy of individualized treatment rules (ITRs), which are derived by modern causal machine learning (ML) algorithms. In particular, we show how to account for additional uncertainty resulting from a training process based on cross-fitting. The primary advantage of Neyman’s approach is that it can be applied to any ITR regardless of the properties of ML algorithms that are used to derive the ITR. We also show, somewhat surprisingly, that for certain metrics, it is more efficient to conduct this ex-post experimental evaluation of an ITR than to conduct an ex-ante experimental evaluation that randomly assigns some units to the ITR. Our analysis demonstrates that Neyman’s repeated sampling framework is as relevant for causal inference today as it has been since its inception.

This paper deals with the statistical inference in compound models, which are defined as a sum of i.i.d. random variables $ \xi _1+\cdots +\xi _N $ ξ 1 + ⋯ + ξ N , where the number of summands, N, is a random variable independent of $ \xi _1, \xi _2,\ldots $ ξ 1 , ξ 2 , ... Using the novel technique based on the superposition of the Mellin and Laplace transforms, we construct a nonparametric estimator for the distribution of N, assuming that the distribution of ξ is known explicitly. Unlike most papers on this topic, we consider the general setting, where the distribution of N is not necessarily of Poisson type. [ABSTRACT FROM AUTHOR]

In this article, a robust estimation method is proposed for a partially linear panel data model with fixed effects. We eliminate the fixed effects based on auxiliary linear regression, then approximate the unknown non parametric component with B-spline function, and obtain the robust estimators of the parametric and non parametric components by combining projection matrix with exponential squared loss function. Under some regularity conditions, the asymptotic properties of the resulting estimators are proved. Some simulation studies illustrate that the proposed method is more robust than the semiparametric least squares dummy variable estimator. The proposed procedure is illustrated by a real data application. [ABSTRACT FROM AUTHOR]

AbstractThis article is concerned with the local linear non parametric regression estimator of a right censored scalar response random variable, given a functional random covariate. First, we investigate its asymptotic normality under the concentration properties of small ball probability functions. Then, we apply the results to present the asymptotic (1−α) confidence interval of the regression function for 0<α<1. To lend further support to our theoretical results, we carry out a simulation study to illustrate the performance and the asymptotic Gaussian behavior of our estimator. Finally, an application to real data is provided. [ABSTRACT FROM AUTHOR]

Abstract.To check the significance of the regression coefficients in the linear component of high-dimensional partial linear models, we proposed some projection-based test statistics. These test statistics are connected with U-statistics of order two and they are applicable for diverging dimensions and heteroscedastic model errors. By using the martingale central limit theorem, we show the asymptotic normalities of the proposed test statistics under the null hypothesis and local alternative hypotheses. The performance of test statistics are evaluated by simulation studies. The simulation results show that the proposed test statistics are powerful and have the correct type-I error asymptotically under the null hypothesis. [ABSTRACT FROM AUTHOR]