Metrika最新文献

Let X, Y be continuous random variables with unknown distributions. The aim of this paper is to study the problem of estimating the probability (theta := {mathbb {P}}(X<Y)) based on independent random samples from the distributions of (X'), (Y'), (zeta ) and (eta ), where (X' = X + zeta ), (Y' = Y + eta ) and X, Y, (zeta ), (eta ) are mutually independent random variables. In this context, (zeta ), (eta ) are referred to as measurement errors. We apply the ridge-parameter regularization method to derive a nonparametric estimator for (theta ) depending on two parameters. Our estimator is shown to be consistent with respect to mean squared error if the characteristic functions of (zeta ), (eta ) only vanish on Lebesgue measure zero sets. Under some further assumptions on the densities of X, Y, (zeta ) and (eta ), 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

Consider the following generalized linear model (GLM) $$begin{aligned} y_i=h(x_i^Tbeta )+e_i,quad i=1,2,ldots ,n, end{aligned}$$ where h(.) is a continuous differentiable function, ({e_i}) are independent identically distributed (i.i.d.) random variables with zero mean and known variance (sigma ^2) . Based on the penalized Lq-likelihood method of linear regression models, we apply the method to the GLM, and also investigate Oracle properties of the penalized Lq-likelihood estimator (PLqE). In order to show the robustness of the PLqE, we discuss influence function of the PLqE. Simulation results support the validity of our approach. Furthermore, it is shown that the PLqE is robust, while the penalized maximum likelihood estimator is not.

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.

In this paper, we obtain the asymptotic form of the joint distribution of maxima and minima of independent observations, when the sample size is a random variable. We also discuss the asymptotic distribution of the Range.

Many industrial experiments involve factors with levels more difficult to change or control than others, which leads to the development of two-level fractional factorial split-plot (FFSP) designs. Recently, mixed-level FFSP designs were proposed due to the requirement of different-level factors. In this paper, we generalize the Bayesian optimal criterion for mixed two- and four-level FFSP designs, and then provide Bayesian minimum aberration (MA) criterion to rank FFSP designs. Bayesian MA criterion can give a natural ordering for the effects involving two-level factors and three components of a four-level factor. We also discuss the relationship between the Bayesian optimal and Bayesian MA criteria. Furthermore, we consider the designs with both qualitative and quantitative factors.

We prove mixing convergence of the least squares estimator of autoregressive parameters for supercritical autoregressive processes of order 2 with Gaussian innovations having real characteristic roots with different absolute values. We use an appropriate random scaling such that the limit distribution is a two-dimensional normal distribution concentrated on a one-dimensional ray determined by the characteristic root having the larger absolute value.

Spatial association measures for univariate static spatial data are widely used. Suppose the data is in the form of a collection of spatial vectors, say (X_{rt}) where (r=1, ldots , R) are the regions and (t=1, ldots , T) are the time points, in the same temporal domain of interest. Using Bergsma’s correlation coefficient (rho ), we construct a measure of similarity between the regions’ series. Due to the special properties of (rho ), unlike other spatial association measures which test for spatial randomness, our statistic can account for spatial pairwise independence. We have derived the asymptotic distribution of our statistic under null (independence of the regions) and alternate cases (the regions are dependent) when, across t the vector time series are assumed to be independent and identically distributed. The alternate scenario of spatial dependence is explored using simulations from the spatial autoregressive and moving average models. Finally, we provide application to modelling and testing for the presence of spatial association in COVID-19 incidence data, by using our statistic on the residuals obtained after model fitting.

This paper provides a least squares regression estimation of the tail index for long memory processes where the innovations are (alpha )-stable random sequences. The estimate is based on the property of the characteristic function of the process near the origin. The asymptotics of the estimator are obtained by choosing suitable regression samples with the help of the properties of the (alpha )-stable distribution. The numerical simulation and an empirical analysis of financial market data are conducted to assess the finite sample performance of the proposed estimator.

In this paper, we propose an estimator of power spot volatility of order p through Edgeworth expansion. We provide a precise description of how to compute the expansion and the first four cumulants are given in an explicit form. We also construct feasible confidence intervals (one-sided and two-sided) for the pth power spot volatility estimator by using Edgeworth expansion. A Monte Carlo simulation study shows that the confidence intervals and probability density curve based on Edgeworth expansion perform better than the conventional case based on Normal approximation.

Consider the semiparametric linear regression estimation problem with right-censored data. Under right censoring, the Buckley–James estimator (BJE) is the standard extension of the least squares estimator. Moreover, an iterative algorithm for the BJE has been implemented in R package called rms. We show that it often does not yield a solution, even if a consistent BJE exists. Yu and Wong (J Stat Comput Simul 72:451–460, 2002) proposed another algorithm to find all possible BJEs. The latter algorithm is modified in this paper so that it indeed finds all BJEs when the underlying regression parameter vector is identifiable. We show that some of these BJE’s can be inconsistent. Thus it is important to decide how to select a proper BJE such that it is consistent if the parameter is identifiable. We suggest either choose one close to the modified semi-parametric maximum likelihood estimator (Yu and Wong in Technometrics 47:34–42, 2005) or a finite boundary point if there are infinitely many BJEs.