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有限混合模型同质性的修正似然比检验AI 解读

Summary Testing for homogeneity in finite mixture models has been investigated by many researchers. The asymptotic null distribution of the likelihood ratio test (LRT) is very complex and difficult to use in practice. We propose a modified LRT for homogeneity in finite mixture models with a general parametric kernel distribution family. The modified LRT has a χ-type of null limiting distribution and is asymptotically most powerful under local alternatives. Simulations show…

局部线性平滑的经验似然置信区间AI 解读

Empirical likelihood is considered in conjunction with the local linear smoother to construct confidence intervals for a nonparametric regression function with bounded support. The coverage error of the empirical likelihood confidence intervals is evaluated and is shown to be of the same order throughout the support of the regression function. This is a significant improvement over confidence intervals based directly on the asymptotic normal distribution of the local linear…

大规模伯努利数据的平滑样条 ANOVA 模型与随机化 GACVAI 解读

We propose the randomized Generalized Approximate Cross Validation (ranGACV) method for choosing multiple smoothing parameters in penalized likelihood estimates for Bernoulli data. The method is intended for application with penalized likelihood smoothing spline ANOVA models. In addition we propose a class of approximate numerical methods for solving the penalized likelihood variational problem which, in conjunction with the ranGACV method allows the application of smoothing…

预防 HIV-1 母婴垂直传播的随机试验分析AI 解读

We analyze data from a randomized trial of breastfeeding versus formula feeding in HIV-1-infected mothers and their infants. Estimates of infant HIV-1-free survival and the timing of vertical transmission of HIV-1 are complicated by the fact that the infants' HIV-1 status at death may be unknown, the time of HIV-1 infection may be interval censored, and the tests used to detect HIV-1 infection in the infants may be less than 100% sensitive or specific. To address these…

预防 HIV-1 母婴传播随机试验的分析AI 解读

We analyze data from a randomized trial of breastfeeding versus formula feeding in HIV-1-infected mothers and their infants. Estimates of infant HIV-1-free survival and the timing of vertical transmission of HIV-1 are complicated by the fact that the infants' HIV-1 status at death may be unknown, the time of HIV-1 infection may be interval censored, and the tests used to detect HIV-1 infection in the infants may be less than 100% sensitive or specific. To address these…

一致的模型设定检验AI 解读

We point out the close relationship between the integrated conditional moment tests in Bierens (1982, Journal of Econometrics 20, 105–134) and Bierens and Ploberger (1997, Econometrica 65, 1129–1152) with the complex-valued exponential weight function and the kernel-based tests in Härdle and Mammen (1993, Annals of Statistics 21, 1926–1947), Li and Wang (1998, Journal of Econometrics 87, 145–165), and Zheng (1996, Journal of Econometrics 75, 263–289). It is well established…

将广义矩方法推广至连续统矩条件AI 解读

This paper proposes a version of the generalized method of moments procedure that handles both the case where the number of moment conditions is finite and the case where there is a continuum of moment conditions. Typically, the moment conditions are indexed by an index parameter that takes its values in an interval. The objective function to minimize is then the norm of the moment conditions in a Hilbert space. The estimator is shown to be consistent and asymptotically…

模糊化生成的非可分时空模型AI 解读

Summary Statistical space–time modelling has traditionally been concerned with separable covariance functions, meaning that the covariance function is a product of a purely temporal function and a purely spatial function. We draw attention to a physical dispersion model which could model phenomena such as the spread of an air pollutant. We show that this model has a non-separable covariance function. The model is well suited to a wide range of realistic problems which will…

连续协变量存在测量误差时的失效时间回归AI 解读

Summary We consider failure time regression analysis with an auxiliary variable in the presence of a validation sample. We extend the nonparametric inference procedure of Zhou and Pepe to handle a continuous auxiliary or proxy covariate. We estimate the induced relative risk function with a kernel smoother and allow the selection probability of the validation set to depend on the observed covariates. We present some asymptotic properties for the kernel estimator and provide…

非参数回归中降低偏差的数据锐化方法AI 解读

We consider methods for kernel regression when the explanatory and/or response variables are adjusted prior to substitution into a conven- tional estimator.This “data-sharpening” procedure is designed to preserve the advantages of relatively simple, low-order techniques, for example, their robustness against design sparsity problems, yet attain the sorts of bias reductions that are commonly associated only with high-order methods.We consider Nadaraya–Watson and local-linear…

条件参数分布的一致性检验AI 解读

This paper proposes a new nonparametric test for conditional parametric distribution functions based on the first-order linear expansion of the Kullback–Leibler information function and the kernel estimation of the underlying distributions. The test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric distribution is correctly specified, whereas asymptotically rejecting the null with probability one if the…

两阶段标记重捕实验分析的非参数方法AI 解读

We present a new approach to the analysis of two-stage mark-recapture experiments where individual covariates are available which describe the detectability of individuals in the population. Central to the theory is a single quantity α, which we call the heterogeneity index and which measures the variability in the detectability of individuals. This theory also has implications for the analysis of independent observer line transect surveys. An estimator of α is provided by…

局部多项式回归的可变带宽选择AI 解读

Summary The performances of data-driven bandwidth selection procedures in local polynomial regression are investigated by using asymptotic methods and simulation. The bandwidth selection procedures considered are based on minimizing ‘prelimit’ approximations to the (conditional) mean-squared error (MSE) when the MSE is considered as a function of the bandwidth h. We first consider approximations to the MSE that are based on Taylor expansions around h=0 of the bias part of…

非线性时间序列的函数系数回归模型AI 解读

The local linear regression technique is applied to estimation of functional-coefficient regression models for time series data. The models include threshold autoregressive models and functional-coefficient autoregressive models as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better postsample forecasting performance. Also proposed are a new bootstrap test for the goodness of fit of models and a bandwidth…

包含交互项与平滑效应的贝叶斯回归建模AI 解读

There have been many recent suggestions as to how to build and estimate flexible Bayesian regression models, using constructs such as trees, neural networks, and Gaussian processes. Although there is much to commend these methods, their implementation and interpretation can be daunting for practitioners. This article presents a spline-based methodology for flexible Bayesian regression that is quite simple in terms of computation and interpretation. Smooth bivariate…

变系数模型的高效估计与推断AI 解读

This article deals with statistical inferences based on the varying-coefficient models proposed by Hastie and Tibshirani. Local polynomial regression techniques are used to estimate coefficient functions, and the asymptotic normality of the resulting estimators is established. The standard error formulas for estimated coefficients are derived and are empirically tested. A goodness-of-fit test technique, based on a nonparametric maximum likelihood ratio type of test, is also…

偏倚函数未知时基于有偏样本的非参数密度估计AI 解读

We present a kernel estimator for the density of a variable when sampling probabilities depend on that variable. Both the density and sampling bias weight functions are unknown and are estimated nonparametrically. To achieve this, the method requires that two independent samples be taken from a fixed finite population. An estimator of population size follows simply from our density estimator. Asymptotic bias and standard errors for these estimators are provided, and the…

当前状态数据下的线性回归AI 解读

In survival analysis, a linear model often provides an adequate approximation after a suitable transformation of the survival times and possibly of the covariates. This article proposes a semiparametric regression method for estimating the regression parameter in the linear model without specifying the distribution of the random error, where the response variable is subject to so-called case 1 interval censoring. The method uses a constructed random-sieve likelihood and…

含交互项与平滑效应的贝叶斯回归建模AI 解读

There have been many recent suggestions as to how to build and estimate flexible Bayesian regression models, using constructs such as trees, neural networks, and Gaussian processes. Although there is much to commend these methods, their implementation and interpretation can be daunting for practitioners. This article presents a spline-based methodology for flexible Bayesian regression that is quite simple in terms of computation and interpretation. Smooth bivariate…

高斯混合筛估计的收敛速度AI 解读

Gaussian mixtures provide a convenient method of density estimation that lies somewhere between parametric models and kernel density estimators.When the number of components of the mixture is allowed to increase as sample size increases, the model is called a mixture sieve.We establish a bound on the rate of convergence in Hellinger distance for density estimation using the Gaussian mixture sieve assuming that the true density is itself a mixture of Gaussians; the underlying…

调查抽样中的局部多项式回归估计AI 解读

Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on local polynomial regression is proposed. Like generalized regression estimators, these estimators are weighted linear combinations of study variables, in which the weights are calibrated to known control totals, but the assumptions on the superpopulation model are considerably weaker. The estimators are shown to be asymptotically design-unbiased and…

Technical analysis, also known as “charting,” has been a part of financial practice for many decades, but this discipline has not received the same level of academic scrutiny and acceptance as more traditional approaches such as fundamental analysis. One of the main obstacles is the highly subjective nature of technical analysis—the presence of geometric shapes in historical price charts is often in the eyes of the beholder. In this paper, we propose a systematic and…

非参数回归中的变量显著性检验AI 解读

A procedure for testing the significance of a subset of explanatory variables in a nonparametric regression is proposed. Our test statistic uses the kernel method. Under the null hypothesis of no effect of the variables under test, we show that our test statistic has an nh p 2 /2 standard normal limiting distribution, where p 2 is the dimension of the complete set of regressors. Our test is one-sided, consistent against all alternatives and detects local alternatives…

加性非线性 ARX 时间序列的非参数估计：局部线性拟合与投影AI 解读

We consider the estimation and identification of the components (endogenous and exogenous) of additive nonlinear ARX time series models. We employ a local polynomial fitting scheme coupled with projections. We establish the weak consistency (with rates) and the asymptotic normality of the projection estimates of the additive components. Expressions for the asymptotic bias and variance are given.