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核密度估计中最优的数据驱动带宽选择AI 解读

A bandwidth selection method is proposed for kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n−½ where n ↑ ∞ denotes sample size. Comparison is given to other bandwidth selection methods, and small sample…

平滑信号检测：基于累积和程序的最优性AI 解读

Cox et al. (1988) show that under a random smooth function model with signal covariance matrix V, a locally most powerful test for the presence of a nonpolynomial signal is based on the statistic yTVy. We show that if a well-known difference-based roughness measure is used to derive a natural choice for V then this statistic is the sum of squares of a residual cusum sequence. Thus we confirm theoretically the long-held impression that the residual cusum sequence is powerful…

利用非参数曲线进行模型检验AI 解读

The use of local likelihood curve estimates in model checking is described. Test statistics are based on deviance differences, and are interpreted using nonparametric bootstrap Monte Carlo. Some theoretical aspects are discussed. Methods are illustrated for regression with discrete data.

逻辑回归相对于线性判别分析的渐近效率AI 解读

SUMMARY We calculate the asymptotic efficiency of logistic regression relative to linear discriminant analysis for testing hypotheses about the parameters when the explanatory variables are normally distributed. The Pitman asymptotic efficiency for hypothesis tests in this context is the same as the asymptotic relative efficiency calculated using misclassification rates and is independent, of the number of explanatory variables and the number of parameters to be tested.

无重复观测的超结构模型AI 解读

Dolby's (1976) ultrastructural model is investigated with emphasis on the case with no replications and one of the error variances known. It is shown that, in this situation, the maximum likelihood estimators are not consistent. The method of moments estimators are consistent and asymptotically normal and best in Fisher's sense within a broad class of asymptotically normal estimators discussed by Gleser (1983). Some connections with the errors-in-variables model are examined.

离散化误差对核密度估计带宽选择的影响AI 解读

It is well known that the cross-validation score function of discretized data often tends to -∞ as the bandwidth tends to zero. This disturbing property causes some difficulty in applying cross-validation to discretized data. Since all data are rounded to some degree, the phenomenon limits the application of cross-validation in practice. Based on characteristic functions, the cause of the difficulty is explained, and a simple modification is suggested. Under some conditions,…

位置模型后验均值的一种表示AI 解读

An exact representation of the posterior mean is developed for a location model and the class of priors that are normal scale mixtures. The result makes use of the conditional distribution of the maximum likelihood estimator and Masreliez's theorem. Directions for future development are indicated.

分层均值与规模未知时利用回归估计量进行后分层AI 解读

Poststratification is often used to increase the precision of survey estimators. When applied to regression estimators, it assumes that the regression relationships in the various strata are different. This gives rise to the use of the separate regression estimator. In this paper, we consider situations where the strata affiliation of the population units is not specified in the frame so that the separate regression estimator is not available, the strata means of the…

线性测量误差模型的影响诊断AI 解读

Influence functions are used to show that extreme observations affect linear measurement error model estimators in directions orthogonal to and along the fitted plane, rather than vertically and horizontally as with least squares estimators. Influence diagnostics patterned after those for least squares and derived for generalized linear models by Pregibon (1981) are adapted to assess the influence of extreme observations on linear measurement error model estimators.…

序贯 Monte Carlo p 值AI 解读

SUMMARY The assessment of statistical significance by Monte Carlo simulation may be costly in computer time. This paper looks at a number of ways of calculating exact Monte Carlo p-values by sequential sampling. Such p-values are shown to have properties similar to those obtained by sampling with a fixed sample size. Both standard and generalized Monte Carlo procedures are discussed and, in particular, a sequential method is proposed for dealing with situations in which…

若干时间序列 Markov 回归模型的适合性检验AI 解读

The asymptotic distribution of residual autocorrelations and a score statistic are derived for checking model adequacy for some Markov regression models for time series. These models are natural extensions of the popular generalized linear models to time series data. The score statistic appears to be somewhat easier to use in practice. Some empirical results are also obtained for the score statistic in some simple cases. A real example is given.

线性模型中对比方差的估计AI 解读

A common problem in the reporting of statistical analyses is the presentation of standard errors of nonindependent effects. In particular, it is desirable to provide a useful indication of the covariance structure of the parameter estimates. The problem is considered for several cases. First, in an analysis of covariance situation, we derive upper and lower bounds for the standard error of an arbitrary linear contrast of treatment effects; the method allows for unequal…

周期函数的频率估计AI 解读

The problem of estimating the frequency and other parameters of a cyclical oscillation is considered, where the data consists of a periodic function observed subject to stationary additive noise. An estimation procedure is proposed and the asymptotic properties of the estimators established. Tests for unknown frequencies to be harmonics of a fundamental frequency are also developed and their asymptotic properties investigated. The procedures are applied to observations on…

非线性多层模型及其离散响应数据应用AI 解读

A procedure is proposed for the analysis of multilevel nonlinear models using a linearization. The case of log linear models for discrete response data is studied in detail.

有限总体均值估计量的渐近设计无偏性AI 解读

Certain regression-type estimators of a finite population mean are examined for their asymptotic design properties. A sufficient condition that implies the design-consistency or asymptotic design-unbiasedness is discussed for a general regression estimator. The leading term of its asymptotic bias is explicitly derived when this condition holds as well as when it does not hold.

基于混合正交表的平衡重复复制法AI 解读

For stratified samples with arbitrary numbers of primary sampling units per stratum, one can divide the units in the stratum into two groups and then apply the balanced half-samples method to the two groups thus formed. The efficiency loss of the grouped balanced half-samples variance estimator can be substantial. Use of a mixed orthogonal array, whose numbers of symbols correspond to the numbers of units per stratum, gives a set of balanced subsamples. Unlike that of Gupta…

学生化均值的鞍点近似及其自助法应用AI 解读

A saddlepoint technique is used to approximate to the density and tail probability of the studentized mean of a random sample. The motivation was to replace bootstrapping of the studentized mean in the way Davison & Hinkley (1988) used the saddlepoint approximation for the unstudentized mean. The method involves first obtaining a bivariate saddlepoint approximation, then, after a nonlinear transformation, integrating out an unwanted variable either numerically or by a…

序贯 t、卡方与 F 检验的精确计算AI 解读

Sequential and group sequential procedures are proposed for monitoring repeated t, X2 or F statistics. These can be used to construct sequential hypothesis tests or repeated confidence intervals when the parameter of interest is a normal mean with unknown variance or a multivariate normal mean with variance matrix known or known up to a scale factor. Exact methods for calculating error probabilities and sample size distributions are described and tables of critical values…

多变量观测不完整的临床试验中的非参数序贯检验AI 解读

This paper addresses sequential testing in randomized clinical trials with multiple endpoints. Patients enter treatments serially and are subject to random loss to followup. The endpoints of interest may be time-to-event variables or other quantitative measurements. The proposed test statistic at a given look is a weighted sum of the linear rank statistics with respect to the marginal distributions of the multiple endpoints. The weights can be chosen to maximize asymptotic…

识别时间序列中过度影响结果的观测AI 解读

The purpose of this paper is to develop a tool for identifying over-influential observations in time series when they are viewed in the time domain. We present a method for obtaining various measures of influence for the autocorrelation function, as well as thresholds for declaring an observation over-influential. An example of the use of these thresholds is also presented.

叠加过程的组成过程数量估计AI 解读

We consider a superposition of an unknown number of independent homogeneous Poisson processes with unknown rates and suppose that when an event occurs, the component process in which it occurred can be identified. The number of component processes and their rates are to be estimated by observing the system for some time. In the general case, it is difficult to estimate all of the parameters but we derive the best unbiased estimators of some parametric functions. Inferences…

季节性时间序列中周期自相关的检验AI 解读

This paper presents statistical procedures for deciding if periodicities exist in the autocorrelation function of a seasonal time series after removal of seasonal means and standard deviations. The procedures are based on asymptotic properties of a Fourier-transformed version of the estimated periodic autocorrelation function. Analyses of simulated and actual data sets illustrate the usefulness of the proposed methods.

列联表的降秩模型AI 解读

Reduced rank models for the analysis of two-way contingency tables are introduced. Two classes of reduced rank models are discerned, with well-known exponents canonical analysis and latent class analysis. The relation between these two classes is discussed. Results on the subject mentioned earlier in the literature are shown to be either redundant or inaccurate.

In genetics, the term interclass correlation has been used to refer to the parent-offspring and son-daughter correlations within families. Under the assumption of variable family sizes and normality, we derive the asymptotic variance of the maximum likelihood estimator of the son-daughter interclass correlation.