Estimation with incomplete data: An improved computational method and the analysis of nested data

Maximum likelihood estimation with incomplete normal nrocedure and (ii.)allows tor a Simple MLI.I v=n,ce nf noofori TiVplilinndv Closed form solutions are described for the general nested case.Exact, ssample, moments are given for the two group case Some. computational comparisions are made with the earlier ESTMAT algorithm.     

Simulation of weibull and gamma autoregressive stationary process

This paper presents two simple non-Gaussian first-order autoregressive markovian processes which are easy to simulate via a computer. The autoregressive Gamma process {X_n:} is constructed according to the stochastic difference equation X_n:=V_n:X_n?1+?_n:, where {?_n:} is an i.i.d. Exponential sequence and {V_n:} is i.i.d. with Power-function distribution defined on the interval [0,1). The autoregressive Weibull process {X_n:} is constructed from the probabilistic model X_n:= k.min (X_n?1:, Y_n:) where {Y_n:} is an i.i.d. Weibull sequence and k > 1.     

Test of independence between tow sets of variates

In this paper asymptotic expansions of the null as well as non-null distributions of the likelihood ratio criterion for testing independence between two sets of variates are obtained. These appear to be better than the ones available in the literature . In factin the null case for p = 1 and p = 2 , t h e expansion reduces to the exact di stribution. In the non-null case, the expansion is given i n terms of non-central beta distributions and for the case when the population canonical correlation coefficients are small.     

空间经济计量滞后模型Bootstrap Moran检验功效的模拟分析

 当误差项不服从独立同分布时,利用Moran’s I统计量的渐近检验,无法有效判断空间经济计量滞后模型2SLS估计残差间存在空间关系与否。本文采用两种基于残差的Bootstrap方法,诊断空间经济计量滞后模型残差中的空间相关关系。大量Monte Carlo模拟结果显示,从功效角度看,无论误差项服从独立同分布与否,与渐近检验相比,Bootstrap Moran检验都具有更好的有限样本性质,能够更有效地进行空间相关性检验。尤其是,在样本量较小和空间衔接密度较高情况下,Bootstrap Moran检验的功效显著大于渐近检验。     

The probability distribution and the expected value of a stopping variable associated with one-sided cusum procedures for non-negative integer valued random variables

The structure of a stopping variable N based on one-sided CUSUM procedures is analyzed. Stopping occurs when a Markovian sequence of maxima of partial sums {M } crosses a certain boundary. On the basis of a recursive relationship between the M_n+1 and M_n a recursive equation is derived for the determination of the defective distributions K_n(x) = P{M ≤ x, N ≤n} . This recursive equation yields a recursive algorithm for the determination of P {N > n} . The paper studies the case when the basic random variables are non-negative integers-valued. In these cases the values of P{N > n} and E{N} can be determined by solving proper systems of linear equations.     

CURRENT STATUS AND RIGHT-CENSORED DATA STRUCTURES WHEN OBSERVING A MARKER AT THE CENSORING TIME

We study nonparametric estimation with two types of data structures. In the first data structure n i.i.d. copies of (C, N(C)) are observed, where N is a finite state counting process jumping at time-variables of interest and C a random monitoring time. In the second data structure n i.i.d. copies of (C ∧ T, I (T ≤ C), N(C ∧ T)) are observed, where N is a counting process with a final jump at time T (e.g., death). This data structure includes observing right-censored data on T and a marker variable at the censoring time.In these data structures, easy to compute estimators, namely (weighted)-pool-adjacent-violator estimators for the marginal distributions of the unobservable time variables, and the Kaplan-Meier estimator for the time T till the final observable event, are available. These estimators ignore seemingly important information in the data. In this paper we prove that, at many continuous data generating distributions the ad hoc estimators yield asymptotically efficient estimators of [Formula: see text]-estimable parameters.     

Root-n-consistent Estimation in Partial Linear Models with Long-memory Errors

We consider estimation of β in the semiparametric regression model y ( i ) - x ^T( i )β + f ( i / n ) + ε( i ) where x ( i ) = g ( i )/ n ) + e ( i , f and g are unknown smooth functions and the processes ε( i ) and e ( i ) are stationary with short- or long-range dependence. For the case of i.i.d. errors, Speckman (1988) proposed a √ n –consistent estimator of β. In this paper it is shown that, under suitable regularity conditions, this estimator is asymptotically unbiased and √ n –consistent even if the errors exhibit long-range dependence. The orders of the finite sample bias and of the required bandwidth depend on the long-memory parameters. Simulations and a data example illustrate the method     

U2n test for uniformity of discrete distributions

Lockhart et al. have given an elegant account of this recently. In this paper, I will show that the method which originally led to U2n works just as well in the discrete case-and suggests a proof in the continuous case.     

A monte carlo of plotting positions

A Monte Carlo study was made of the effects of using simple linear regression, on the appropriate probability paper, to estimate parameters, quantiles and cumulative probability for several distributions. These distributions were the Normal, Weibull (shape parameters 1, 2, and 4) and the Type I largest extreme-value distributions. The specific objective was to observe differences arising from choice of plotting positions. Plotting positions used were i/(n+l), (i?3)/(n+.04), (i?.5)/n, either (i?.375)/(n+.25) or (i?.4)/(n+.2), and either F[E(Y_i)] or F[E(£n Y)]. For each combination of 4 sample sizes (n=10(10)(40)), distribution, and plotting position, regression lines were found for each of N =9999 samples. Each regression line was used to estimate: (1) quantiles of 9 specific probabilities, (2) probabilities of 9 specific quantiles, and (3) return periods corresponding to 9 specific quantiles. Compa[rgrave]ison of the mean, variances, mean square error and medians of these estimates and of the regression coefficients confirm some results of Harter [Commun. Statist. A13(13), 1984] and provide further insight.     

Regression coefficient analysis for correlated binomial outcomes

At present, the generalized estimating equation (GEE) and weighted least-squares (WLS) regression methods are the most widely used methods for analyzing correlated binomial data; both are easily implemented using existing software packages. We propose an alternative technique, i.e. regression coefficient analysis (RCA), for this type of data. In RCA, a regression equation is computed for each of n individuals; regression coefficients are averaged across the n equations to produce a regression equation, which predicts marginal probabilities and which can be tested to address hypotheses of different slopes between groups, slopes different from zero, different intercepts, etc. The method is computationally simple and can be performed using standard software. Simulations and examples are used to compare the power and robustness of RCA with those of the standard GEE and WLS methods. We find that RCA is comparable with the GEE method under the conditions tested, and suggest that RCA, within specified limitations, is a viable alternative to the GEE and WLS methods in the analysis of correlated binomial data.     

Approximate mean squared errors of estimations of reliability in the two-parameter exponential case

Combining the method used i n Chao (1981) and conditional procedure, we extend our previous results for one-parameter exponential to two-parameter case, i .e. we provide simple approximation formulas for the mean squared errors of the maximum likelihood and minimum variance unbiased estimators of reliability of general k-out-of-m systems when the component lifetimes are independent and follow a two-parameter exponential distribution.     

Modified regression coefficient analysis for repeated binary measurements

Myers & Broyles (2000a, 2000b) illustrate that regression coefficient analysis (RCA) is a viable alternative to a generalized estimating equation (GEE) in the analysis of correlated binomial data. Since the regression coefficients (b i ' s ) may have different precisions, we modify RCA by weighting b i ' s by the inverses of their variances for statistical optimality. We perform the simulation study to evaluate the performance of RCA, modified RCA and GEE in terms of empirical type I errors and empirical powers of the regression coefficients in repeated binary measurement designs with and without dropouts. Two thousand data sets are generated using autoregressive (AR(1)) and compound symmetry (CS) correlation structures. We compare the type I errors and powers of RCA, modified RCA and GEE for the analysis of repeated binary measurement data as affected by different dropout mechanisms such as random dropouts and treatment dependent dropouts.     

On regression modelling with dummy variables versus separate regressions per group: Comment on Holgersson et al.

In a recent issue of this journal, Holgersson et al. [Dummy variables vs. category-wise models, J. Appl. Stat. 41(2) (2014), pp. 233–241, doi:10.1080/02664763.2013.838665] compared the use of dummy coding in regression analysis to the use of category-wise models (i.e. estimating separate regression models for each group) with respect to estimating and testing group differences in intercept and in slope. They presented three objections against the use of dummy variables in a single regression equation, which could be overcome by the category-wise approach. In this note, I first comment on each of these three objections and next draw attention to some other issues in comparing these two approaches. This commentary further clarifies the differences and similarities between dummy variable and category-wise approaches.     

The probability generating function of empty cell variable in a randomized occupancy problem

Let M_o denote the number of empty cells when n distinguishable balls are distributed independently and at random in ra cells such that each ball stays with probability p in its cell, and falls through with probability 1-p. We find the probability generating function of M_o by solving a partial differential equation satisfied by a suitable generating function. The corresponding function for the classical case p = 1 is well-known, but obtained by different methods.     

Interchangeability of the ratio and product methods in sample surveys

The paper demonstrates the interchangeability of the ratio and product methods of estimation i n sample surveys through translati n g the unbiased estimator of the population total of the auxiiart variate (or the study varia te). The values of the translation parameters minimizing the mean squared error are obtained. The allowable departures from this optimum, which still ensure a reduction in the mean squared error, as compared to the traditional case, are indicated.     

C337. Misspecified location and scale. 11. independence of and s2

A hierarchical Bayesian approach to the problem of estimating the largest normal mean is considered. Calculation of the posterior mean and the posterior variance involves, at worst, 3-dimensional numerical integration, for which an efficient Monte Carlo method of evaluation is given. An example is presented to illustrate the methodology. In the two populations case, computation of the posterior estimates can be substantially simplified and in special cases can actually be performed using closed form solutions. A simulation study has been done to compare mean square errors of some hierarchical Bayesian estimators that are expressed in closed forms and several existing estimators of the larger mean.     

Distribution of the coates-diggle test statistic in case of replicated observations

A closed form expression for the distribution of a test statistic for comparing the spectral densities of stationary processes is given. This test statistic was introduced by COATES and DIGGLE ( 1986 ) for the unreplicated case and has been extended to the case of replicated observations by POTSCHER and RESCHENHOFER ( 1988 ). A simple method for computing approximate critical values in case of large numbers of replications is also provided. As a by-product an explicit expression for the distribution function of the range of independent variates each distributed as the logarithm of an F-variate i.e up to a factor of 2 each followin Fishers z-distriution is obtained     

Tests of Fit for Exponentiality based on the Empirical Laplace Transform

The Laplace transform \psi(t)=E[{\rm exp}(-tX)] of a random variable X with exponential density u exp( m u x ), x S 0, satisfies the equation (\lambda+t)\psi(t)-\lambda=0 , t S 0. We study the behavior of a class of consistent tests for exponentiality based on a suitably weighted integral of [({\hat\lambda}_n+t)\psi_n(t)-{\hat\lambda}_n]^2 , where {\hat\lambda}_n is the maximum-likelihood estimate of u , and é n is the empirical Laplace transform, each based on an i.i.d. sample X 1 , …, X n . As the decay of the weight function tends to infinity, the test statistic approaches the square of the first nonzero component of Neyman's smooth test for exponentiality. The new tests are compared with other omnibus tests for exponentiality.     

Asymptotic distribution theory for the kalman filter state estimator

An asymptotic distribution theory for the state estimate from a Kalman filter in the absence of the usual Gaussian assumption is presented. It is found that the stability properties of the state transition matrix playa key role in the distribution theory. Specifically, when the state equation is neutrally stable (i.e., borderline stable-unstable) the state estimate is asymptotically normal when the random terms in the model have arbitrary distributions. This case includes the popular random walk state equation. However, when the state equation is either stable or unstable, at least some of the random terms in the model must be normally distributed beyond some finite time before the state estimate is asymptotically normal.     

On the Distance Between Cumulative Sum Diagram and Its Greatest Convex Minorant for Unequally Spaced Design Points

Abstract.  The supremum difference between the cumulative sum diagram, and its greatest convex minorant (GCM), in case of non-parametric isotonic regression is considered. When the regression function is strictly increasing, and the design points are unequally spaced, but approximate a positive density in even a slow rate ( n ^−1/3), then the difference is shown to shrink in a very rapid (close to n ^−2/3) rate. The result is analogous to the corresponding result in case of a monotone density estimation established by Kiefer and Wolfowitz, but uses entirely different representation. The limit distribution of the GCM as a process on the unit interval is obtained when the design variables are i.i.d. with a positive density. Finally, a pointwise asymptotic normality result is proved for the smooth monotone estimator, obtained by the convolution of a kernel with the classical monotone estimator.