The asymptotic covariance structure of log-linear model estimated parameters for the multiple recapture census

This paper presents a matrix formulation for log-linear model analysis of the incomplete contingency table which arises from multiple recapture census data. Explicit matrix product expressions are given for the asymptotic covariance structure of the maximum likelihood estimators of both the log-linear model parameter vector and the predicted value vector for the observed and missing cells. These results are illustrated for data pertaining to a population of children possessing a common congenital anomaly.     

Likelihood‐based Inference with Missing Data Under Missing‐at‐Random

Likelihood‐based inference with missing data is challenging because the observed log likelihood is often an (intractable) integration over the missing data distribution, which also depends on the unknown parameter. Approximating the integral by Monte Carlo sampling does not necessarily lead to a valid likelihood over the entire parameter space because the Monte Carlo samples are generated from a distribution with a fixed parameter value. We consider approximating the observed log likelihood based on importance sampling. In the proposed method, the dependency of the integral on the parameter is properly reflected through fractional weights. We discuss constructing a confidence interval using the profile likelihood ratio test. A Newton–Raphson algorithm is employed to find the interval end points. Two limited simulation studies show the advantage of the Wilks inference over the Wald inference in terms of power, parameter space conformity and computational efficiency. A real data example on salamander mating shows that our method also works well with high‐dimensional missing data.     

Principal components regression estimator of the parameters in partially linear models

ABSTRACT

As a compromise between parametric regression and non-parametric regression models, partially linear models are frequently used in statistical modelling. This paper is concerned with the estimation of partially linear regression model in the presence of multicollinearity. Based on the profile least-squares approach, we propose a novel principal components regression (PCR) estimator for the parametric component. When some additional linear restrictions on the parametric component are available, we construct a corresponding restricted PCR estimator. Some simulations are conducted to examine the performance of our proposed estimators and the results are satisfactory. Finally, a real data example is analysed.     

Fisher’s observed information matrix for location and scale parameters under type i censoring

An expression for Fisher's observed information matrix is given under type I censoring for any location-scale distribution under mild requirements. It is illustrated on a data set which has been analyzed by several authors.     

Selection of error probability laws by generalized modified profile likelihood

Although error probability law selection of models of location-scale forms is of importance in some sense, the commonly used model selection procedures, such as AIC and BIC, do not apply to it. By treating error probability law as a “parameter” of interest, location and scale as nuisance parameters, this paper proposes that generalized modified profile likelihood (GMPL), considered as a quasi-likelihood function of error probability law, be used to select the error probability laws. The GMPL method achieves minimax rate optimality and proves to be consistent. Simulations show its good performance for finite and even small samples. Note that it is straightforward to generalize the GMPL of location-scale models to various models of location-scale forms particularly including the various linear regression models and their variations, to select their error probability laws. The author believes that GMPL and its variations would be quite promising for various model selection problems.     

An EM type estimation procedure for the destructive exponentially weighted Poisson regression cure model under generalized gamma lifetime

In this paper, we assume the number of competing causes to follow an exponentially weighted Poisson distribution. By assuming the initial number of competing causes can undergo destruction and that the population of interest has a cure fraction, we develop the EM algorithm for the determination of the MLEs of the model parameters of such a general cure model. This model is more flexible than the promotion time cure model and also provides an interesting and realistic interpretation of the biological mechanism of the occurrence of an event of interest. Instead of assuming a particular parametric distribution for the lifetime, we assume the lifetime to belong to the wider class of generalized gamma distribution. This allows us to carry out a model discrimination to select a parsimonious lifetime distribution that provides the best fit to the data. Within the EM framework, a two-way profile likelihood approach is proposed to estimate the shape parameters. An extensive Monte Carlo simulation study is carried out to demonstrate the performance of the proposed estimation method. Model discrimination is carried out by means of the likelihood ratio test and information-based methods. Finally, a data on melanoma is analyzed for illustrative purpose.     

Multiple-index varying-coefficient models for longitudinal data

In haemodialysis patients, vascular access type is of paramount importance. Although recent studies have found that central venous catheter is often associated with poor outcomes and switching to arteriovenous fistula is beneficial, studies have not fully elucidated how the effect of switching of access on outcomes changes over time for patients on dialysis and whether the effect depends on switching time. In this paper, we characterise the switching access type effect on outcomes for haemodialysis patients. This is achieved by using a new class of multiple-index varying-coefficient (MIVC) models. We develop a new estimation procedure for MIVC models based on local linear, profile least-square method and Cholesky decomposition. Monte Carlo simulation studies show excellent finite sample performance. Finally, we analyse the dialysis data using our method.     

A profile Godambe information of power transformations for ARCH time series

Due to Godambe (1985 Godambe, V.P. (1985). The foundation of finite sample estimation in stochastic processes. Biometrika 72:419–428.[Crossref], [Web of Science ®] , [Google Scholar]), one can obtain the Godambe optimum estimating functions (EFs) each of which is optimum (in the sense of maximizing the Godambe information) within a linear class of EFs. Quasi-likelihood scores can be viewed as special cases of the Godambe optimum EFs (see, for instance, Hwang and Basawa, 2011 Hwang, S.Y., Basawa, I.V. (2011). Godambe estimating functions and asymptotic optimal inference. Stat. Probab. Lett. 81:1121–1127.[Crossref], [Web of Science ®] , [Google Scholar]). The paper concerns conditionally heteroscedastic time series with unknown likelihood. Power transformations are introduced in innovations to construct a class of Godambe optimum EFs. A “best” power transformation for Godambe innovation is then obtained via maximizing the “profile” Godambe information. To illustrate, the KOrea Stock Prices Index is analyzed for which absolute value transformation and square transformation are recommended according to the ARCH(1) and GARCH(1,1) models, respectively.     

Phase I monitoring of social network with baseline periods using poisson regression

Social network analysis is an important analytic tool to forecast social trends by modeling and monitoring the interactions between network members. This paper proposes an extension of a statistical process control method to monitor social networks by determining the baseline periods when the reference network set is collected. We consider probability density profile (PDP) to identify baseline periods using Poisson regression to model the communications between members. Also, Hotelling T² and likelihood ratio test (LRT) statistics are developed to monitor the network in Phase I. The results based on signal probability indicate a satisfactory performance for the proposed method.     

Simultaneous confidence interval construction for many-to-one comparisons of proportion differences based on correlated paired data

In some medical researches such as ophthalmological, orthopaedic and otolaryngologic studies, it is often of interest to compare multiple groups with a control using data collected from paired organs of patients. The major difficulty in performing the data analysis is to adjust the multiplicity between the comparison of multiple groups, and the correlation within the same patient''s paired organs. In this article, we construct asymptotic simultaneous confidence intervals (SCIs) for many-to-one comparisons of proportion differences adjusting for multiplicity and the correlation. The coverage probabilities and widths of the proposed CIs are evaluated by Monte Carlo simulation studies. The methods are illustrated by a real data example.