Asymptotic properties of maximum likelihood estimators based on progressive Type-II censoring

Hoadley (Ann Math Stat 42:1977–1991, 1971) studied the weak law of large numbers for independent and non-identically distributed random variables. Using that result along with the missing information principle, we establish the consistency and asymptotic normality of maximum likelihood estimators based on progressively Type-II censored samples.     

The asymptotic properties of maximum likelihood estimators for marked poisson processes with a cyclic intensity measure

In this paper we are concerned with the large sample behavior of the MLE for a class of marked Poisson processes arising in hydrology. We establish strong consistency, asymptotic normality and asymptotic efficiency of the MLE. As an application we present the asymptotic distribution of the design discharge of a river flow.     

Estimation of multiple poisson means: A compromise between maximum likelihood and empirical bayes estimators

For estimatingp(⩾ 2) independent Poisson means, the paper considers a compromise between maximum likelihood and empirical Bayes estimators. Such compromise estimators enjoy both good componentwise as well as ensemble properties. Research supported by the NSF Grant Number MCS-8218091.     

Inference robustness of ARIMA models under non-normality —Special application to stock price data

Wold's decomposition theorem [Wold] states that every weakly stationary stochastic process can be written as a linear combination of orthogonal shocks. For practical reasons, however, it is desirable to employ models which use parameters parsimoniously.Box andJenkins [1970] show how parsimony can be achieved by representing the linear process in terms of a small number of autoregressive and moving average terms (ARIMA-models). The Gaussian hypothesis assumes that the shocks follow a normal distribution with fixed mean and variance. In this case the process is characterized by first and second order moments. The normality assumption seems reasonable for many kinds of series. However, it was pointed out byKendall [1953],Mandelbrot [1963, 1967],Fama [1965],Mandelbrot andTaylor [1967] that particularly for stock price data the distribution of the shocks appears leptokurtic: In this paper we investigate the sensitivity of ARIMA models to non-normality of the distribution of the shocks. We suppose that the distribution function of the shocks is a member of the symmetric exponential power family, which includes the normal as well as leptokurtic and platikurtic distributions. A Bayesian approach is adopted and the inference robustness of ARIMA models with respect to

1. the estimation of parameters
2. the forecasts of future observations is discussed.

     

Nearly-singular design in GMM and generalized empirical likelihood estimators

Nearly-Singular design relaxes the nonsingularity assumption of the limit weight matrix in GMM, and the nonsingularity of the limit variance matrix for the first order conditions in GEL. The sample versions of these matrices are nonsingular, but in large samples we assume these sample matrices converge to a singular matrix. This can result in size distortions for the overidentifying restrictions test and large bias for the estimators. This nearly-singular design may occur because of the similar instruments in these matrices. We derive the large sample theory for GMM and GEL estimators under nearly-singular design. The rate of convergence of the estimators is slower than root n$n$.     

Goodness of fit in confirmatory factor analysis: The effects of sample size and model parsimony

The purpose of the present investigation is to examine the influence of sample size (N) and model parsimony on a set of 22 goodness-of-fit indices including those typically used in confirmatory factor analysis and some recently developed indices. For sample data simulated from two known population data structures, values for 6 of 22 fit indices were reasonably independent ofN and were not significantly affected by estimating parameters known to have zero values in the population: two indices based on noncentrality described by McDonald (1989; McDonald and Marsh, 1990), a relative (incremental) index based on noncentrality (Bentler, 1990; McDonald & Marsh, 1990), unbiased estimates of LISREL's GFI and AGFI (Joreskog & Sorbom, 1981) presented by Steiger (1989, 1990) that are based on noncentrality, and the widely known relative index developed by Tucker and Lewis (1973). Penalties for model complexity designed to control for sampling fluctuations and to address the inevitable compromise between goodness of fit and model parsimony were evaluated.     

Polychoric versus Pearson correlations in exploratory and confirmatory factor analysis of ordinal variables

Given that the use of Likert scales is increasingly common in the field of social research it is necessary to determine which methodology is the most suitable for analysing the data obtained; although, given the categorization of these scales, the results should be treated as ordinal data it is often the case that they are analysed using techniques designed for cardinal measures. One of the most widely used techniques for studying the construct validity of data is factor analysis, whether exploratory or confirmatory, and this method uses correlation matrices (generally Pearson) to obtain factor solutions. In this context, and by means of simulation studies, we aim to illustrate the advantages of using polychoric rather than Pearson correlations, taking into account that the latter require quantitative variables measured in intervals, and that the relationship between these variables has to be monotonic. The results show that the solutions obtained using polychoric correlations provide a more accurate reproduction of the measurement model used to generate the data.     

Quick consistency of quasi-maximum likelihood estimators in a multivariate poisson process

Recent results by the present author on quick consistency of quasi-maximum likelihood estimators of parameters in a multivariate Poisson process are strengthened at the cost of replacing the inverse continuity assumption with the strong uniform identifiability condition.     

Cooperation and conflict among nations: An application of multi-sample confirmatory factor analysis

The measurement of cooperation and conflict among nations differs greatly among several empirical studies of international relations. In the multidimensional approach to the measurement of both concepts, cooperation and conflict are considered to be unmeasured traits of various indicators in different areas of interest. Insight into the validity of the measurement theory can be gained from the fit of the estimated measurement model and from the estimates of the unknown parameters. These estimates are obtained through confirmatory factor analysis of data on observable policy Indicators of both concepts (see e.g., Jöreskog, 1969). The reliability of the estimated model can be investigated by means of multi-sample confirmatory factor analysis, which allows one to fit a specified model to several data sets simultaneously. Maximum likelihood estimates of the unknown parameters of one-sample and multi-sample confirmatory factor analysis models, based on data available in COPDAB, can be obtained by using the LISREL-VI program (see Jöreskog and Sörbom (1986). The results indicate that cooperation and conflict in foreign policies of nations have de-escalating effects upon each other.     

The conditional maximum likelihood estimator of the shape parameter in the gamma distribution

Summary The conditional maximum likelihood estimator of the shape parameter in the gamma distribution is studied for a finite sample size in comparison with the (unconditional) maximum likelihood estimator. The former estimator is concluded to be strictly superior to the latter. The reasons for the conclusion include the undesirable behavior of the residual likelihood, the consistency and relatively less bias of the conditional maximum likelihood estimator. Simulation studies for risk comparisons also support the conclusion.     

On the robustness of location estimators in models of firm growth under heavy-tailedness

Focusing on the model of demand-driven innovation and spatial competition over time in Jovanovic and Rob (1987), we study the effects of the robustness of estimators employed by firms to make inferences about their markets on the firms’ growth patterns. We show that if consumers’ signals in the model are moderately heavy-tailed and the firms use the sample mean of the signals to estimate the ideal product, then the firms’ output levels exhibit positive persistence. In such a setting, large firms have an advantage over their smaller counterparts. These properties are reversed for signals with extremely heavy-tailed distributions. In such a case, the model implies anti-persistence in output levels, together with a surprising pattern of oscillations in firm sizes, with smaller firms being likely to become larger ones next period, and vice versa. We further show that the implications of the model under moderate heavy-tailedness continue to hold under the only assumption of symmetry of consumers’ signals if the firms use a more robust estimator of the ideal product, the sample median.     

Identification-commitment inventory (ICI model): confirmatory factor analysis and construct validity

The aim of this study is to confirm the factorial structure of the Identification-Commitment Inventory (ICI) developed within the frame of the Human System Audit (HSA) (Quijano et al. in Revist Psicol Soc Apl 10(2):27–61, 2000; Pap Psicól Revist Col Of Psicó 29:92–106, 2008). Commitment and identification are understood by the HSA at an individual level as part of the quality of human processes and resources in an organization; and therefore as antecedents of important organizational outcomes, such as personnel turnover intentions, organizational citizenship behavior, etc. (Meyer et al. in J Org Behav 27:665–683, 2006). The theoretical integrative model which underlies ICI Quijano et al. (2000) was tested in a sample (N = 625) of workers in a Spanish public hospital. Confirmatory factor analysis through structural equation modeling was performed. Elliptical least square solution was chosen as estimator procedure on account of non-normal distribution of the variables. The results confirm the goodness of fit of an integrative model, which underlies the relation between Commitment and Identification, although each one is operatively different.     

Maximum likelihood and restricted maximum likelihood estimation for a class of Gaussian Markov random fields

This work describes a Gaussian Markov random field model that includes several previously proposed models, and studies properties of its maximum likelihood (ML) and restricted maximum likelihood (REML) estimators in a special case. Specifically, for models where a particular relation holds between the regression and precision matrices of the model, we provide sufficient conditions for existence and uniqueness of ML and REML estimators of the covariance parameters, and provide a straightforward way to compute them. It is found that the ML estimator always exists while the REML estimator may not exist with positive probability. A numerical comparison suggests that for this model ML estimators of covariance parameters have, overall, better frequentist properties than REML estimators.     

Finite sample properties of maximum likelihood estimator in spatial models

We investigate the finite sample properties of the maximum likelihood estimator for the spatial autoregressive model. A stochastic expansion of the score function is used to develop the second-order bias and mean squared error of the maximum likelihood estimator. We show that the results can be expressed in terms of the expectations of cross products of quadratic forms, or ratios of quadratic forms in a normal vector which can be evaluated using the top order invariant polynomial. Our numerical calculations demonstrate that the second-order behaviors of the maximum likelihood estimator depend on the degree of sparseness of the weights matrix.     

Asymptotic normality of the maximum likelihood estimate in Markov processes

Summary In this note the asymptotic normality of the maximum likelihood estimate in a Markov process is established. The underlying process is assumed to be stationary and also to satisfy certain additional regularity conditions. The assumptions which are used herein are slightly different from those usually found in the literature and are less restrictive. This paper was prepared with the partial support of the National Science Foundation, Grant GP-6242.     

Development and validation of an Integrated Organizational Safety Climate Questionnaire with multilevel confirmatory factor analysis

Meta-analytic and traditional reviews on safety climate reveal theoretical and methodological safety climate issues still open. The main aim of this study is to propose a questionnaire which combines recent and different approaches to safety climate, trying to give a contribute about these issues. The present research led to the development of a new questionnaire to measure safety climate, suitable for blue-collar workers, and to the evaluation of its psychometric properties, and usefulness to measure safety climate in the industrial sector. Multilevel confirmatory factor analysis (MCFA) was used to properly evaluate the factor structure underlying the safety climate questionnaire composed of three scales: organizational safety climate scale, supervisor’s safety climate scale and co-workers’ safety climate scale. The clear distinction, made with the use of three different scales, among safety agents (organization, supervisor, co-workers), allows the assessment of workers’ perceptions focused on each level, and allows to deeply explore, for instance, lateral relationships of supervisor’s safety climate and co-workers’ safety climate, analysing the interactions between the roles of these two safety agents. A two-level design was used, considering the individual level and the work-group level. Data collection involved 1,617 blue-collars from eight Italian manufacturing companies. The MCFA results demonstrated the importance to use proper analysis to study the factor structure of a multilevel construct as safety climate, and confirmed the theoretical structure of safety climate purposed from Griffin and colleagues, using not only psychological climate (i.e., the individual level), but also the group level safety climate.     

A family of empirical likelihood functions and estimators for the binary response model

The minimum discrimination information principle is used to identify an appropriate parametric family of probability distributions and the corresponding maximum likelihood estimators for binary response models. Estimators in the family subsume the conventional logit model and form the basis for a set of parametric estimation alternatives with the usual asymptotic properties. Sampling experiments are used to assess finite sample performance.     

Asymptotic properties of the maximum likelihood estimator in dichotomous logit models

The existence and strong consistency of the maximum likelihood estimator are analyzed in the context of dichotomous logit models. Sufficient conditions are given for the asymptotic normality of this estimator.     

Constructing measures for school process variables: the potential of multilevel confirmatory factor analysis

This article investigates the potential of multilevel confirmatory factor analysis compared to using conventional confirmatory factor analysis, as regards the construction of measures for school process variables within educational effectiveness research. Since both techniques have not been systematically compared within educational research, we propose to contrast several aspects: factor structure, pattern of factor loadings, communalities of the indicators, variance extracted by the factors, internal consistency of the factors, and inter-factor correlations. To this end, teacher questionnaire data are used to construct measures for school process variables. Our results show no substantial differences when comparing both techniques at the teacher level. However, when contrasting the different levels within the more complex technique, we notice a fairly large discrepancy between the teacher-level results and the school-level results.