Testing for parameter constancy in the time series direction in panel data models

We propose tests for parameter constancy in the time series direction in panel data models. We construct a locally best invariant test based on Tanaka [Time series analysis: nonstationary and noninvertible distribution theory. New York: Wiley; 1996] and an asymptotically point optimal test based on Elliott and Müller [Efficient tests for general persistent time variation in regression coefficients. Rev Econ Stud. 2006;73:907–940]. We derive the limiting distributions of the test statistics as T→∞ while N is fixed, and calculate the critical values by applying numerical integration and response surface regression. Simulation results show that the proposed tests perform well if we apply them appropriately.     

Relabelling algorithms for mixture models with applications for large data sets

Mixture models are flexible tools in density estimation and classification problems. Bayesian estimation of such models typically relies on sampling from the posterior distribution using Markov chain Monte Carlo. Label switching arises because the posterior is invariant to permutations of the component parameters. Methods for dealing with label switching have been studied fairly extensively in the literature, with the most popular approaches being those based on loss functions. However, many of these algorithms turn out to be too slow in practice, and can be infeasible as the size and/or dimension of the data grow. We propose a new, computationally efficient algorithm based on a loss function interpretation, and show that it can scale up well in large data set scenarios. Then, we review earlier solutions which can scale up well for large data set, and compare their performances on simulated and real data sets. We conclude with some discussions and recommendations of all the methods studied.     

Existence,uniqueness and consistency of estimation of life characteristics of three-parameter Weibull distribution based on Type-II right censored data

In this paper, we propose a new method of estimation for the parameters and quantiles of the three-parameter Weibull distribution based on Type-II right censored data. The method, based on a data transformation, overcomes the problem of unbounded likelihood. In the proposed method, under mild conditions, the estimates always exist uniquely, and the estimators are also consistent over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method of estimation performs well compared to some prominent methods in terms of bias and root mean squared error in small-sample situations. Finally, two real data sets are used to illustrate the proposed method of estimation.     

Linear estimation for the extended exponential power distribution

Tiao and Lund [The use of OLUMV estimators in inference robustness studies of the location parameter of a class of symmetric distributions. J Amer Statist Assoc. 1970;65(329):370–386] tabulated the coefficients of the best linear unbiased estimators (BLUEs) of location and scale for a particular family of symmetric distributions. This family was a reparameterization of the extended exponential power distribution (EEPD) with the shape parameter restricted to be greater than or equal to one. In this work, we consider the BLU estimation of the location and scale parameters of the EEPD when the shape parameter is one-third and one-half. We obtain closed-form expressions for the single and product moments of the order statistics when the shape parameter is in general in the form of a reciprocal of an integer. These expressions are then used to determine the BLUEs and the corresponding variances for complete samples of size 20 and less. We consider some other linear estimators of the location and scale parameters and then compare them with the BLUEs. Finally, we present a numerical example to illustrate the developed results.     

Estimation of parameters of SDE driven by fractional Brownian motion with polynomial drift

ABSTRACT

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of the underlying processes.     

Quasi-complete separation in random effects of binary response mixed models

ABSTRACT

Clustered observations such as longitudinal data are often analysed with generalized linear mixed models (GLMM). Approximate Bayesian inference for GLMMs with normally distributed random effects can be done using integrated nested Laplace approximations (INLA), which is in general known to yield accurate results. However, INLA is known to be less accurate for GLMMs with binary response. For longitudinal binary response data it is common that patients do not change their health state during the study period. In this case the grouping covariate perfectly predicts a subset of the response, which implies a monotone likelihood with diverging maximum likelihood (ML) estimates for cluster-specific parameters. This is known as quasi-complete separation. In this paper we demonstrate, based on longitudinal data from a randomized clinical trial and two simulations, that the accuracy of INLA decreases with increasing degree of cluster-specific quasi-complete separation. Comparing parameter estimates by INLA, Markov chain Monte Carlo sampling and ML shows that INLA increasingly deviates from the other methods in such a scenario.     

Estimates of the quantiles of kendall's partial rank correlation coefficient

The sampling distribution of kendall's partial rank correlation coefficient, J_xy?z, is not known for N>4, where N is the number of subjectts. Moran (1951) used a direcr conbinatorial method to obtain the distribution of J_xy?z forN=4; however, ten minor computationa; errors in his Table 2apparently resulted in how erroneous entries for his frequency table. Since the parctial limits of the direct combinatorial approach have been reached once N>4, the first main objective of this paper was to obtain the exact distribution of J_xy?z for N=f, 6, and 7 using an electronic computer. The second was to use the Monte Carlo method to obtain reliable estimates of the quantiles of J_xy?z for N=8,9,...,30     

A comparison of maximum likelihood and least squares for the estimation of a cumulative distribution

Monte Carlo methods are used to compare the methods of maximum likelihood and least squares to estimate a cumulative distribution function. When the probabilistic model used is correct or nearly correct, the two methods produce similar results with the MLE usually slightly superior When an incorrect model is used, or when the data is contaminated, the least squares technique often gives substantially superior results.