The effects of sampling strategies on the small sample properties of the logit estimator

Empirical researchers face a trade-off between the lower resource costs associated with smaller samples and the increased confidence in the results gained from larger samples. Choice of sampling strategy is one tool researchers can use to reduce costs yet still attain desired confidence levels. This study uses Monte Carlo simulation to examine the impact of nine sampling strategies on the finite sample performance of the maximum likelihood logit estimator. The results show stratified random sampling with balanced strata sizes and a bias correction for choice-based sampling outperforms all other sampling strategies with respect to four small-sample performance measures.     

Acceleration of the Multiple-Try Metropolis algorithm using antithetic and stratified sampling

The Multiple-Try Metropolis is a recent extension of the Metropolis algorithm in which the next state of the chain is selected among a set of proposals. We propose a modification of the Multiple-Try Metropolis algorithm which allows for the use of correlated proposals, particularly antithetic and stratified proposals. The method is particularly useful for random walk Metropolis in high dimensional spaces and can be used easily when the proposal distribution is Gaussian. We explore the use of quasi Monte Carlo (QMC) methods to generate highly stratified samples. A series of examples is presented to evaluate the potential of the method.     

Computing the conditional stationary distribution in Markov chains of level-dependent M/G/1-type

This paper considers the computation of the conditional stationary distribution in Markov chains of level-dependent M/G/1-type, given that the level is not greater than a predefined threshold. This problem has been studied recently and a computational algorithm is proposed under the assumption that matrices representing downward jumps are nonsingular. We first show that this assumption can be eliminated in a general setting of Markov chains of level-dependent G/G/1-type. Next we develop a computational algorithm for the conditional stationary distribution in Markov chains of level-dependent M/G/1-type, by modifying the above-mentioned algorithm slightly. In principle, our algorithm is applicable to any Markov chain of level-dependent M/G/1-type, if the Markov chain is irreducible and positive-recurrent. Furthermore, as an input to the algorithm, we can set an error bound for the computed conditional distribution, which is a notable feature of our algorithm. Some numerical examples are also provided.     

Fatal shortcomings of stationary AR (1) exogeneous variables in econometric monte carlo tudies of estimators

The paper first shows that the stationary normal AR(1) process (SNAR1), the most frequently used process for generating exogenous variables in econometric Monte Carlo studies, cannot generate realistic exogenous variables, which are generally trended and similar to those generated by ARIMA (p,d,q) process withd≧1 and positive drift (trend). Then, it illustrates that in the context of AR(1) disturbances,trends in exogenous variables can frequently alter the very ranking of two competing estimators, the ordinary least squares estimator (OLS) and the Cochrane-Orcutt estimators (CO). For three common econometric models—a standard regression model, a dynamic model (i.e., a model with a lagged dependent variable), and a seemingly unrelated regression model, OLS becomes superior in many cases. This is so in spite of the fact that the CO estimator in the study utilizes the true value of the first-order autocorrelation coefficient of the disturbances. The message to be derived from these findings should be ccear. If one accepts the fact that most if not all economic time series are trended, and endorses a proposition that the fundamental if not sole purpose of Monte Carlo studies in econometrics should be to provide useful guidelines to practicing econometricians, then, he must not employ SNARl (nor anyother artificially created nontrended series) as a generator of exogenous variables in a Monte Carlo study, at least in the econometrics of autocorrelated disturbances. Alternative methods of generating stochastic exogenous variables that are trended are suggested in the paper. For almost four decades, the principle of the autoregressive transformation of a regression model with first-order autocorrelated disturbances (the Coestimation priciple) has been taken for granted as a method of correcting for the autocorrelation in the disturbances—be it in the two-stage Cochrane—Orcutt estimator, the iterative Cochrane-Orcutt estimator, or an estimator utilizing nonlinear techniques or search procedures. (Comitting the first observation due to transformation is not considered very crucial in general.) The results of the pertinent Monte Carlo studies appear to justify such a procedure only because most studies have employed SNARl exogenous variables, not trended ones. Thus, Monte Carlo experimenters must be blamed, at least partially, for this prevailining malpractice. It is hoped that they will not commit additional sins by not using realistic data in their future experiments.     

Bayesian estimation for the M/G/1 queue using a phase-type approximation

This article deals with Bayesian inference and prediction for M/G/1 queueing systems. The general service time density is approximated with a class of Erlang mixtures which are phase-type distributions. Given this phase-type approximation, an explicit evaluation of measures such as the stationary queue size, waiting time and busy period distributions can be obtained. Given arrival and service data, a Bayesian procedure based on reversible jump Markov Chain Monte Carlo methods is proposed to estimate system parameters and predictive distributions.     

The analysis of unreliable M[X]/G/1 queuing system with loss,vacation and two delays of verification

This paper considers an M^[X]/G/1 queue with breakdowns, repair, Bernoulli vacation, two delays and geometric loss. In this paper, a special attention is given to the limiting distribution of system states. We obtain simplified expressions for the Probability Generating Functions (PGFs) of the joint distribution of server state and system size. Some performance measures were derived from the analysis of the steady state probabilities. PGF of a departure point system size distribution is developed. Particular cases of the studied system were investigated. The effect of system parameters on the main performance measures are illustrated and discussed.     

Comment on basic structure of the asymptotic theory in dynamic nonlinear econometric models

In this paper we compare the performance of the exogeneity tests of Revankar, Revankar and Hartley and Wu-Hausman for the cases of two and three included endogenous variables. The distribution and power functions are evaluated using the conditional distributions given in Kariya and Hodoshima. Our results indicate that the Revankar's test is the most powerful for large values of the concentration parameter and the Revankar and Hartley test is the most powerful for small values of the concentration parameter.     

Relative efficiency of a parameter for a M/G/1 queueing system based on reduced and full likelihood functions

The present paper derives the relative efficiency of a parameter for the M/G/1 queueing system based on reduced and full likelihood functions. Monte Carlo simulations were carried out to study the finite sample properties for estimating the parameters of a M/G/1 queueing system. The simulation runs were conducted using various traftic intensities with increaseing sample sizes. The simulation results indicate that the loss in efficiency is quite small due to the use of a reduced likelihood function approach for estimating the parameter instead of the full likelihood, even for a moderate sample size of 50     

Error-rate estimation in two-group discriminant analysis using the linear discriminant function

Fisher's linear discriminant function, adapted by Anderson for allocating new observations into one of two existing groups, is considered in this paper. Methods of estimating the misclassification error rates are reviewed and evaluated by Monte Carlo simulations. The investigation is carried out under both ideal (Multivariate Normal data) and non-ideal (Multivariate Binary data) conditions. The assessment is based on the usual mean square error (MSE) criterion and also on a new criterion of optimism. The results show that although there is a common cluster of good estimators for both ideal and non-ideal conditions, the single best estimators vary with respect to the different criteria     

Detecting a Change in the Correlation Coefficient in a Sequence of Bivariate Normal Variables

We consider the problem of testing the hypothesis that the correlation coefficient is stable in a sequence of n observations of independent, bivariate normal random variables against the alternative that the correlation coefficient changes after an unknown point t(t < n). We propose an estimate of the changepoint t and report on power comparisons between the commonly used test for this problem and our proposed test. Some applications to finance are discussed.     

C73. The diminishing significance of a p-value as the sample size increases

Barnard (1963), Birnbaum (1974), and others have proposed exact inference procedures based on simulation. This article surveys existing results in this general area and fills several important holes, addressing philosophical problems and the matter of determining a simulation size. Applications to multiple comparisons, sequential analysis, and statistical consulting are discussed.     

Bayesian inference in the triangular cointegration model using a jeffreys prior

This paper presents a strategy for conducting Bayesian inference in the triangular cointegration model. A Jeffreys prior is used to circumvent an identification problem in the parameter region in which there is a near lack of cointegration. Sampling experiments are used to compare the repeated sampling performance of the approach with alternative classical cointegration methods. The Bayesian procedure is applied to testing for substitution between private and public consumption for a range of countries, with posterior estimates produced via Markov Chain Monte Carlo simulators.     

Estimations of the parameter of a Dirichlet distribution using residual allocation model representations and sampling properties

Estimating the parameter of a Dirichlet distribution is an interesting question since this distribution arises in many situations of applied probability. Classical procedures are based on sample of Dirichlet distribution. In this paper we exhibit five different estimators from only one observation. They are based either on residual allocation model decompositions or on sampling properties of Dirichlet distributions. Two ways are investigated: the first one uses fragments’ size and the second one uses size-biased permutations of a partition. Numerical computations based on simulations are supplied. The estimators are finally used to estimate birth probabilities per month.     

Spatial sampling in the presence of a trend

The spatial sampling designs suggested by Quenouille (1949) are investigated under a number of trend assumptions, namely a linear trend, linear trend and periodic variation, and spatially correlated populations. The results obtained provide a planar analogue to the one-dimensional results appearing in Cochram (1977, Ch. ε). Centrally located systematic sampling and the planar analogue of Yates' (1948) method of end corrections are put forward as methods which eliminate the linear trend. The comparisons of the two methods provide the planar analogue to results obtained by Bellhouse and Rao (1975).