Financial liberalization and long-run stability of money demand in Nigeria

A stable money demand function is essential when using monetary aggregate as a monetary policy. Thus, there is need to examine the stability of the money demand function in Nigeria after the deregulation of the financial sector. To achieve this, the study employed CUSUM (cumulative sum) and CUSUMSQ (CUSUM of square) tests after using autoregressive distributive lag bounds test to determine the existence of a long run relationship between monetary aggregates and their determinants. Results of the study show that a long-run relationship holds and that the demand for money is stable in Nigeria. In addition, the inflation rate is found to be a better proxy for an opportunity variable when compared to interest rate. The main implication of the study is that interest rate is ineffective as a monetary policy instrument in Nigeria.     

An upper bound on the minimal total cost of the transportation problem with varying demands and supplies

In general cases, to find the exact upper bound on the minimal total cost of the transportation problem with varying demands and supplies is an NP-hard problem. In literature, there are only two approaches with several shortcomings to solve the problem. In this paper, the problem is formulated as a bi-level programming model, and proven to be solvable in a polynomial time if the sum of the lower bounds for all the supplies is no less than the sum of the upper bounds for all the demands; and a heuristic algorithm named TPVDS-A based on genetic algorithm is developed as an efficient and robust solution method of the model. Computational experiments on benchmark and new randomly generated instances show that the TPVDS-A algorithm outperforms the two existing approaches.     

Are the Order Statistics Ordered? A Survey of Recent Results

The distributions of coherent systems with components with exchangeable lifetimes can be represented as mixtures of distributions of order statistics (k-out-of-n systems) from possibly dependent samples by using the concept of the signature of Samaniego (1985 Samaniego , F. ( 1985 ). On closure of the IFR class under formation of coherent systems . IEEE Trans. Reliabil. R-34 : 69 – 72 .[Crossref], [Web of Science ®] , [Google Scholar]). This representation, together with Rychlik's (1993 Rychlik , T. ( 1993 ). Bounds for expectation of L-estimates for dependent samples . Statistics 24 : 1 – 7 .[Taylor & Francis Online] , [Google Scholar]) results, can be used to obtain sharp bounds on the distribution (or the reliability) function and on the expected lifetime of the system. Also, this representation can be used to determine the asymptotic behavior of the hazard rate of the system when the order statistics are ordered in the hazard rate order. Moreover, the lifetime distributions of coherent systems (and in particular, of order statistics) can also be represented as generalized mixtures (that is, mixtures with some negative weights) of distributions of series system lifetimes by using the concept of the minimal signature defined by Navarro et al. (2007a Navarro , J. , Ruiz , J. M. , Sandoval , C. J. ( 2007a ). Properties of coherent systems with dependent components . Commun. Statist. Theory Methods 36 : 175 – 191 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). This representation can also be used to determine the final behavior of the hazard rate of the system through the behavior of the hazard rate of the series systems. In particular, it can be used to show that the order statistics are, under some conditions, asymptotically hazard rate ordered. However, in general, this result is not true, that is, the order statistics need not be hazard rate ordered.     

Extensions of Samuelson's Inequality

In this note we obtain upper and lower bounds for the kth largest number in a set of real numbers in terms of their mean and standard deviation. For each inequality necessary and sufficient conditions for equality are given.     

More on Confidence Intervals for Partially Identified Parameters

This paper extends Imbens and Manski's (2004) analysis of confidence intervals for interval identified parameters. The extension is motivated by the discovery that for their final result, Imbens and Manski implicitly assumed locally superefficient estimation of a nuisance parameter. I reanalyze the problem both with assumptions that merely weaken this superefficiency condition and with assumptions that remove it altogether. Imbens and Manski's confidence region is valid under weaker assumptions than theirs, yet superefficiency is required. I also provide a confidence interval that is valid under superefficiency, but can be adapted to the general case. A methodological contribution is to observe that the difficulty of inference comes from a preestimation problem regarding a nuisance parameter, clarifying the connection to other work on partial identification.     

Bounds in Competing Risks Models and the War on Cancer

In 1971, President Nixon declared war on cancer. Thirty years later, many declared this war a failure: the age‐adjusted mortality rate from cancer in 2000 was essentially the same as in the early 1970s. Meanwhile the age‐adjusted mortality rate from cardiovascular disease fell dramatically. Since the causes that underlie cancer and cardiovascular disease are likely dependent, the decline in mortality rates from cardiovascular disease may partially explain the lack of progress in cancer mortality. Because competing risks models (used to model mortality from multiple causes) are fundamentally unidentified, it is difficult to estimate cancer trends. We derive bounds for aspects of the underlying distributions without assuming that the underlying risks are independent. We then estimate changes in cancer and cardiovascular mortality since 1970. The bounds for the change in duration until death for either cause are fairly tight and suggest much larger improvements in cancer than previously estimated.     

Using information on realized effects to determine prospective causal effects

The potential outcomes approach to causal inference postulates that each individual has a number of possibly latent outcomes, each of which would be observed under a different treatment. For any individual, some of these outcomes will be unobservable or counterfactual. Information about post-treatment characteristics sometimes allows statements about what would have happened if an individual or group with these characteristics had received a different treatment. These are statements about the realized effects of the treatment. Determining the likely effect of an intervention before making a decision involves inference about effects in populations defined only by characteristics observed before decisions about treatment are made. Information on realized effects can tighten bounds on these prospectively defined measures of the intervention effect. We derive formulae for the bounds and their sampling variances and illustrate these points with data from a hypothetical study of the efficacy of screening mammography.     

Probabilities and moments of generalized discrete distributfons using finite difference operators

The probabilities and factorial moments of the univar iate and multivariate generalized (or compound) discrete di st r-Lbut Lons with probability generating functions H(t)=F(G(t)) and H(t₁,…,t_k)=F(G(t₁,…,t_k))or H(t₁,…,t_k) = F(G₁(t₁),…, G_k( t_k)) are derived using finite difference operators.     

Lower confidence bounds for percentiles of weibull and birnbaum-saunders distributions

Approximate lower confidence bounds on percentiles of the Weibull and the Birnbaum-Saunders distributions are investigated. Asymptotic lower confidence bounds based on Bonferroni's inequality and the Fisher information are discussed, and parametric bootstrap methods to provide better bounds are considered. Since the standard percentile bootstrap method typically does not perform well for confidence bounds on quantiles, several other bootstrap procedures are studied via extensive computer simulations. Results of the simulations indicate that the bootstrap methods generally give sharper lower bounds than the Bonferroni bounds but with coverages still near the nominal confidence level. Two illustrative examples are also presented, one for tensile strength of carbon micro-composite specimens and the other for cycles-to-failure data.     

Some properties of discrete bathtub-shaped distributions

The existence and the usefulness of discrete bathtub-shaped and upside down bathtub-shaped distributions have been demonstrated in some papers of recent origin. However, the general properties of these two classes of distributions do not seem to have been discussed. This article proposes to study some reliability properties of such distributions. We investigate the closure properties with reference to convolution, mixing, series and parallel systems, etc. and existence of bounds on reliability functions, moment properties, and convergence.