Assessing and Improving the Performance of Nearly Efficient Unit Root Tests in Small Samples

Abstract

The development of unit root tests continues unabated, with many recent contributions using techniques such as generalized least squares (GLS) detrending and recursive detrending to improve the power of the test. In this article, the relation between the seemingly disparate tests is demonstrated by algebraically nesting all of them as ratios of quadratic forms in normal variables. By doing so, and using the exact sampling distribution of the ratio, it is straightforward to compute, examine, and compare the test' critical values and power functions. It is shown that use of GLS detrending parameters other than those recommended in the literature can lead to substantial power improvements. The open and important question regarding the nature of the first observation is addressed. Tests with high power are proposed irrespective of the distribution of the initial observation, which should be of great use in practical applications.     

Probability density function of quotient of order statistics from the pareto,power and weibull distributions

This paper deals with the probability density functions of quotient of order statistics. We use the Mellin transform technique, to find the distribution of the quotient Z= X/Xwhere X.,X(i < j) are the ith and jth order statistics from the Pareto, Power and Weibull distributions     

An approximation for the hotelling-lawley trace in the noncentral case

A procedure for estimating power in conjunction with the Hotelling-Lawley trace is developed. By approximating a non-central Wishart distribution with a central Wishart, and using McKeon's (1974) F-type approximation, a relatively simple procedure for obtaining power estimates is obtained. The accuracy of the approximation is investigated by comparing the approximate results with those for a wide range of conditions given in Olson's (1973) extensive Monte Carlo study. Siotani's (1971) asymptotic expansion is used to provide further comparative assessments. It is demonstrated that the approximation is of sufficient accuracy to be used in practical applications.     

A computational investigation of conover's kolmogorov-smirnov test for discrete distributions

The tabled significance values of the Kolmogorov-Smirnov goodness-of-fit statistic determined for continuous underlying distributions are conservative for applications involving discrete underlying distributions. Conover (1972) proposed an efficient method for computing the exact significance level of the Kolmogorov-Smirnov test for discrete distributions; however, he warned against its use for large sample sizes because “the calculations become too difficult.”

In this work we explore the relationship between sample size and the computational effectiveness of Conover's formulas, where “computational effectiveness” is taken to mean the accuracy attained with a fixed precision of machine arithmetic. The nature of the difficulties in calculations is pointed out. It is indicated that, despite these difficulties, Conover's method of computing the Kolmogorov-Smirnov significance level for discrete distributions can still be a useful tool for a wide range of sample sizes.     

On the use of the scholz-sievers method for dlstribution-free inference about the difference in slopes of two regression lines

A simple adaptation of a distribution-free method due to Scholz (1978) and Sievers (1978) for inference in a single regression setting is proposed for inference about the difference in slopes of two regression lines. We assume that the data are obtained from a designed experiment with common regression constants. A comparison of the proposed method to its competitors-one due to Hollander and the other due to Rao and Gore-indicates superiority of the new method.     

Locating “youth voice:” Considering the contexts of speaking in foster care

Within social services, an increasingly significant movement supports giving “voice” to children and youth, enabling them to express their views and to have those views taken into account in matters that affect them. In this article, the author draws from narratives of young people who grew up in foster care, examining stories of their efforts to impact the course of their own lives. The article explores the ways that very specific contexts and relationships of power shaped the utterances of young people in the foster care system and distorted, muted, or amplified their abilities to express their need and interests. This is a beginning attempt to identify ways that contexts of speaking in foster care can be understood and altered in order to strengthen the capacity of young people to voice their concerns and aspirations.     

Linearity of regression for non-adjacent record values

Let X₁,X₂,… be a sequence of iid random variables having a continuous distribution; by R₁,R₂,… denote the corresponding record values. All the distributions allowing linearity of regressions either E(R_m+k|R_m) or E(R_m|R_m+k) are identified.     

要素所有者的谈判力与企业权益分配格局

在全面解释“谈判力”涵义的基础上,着重论证了谈判力与企业权益分配格局的关系,并据此提出了改进我国企业权益分配状况的建议。     

The finite-sample performance of robust unit root tests

This paper investigates the relative small sample performance of several robust unit root tests by means of a simulation study. It is confirmed that the traditional least-squares based Dickey-Fuller test has substantially lower power than several robust alternatives if the error distribution is fat-tailed while its power gain is small at the normal model. Particularly good results are achieved by a quasi-maximum likelihood test. However, all robust tests under consideration exhibit severe size distortions if the disturbances follow a skewed distribution. Moreover, under additive outliers, robust tests fail to produce stable sizes and good power properties. Consequently, the value of using robust unit root tests depends heavily of the type of nonnormality at hand.     

Tests for Equality of Parameters of Two Exponential Distributions with Common Known Coefficient of Variation

ABSTRACT

This article considers the problem of testing equality of parameters of two exponential distributions having common known coefficient of variation, both under unconditional and conditional setup. Unconditional tests based on BLUE'S and LRT are considered. Using the Conditionality Principle of Fisher, an UMP conditional test for one-sided alternative is derived by conditioning on an ancillary. This test is seen to be uniformly more powerful than unconditional tests in certain given ranges of ancillary. Simulation studies on the power functions of the tests are done for this purpose.