A nonparametric test for trend based on initial ranks

Hofmann, Glenn; Balakrishnan, Nagraj

doi:10.1080/10629360600564924

Cited by 9 publications

(11 citation statements)

References 6 publications

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“…Compared with the nonparametric test statistics in Hofmann and Balakrishnan (2006) (see Appendix B TableB.1), which require the whole data set, the proposed test achieves much higher power by using only one-quarter of the full data set under the normal distribution assumption. Chapter 5 Illustrative Example…”

Section: Results and Commentsmentioning

confidence: 99%

“…Compared with the tests in Hofmann and Balakrishnan (2006) (see Appendix B Table B.3), the proposed test statistic shows smaller p values in 4 out of 7 cases for n = 12 and smaller p values in all the cases for n = 24, and hence appears to be better able to detect the trend in the latter case for this data set. Note that we only use at most one-quarter of the data for n = 12 and one-half of the data for n = 24 in each interval to calculate the values of the test statistic.…”

Section: Median P-valuesmentioning

confidence: 98%

“…For the purpose of comparison, we use the data set presented in Hofmann and Balakrishnan (2006), which is originally from Box et al (1994). Figure 5.1 presents the data set of monthly averages of hourly ozone readings in downtown Los Angeles during the period [1955][1956][1957][1958][1959][1960][1961][1962][1963][1964][1965][1966][1967][1968][1969][1970][1971][1972].…”

Section: Ozone Datamentioning

confidence: 99%

“…When using the complete data set, all test statistics in Hofmann and Balakrishnan (2006) 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 …”

Section: Ozone Datamentioning

confidence: 99%

“…Linear, logarithmic and polynomial trends are the most commonly considered ones (Hofmann and Balakrishnan, 2006). …”

Section: What Is the Typical Form Of Trend?mentioning

confidence: 99%

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A parametric test for trend based on moving order statistics

Tan

2015

Journal of Statistical Computation and Simulation

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When researchers work on time series or sequence, certain fundamental questions will naturally arise. One of them will be whether the series or sequence exhibits a gradual trend over time. In this thesis, we propose a test statistic based on moving order statistics and establish an exact procedure to test for the presence of monotone trends. We show that the test statistic under the null hypothesis that there is no trend follows the closed skew normal distribution. An efficient algorithm is then developed to generate realizations from this null distribution. A simulation study is conducted to evaluate the proposed test under the alternative hypotheses with linear, logarithmic and quadratic trend functions. Finally, a practical example is provided to illustrate the proposed test procedure.

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Section: Results and Commentsmentioning

confidence: 99%

Section: Median P-valuesmentioning

confidence: 98%

Section: Ozone Datamentioning

confidence: 99%

“…When using the complete data set, all test statistics in Hofmann and Balakrishnan (2006) 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 …”

Section: Ozone Datamentioning

confidence: 99%

“…Linear, logarithmic and polynomial trends are the most commonly considered ones (Hofmann and Balakrishnan, 2006). …”

Section: What Is the Typical Form Of Trend?mentioning

confidence: 99%

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