In this review article, we revisit derivation of the cumulative density function (CDF) of the test statistic of the one-sample Kolmogorov-Smirnov test. Even though several such proofs already exist, they often leave o...In this review article, we revisit derivation of the cumulative density function (CDF) of the test statistic of the one-sample Kolmogorov-Smirnov test. Even though several such proofs already exist, they often leave out essential details necessary for proper understanding of the individual steps. Our goal is filling in these gaps, to make our presentation accessible to advanced undergraduates. We also propose a simple formula capable of approximating the exact distribution to a sufficient accuracy for any practical sample size.展开更多
In this article, we study the Kolmogorov-Smirnov type goodness-of-fit test for the inhomogeneous Poisson process with the unknown translation parameter as multidimensional parameter. The basic hypothesis and the alter...In this article, we study the Kolmogorov-Smirnov type goodness-of-fit test for the inhomogeneous Poisson process with the unknown translation parameter as multidimensional parameter. The basic hypothesis and the alternative are composite and carry to the intensity measure of inhomogeneous Poisson process and the intensity function is regular. For this model of shift parameter, we propose test which is asymptotically partially distribution free and consistent. We show that under null hypothesis the limit distribution of this statistic does not depend on unknown parameter.展开更多
Let X<sub>1</sub>, X<sub>2</sub>, … be i. i. d. random vectors defined on a probability space （Ω, τ, P ） and take values in P<sup>p</sup> （p≥1 ） with common law P. We can co...Let X<sub>1</sub>, X<sub>2</sub>, … be i. i. d. random vectors defined on a probability space （Ω, τ, P ） and take values in P<sup>p</sup> （p≥1 ） with common law P. We can construct PP Kolmogorov-Smimov statistics as follows by the projection pursuit （abbreviated to PP ）method:展开更多
文摘In this review article, we revisit derivation of the cumulative density function (CDF) of the test statistic of the one-sample Kolmogorov-Smirnov test. Even though several such proofs already exist, they often leave out essential details necessary for proper understanding of the individual steps. Our goal is filling in these gaps, to make our presentation accessible to advanced undergraduates. We also propose a simple formula capable of approximating the exact distribution to a sufficient accuracy for any practical sample size.
文摘In this article, we study the Kolmogorov-Smirnov type goodness-of-fit test for the inhomogeneous Poisson process with the unknown translation parameter as multidimensional parameter. The basic hypothesis and the alternative are composite and carry to the intensity measure of inhomogeneous Poisson process and the intensity function is regular. For this model of shift parameter, we propose test which is asymptotically partially distribution free and consistent. We show that under null hypothesis the limit distribution of this statistic does not depend on unknown parameter.
文摘Let X<sub>1</sub>, X<sub>2</sub>, … be i. i. d. random vectors defined on a probability space （Ω, τ, P ） and take values in P<sup>p</sup> （p≥1 ） with common law P. We can construct PP Kolmogorov-Smimov statistics as follows by the projection pursuit （abbreviated to PP ）method:
