Computation of Limit Distributions of Statistics for Normality Tests of Type $\omega ^2 $

Martynov, G. V.

doi:10.1137/1121001

Cited by 9 publications

(4 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Of course, this problem becames much more complicate than the first one with the simple basic hypothesis. More about GoF tests can be found, e.g., [12], [13] or any other book on this subject. Another possibility is to find such transformormation L [U n ] of the statis-…”

Section: Introductionmentioning

confidence: 99%

On asymptotically distribution free tests with parametric hypothesis for ergodic diffusion processes

Kleptsyna

Kutoyants

2014

Stat Inference Stoch Process

View full text Add to dashboard Cite

We consider the problem of the construction of the asymptotically distribution free test by the observations of ergodic diffusion process. It is supposedd that under the basic hypothesis the trend coefficient depends on the finite dimensional parameter and we study the Cramér-von Mises type statistics. The underlying statistics depends on the deviation of the local time estimator from the invariant density with parameter replaced by the maximum likelihood estimator. We propose a linear transformation which yields the convergence of the test statistics to the integral of Wiener process. Therefore the test based on this statistics is asymptotically distribution free.MSC 2000 Classification: 62M02, 62G10, 62G20.

show abstract

Section: Introductionmentioning

confidence: 99%

On asymptotically distribution free tests with parametric hypothesis for ergodic diffusion processes

Kleptsyna

Kutoyants

2014

Stat Inference Stoch Process

View full text Add to dashboard Cite

show abstract

“…[32,) to invert numerically a finite product approximation of the righthand side of (1.9) leading to the desired values of P(J 2 x), for specified choices of x. For related methods of the kind, refer to [30,38,39] (see Remark 2.1 in the sequel). This, in turn, requires a prior explicit knowledge of the eigenvalues {λ k : k 1}, which are implicit in terms of…”

Section: A Probabilist Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

“…A general description of the numerical methods which may be used to evaluate the above quantities, is to be found in [38][39][40] and [18]. The approach which has been followed here for the computation of the constants in Table 1 is based on the Smirnov formula [50,51]…”

Section: Remark 21mentioning

confidence: 99%

A Karhunen–Loeve decomposition of a Gaussian process generated by independent pairs of exponential random variables

Deheuvels

Martynov

2008

Journal of Functional Analysis

View full text Add to dashboard Cite

We obtain the explicit Karhunen-Loeve decomposition of a Gaussian process generated as the limit of an empirical process based upon independent pairs of exponential random variables. The orthogonal eigenfunctions of the covariance kernel have simple expressions in terms of Jacobi polynomials. Statistical applications, in extreme value and reliability theory, include a Cramér-von Mises test of bivariate independence, whose null distribution and critical values are tabulated.

show abstract

“…< (1 -|/>|) -1 lim sup n -1 E|e.| = (1 -|p|) -1 E|e|, a.s.. The first inequality above and (al) in turn imply that(13) n" 1 / 2 max 1^1=0^1).By (a2), f and q are uniformly continuous. Hence, by(13),…”

mentioning

confidence: 86%

Weak Convergence of a Weighted Residual Empirical Process in Autoregression

Koul¹,

Sen²

1991

Statistics &Amp; Risk Modeling

View full text Add to dashboard Cite

This paper proves the weak convergence of certain randomly weighted residual empirical processes in the first order autoregression model to a continuous Gaussian process. The result is used to derive the asymptotic uniform linearity of the given processes and of certain class of linear rank statistics based on the residuals in the estimated parameters. These latter results are used to study the asymptotic behavior of certain goodness-offit tests and R-estimators of the autoregression parameter.

show abstract

Computation of Limit Distributions of Statistics for Normality Tests of Type $\omega ^2 $

Cited by 9 publications

References 5 publications

On asymptotically distribution free tests with parametric hypothesis for ergodic diffusion processes

On asymptotically distribution free tests with parametric hypothesis for ergodic diffusion processes

A Karhunen–Loeve decomposition of a Gaussian process generated by independent pairs of exponential random variables

Weak Convergence of a Weighted Residual Empirical Process in Autoregression

Contact Info

Product

Resources

About