Mathematicshttp://hdl.handle.net/2022/134312018-07-17T17:18:11Z2018-07-17T17:18:11ZA multivariate Wald‐Wolfowitz rank test against serial dependencePuri, Madan L.Hallin, Marchttp://hdl.handle.net/2022/222652018-07-07T07:26:35Z1995-03-01T00:00:00ZA multivariate Wald‐Wolfowitz rank test against serial dependence
Puri, Madan L.; Hallin, Marc
Rank‐based cross‐covariance matrices, extending to the case of multivariate observed series the (univariate) rank autocorrelation coefficients introduced by Wald and Wolfowitz (1943), are considered. A permutational central limit theorem is established for the joint distribution of such matrices, under the null hypothesis of (multivariate) randomness as well as under contiguous alternatives of (multivariate) ARMA dependence. A rank‐based, permutationaily distribution‐free test of the portmanteau type is derived, and its asymptotic local power is investigated. Finally, a modified rank‐based version of Tiao and Box's model specification procedure is proposed, which is likely to be more reliable under non‐Gaussian conditions, and more robust against gross errors.
Publisher's, offprint version
1995-03-01T00:00:00ZAsymptotic normality of the lengths of a class of nonparametric confidence intervals for a regression parameterPuri, Madan L.Wu, Tiee‐Jianhttp://hdl.handle.net/2022/222642018-07-07T07:26:43Z1984-09-01T00:00:00ZAsymptotic normality of the lengths of a class of nonparametric confidence intervals for a regression parameter
Puri, Madan L.; Wu, Tiee‐Jian
In the linear regression model, the asymptotic distributions of certain functions of confidence bounds of a class of confidence intervals for the regression parameter arc investigated. The class of confidence intervals we consider in this paper are based on the usual linear rank statistics (signed as well as unsigned). Under suitable assumptions, if the confidence intervals are based on the signed linear rank statistics, it is established that the lengths, properly normalized, of the confidence intervals converge in law to the standard normal distributions; if the confidence intervals arc based on the unsigned linear rank statistics, it is then proved that a linear function of the confidence bounds converges in law to a normal distribution.
Publisher's, offprint version
1984-09-01T00:00:00ZAsymptotic Normality of Nearest Neighbor Regression Function Estimates Based on Nonstationary Dependent ObservationsHarel, MichelPuri, Madan L.http://hdl.handle.net/2022/222632018-07-07T07:26:37Z1995-01-01T00:00:00ZAsymptotic Normality of Nearest Neighbor Regression Function Estimates Based on Nonstationary Dependent Observations
Harel, Michel; Puri, Madan L.
In this paper the convergence of the regression function estimators and the central limit theorem for these estimators are proved for the case when the underlying sequence of random variables is dependent and nonstationary.
Offprint, publisher's version
1995-01-01T00:00:00ZSome distribution-free k-sample rank tests of homogeneity against ordered alternativesPuri, Madan L.http://hdl.handle.net/2022/221992018-06-15T08:15:21Z1965-05-01T00:00:00ZSome distribution-free k-sample rank tests of homogeneity against ordered alternatives
Puri, Madan L.
A problem which occurs frequently in statistical analysis is that of deciding whether several samples should be regarded as coming from the same population. This problem, usually referred to as the k-sample problem, when expressed formally is stated as follows: Let $X_{ii} , j = 1, · · · , m_i, i = 1, · · · , k,$ be a set of independent random variables and let $F_i(x)$ be the probability distribution function of $X_{ii}$ . The set of admissible hypotheses designates that each $F_i$ belongs to some class of distribution functions $\Omega$.
Publisher's, offprint version.
1965-05-01T00:00:00Z