In linear regression analysis, estimation of the regression parameters in measurement error model is considered in this paper. Methods of estimation have been proposed and improved in many literature. We give an approximated confidence region of regression parameters and examine the accuracy of approximation by simulation.

Aoshima and Yata [1] observed that classification accuracy of Euclidean distance-based classifiers have good performance at high dimensions. For practical use, it is necessary to estimate the misclassification probability using the training data set. Although cross-validation is usually used for such problems, it does not necessarily have good estimation accuracy at high dimension. In this paper, we propose a new estimator of misclassification probabilities at high-dimensional settings. Our estimator is obtained using the asymptotic multivariate normality of discriminant functions at high-dimensional settings. Finally, we numerically justify the high accuracy of our proposed estimator in finite sample applications, inclusive of high-dimensional scenarios.

For square contingency tables with ordered categories, Saigusa et al. (2018) proposed the marginal cumulative complementary log-log model being an extension of the marginal homogeneity model. The present paper considers the marginal cumulative complementary log-log and conditional marginal cumulative complementary log-log models for multi-way tables. It also gives the decompositions of the marginal homogeneity model into the proposed model and a model of the equality of marginal means for multi-way tables. An example is given.

This paper presents the holonomic properties and recurrence formula for the distribution of the sample correlation coefficient. The probability density function (pdf) is holonomic. Therefore, it is computed exactly based on the holonomic gradient method (HGM). The initial values for computation are expressed in terms of Gaussian hypergeometric functions with specific parameters that can be transformed to a rational equation of gamma functions. Using the integral algorithm in the $D$-module theory, the cumulative distribution function (cdf) is also holonomic. It can be computed using HGM. Next, we derive the recurrence formula for the Gaussian hypergeometric function related to the degrees of freedom and apply it to exact computation of the pdf under a fixed population correlation coefficient and increasing degrees of freedom. We conclude with discussion of the quantile function of the sample correlation coefficient which satisfies a nonlinear differential equation of second order.

We set the goal to study the properties of $LP$-Sasakian manifolds equipped with a quarter-symmetric non-metric connection. It is proved that the $LP$-Sasakian manifold endowed with a quarter-symmetric non-metric connection is partially Ricci semisymmetric with respect to the quarter-symmetric non-metric connection if and only if it is an $\eta$-Einstein manifold. We also study the properties of semisymmetric, Ricci recurrent $LP$-Sasakian manifolds and $\eta$-parallel Ricci tensor with respect to the quarter-symmetric non-metric connection. In the end, the non-trivial example of a $4$-dimensional $LP$-Sasakian manifold with a quarter-symmetric non-metric connection is given.