Abstract: The purpose of this article is to find a method
of comparing designs for ordinal regression models using
quantile dispersion graphs in the presence of linear predictor
misspecification. The true relationship between response variable
and the corresponding control variables are usually unknown.
Experimenter assumes certain form of the linear predictor of the
ordinal regression models. The assumed form of the linear predictor
may not be correct always. Thus, the maximum likelihood estimates
(MLE) of the unknown parameters of the model may be biased due to
misspecification of the linear predictor. In this article, the uncertainty
in the linear predictor is represented by an unknown function. An
algorithm is provided to estimate the unknown function at the
design points where observations are available. The unknown function
is estimated at all points in the design region using multivariate
parametric kriging. The comparison of the designs are based on
a scalar valued function of the mean squared error of prediction
(MSEP) matrix, which incorporates both variance and bias of the
prediction caused by the misspecification in the linear predictor. The
designs are compared using quantile dispersion graphs approach.
The graphs also visually depict the robustness of the designs on the
changes in the parameter values. Numerical examples are presented
to illustrate the proposed methodology.
Abstract: The log periodogram regression is widely used in empirical
applications because of its simplicity, since only a least squares
regression is required to estimate the memory parameter, d, its good
asymptotic properties and its robustness to misspecification of the
short term behavior of the series. However, the asymptotic distribution
is a poor approximation of the (unknown) finite sample distribution
if the sample size is small. Here the finite sample performance of different
nonparametric residual bootstrap procedures is analyzed when
applied to construct confidence intervals. In particular, in addition to
the basic residual bootstrap, the local and block bootstrap that might
adequately replicate the structure that may arise in the errors of the
regression are considered when the series shows weak dependence in
addition to the long memory component. Bias correcting bootstrap
to adjust the bias caused by that structure is also considered. Finally,
the performance of the bootstrap in log periodogram regression based
confidence intervals is assessed in different type of models and how
its performance changes as sample size increases.
Abstract: Martingale model diagnostic for assessing the fit of logistic regression model to recurrent events data are studied. One way of assessing the fit is by plotting the empirical standard deviation of the standardized martingale residual processes. Here we used another diagnostic plot based on martingale residual covariance. We investigated the plot performance under several types of model misspecification. Clearly the method has correctly picked up the wrong model. Also we present a test statistic that supplement the inspection of the two diagnostic. The test statistic power agrees with what we have seen in the plots of the estimated martingale covariance.
Abstract: This paper examines many mathematical methods for
molding the hourly price forward curve (HPFC); the model will be
constructed by numerous regression methods, like polynomial
regression, radial basic function neural networks & a furrier series.
Examination the models goodness of fit will be done by means of
statistical & graphical tools. The criteria for choosing the model will
depend on minimize the Root Mean Squared Error (RMSE), using the
correlation analysis approach for the regression analysis the optimal
model will be distinct, which are robust against model
misspecification. Learning & supervision technique employed to
determine the form of the optimal parameters corresponding to each
measure of overall loss. By using all the numerical methods that
mentioned previously; the explicit expressions for the optimal model
derived and the optimal designs will be implemented.
Abstract: For decades financial economists have been attempted to determine the optimal investment policy by recognizing the option value embedded in irreversible investment whose project value evolves as a geometric Brownian motion (GBM). This paper aims to examine the effects of the optimal investment trigger and of the misspecification of stochastic processes on investment in real options applications. Specifically, the former explores the consequence of adopting optimal investment rules on the distributions of corporate value under the correct assumption of stochastic process while the latter analyzes the influence on the distributions of corporate value as a result of the misspecification of stochastic processes, i.e., mistaking an alternative process as a GBM. It is found that adopting the correct optimal investment policy may increase corporate value by shifting the value distribution rightward, and the misspecification effect may decrease corporate value by shifting the value distribution leftward. The adoption of the optimal investment trigger has a major impact on investment to such an extent that the downside risk of investment is truncated at the project value of zero, thereby moving the value distributions rightward. The analytical framework is also extended to situations where collection lags are in place, and the result indicates that collection lags reduce the effects of investment trigger and misspecification on investment in an opposite way.
Abstract: Recurrent event data is a special type of multivariate
survival data. Dynamic and frailty models are one of the approaches
that dealt with this kind of data. A comparison between these two
models is studied using the empirical standard deviation of the
standardized martingale residual processes as a way of assessing the
fit of the two models based on the Aalen additive regression model.
Here we found both approaches took heterogeneity into account and
produce residual standard deviations close to each other both in the
simulation study and in the real data set.