Forecast rationality under squared error loss implies various bounds on second moments of the data across forecast horizons. For example, the mean squared forecast error should be increasing in the horizon, and the mean squared forecast should be decreasing in the horizon. We propose rationality tests based on these restrictions, including new ones that can be conducted without data on the targ...

Many performance metrics have been introduced in the literature for the evaluation of classification performance, each of them with different origins and areas of application. These metrics include accuracy, unweighted accuracy, the area under the ROC curve or the ROC convex hull, the mean absolute error and the Brier score or mean squared error (with its decomposition into refinement and calib...

Motor learning can be defined as changing performance so as to optimize some function of the task, such as accuracy. The measure of accuracy that is optimized is called a loss function and specifies how the CNS rates the relative success or cost of a particular movement outcome. Models of pointing in sensorimotor control and learning usually assume a quadratic loss function in which the mean sq...

X1, . . . , Xn iid ∼ N (θ, σ), with σ known. Our goal is to estimate θ under squared-error loss. For our first guess, pick the natural estimator X. Note that it has constant risk σ 2 n , which suggests minimaxity because we know that Bayes estimators with constant risk are also minimax estimators. However, X is not Bayes for any prior, because under squared-error loss unbiased estimators are Ba...

Error measures for the evaluation of forecasts are usually based on the size of the forecast errors. Common measures are e.g. the Mean Squared Error (MSE), the Mean Absolute Deviation (MAD) or the Mean Absolute Percentage Error (MAPE). Alternative measures for the comparison of forecasts are turning points or hits-and-misses, where an indicator loss function is used to decide, if a forecast is ...

Estimation in truncated parameter space is one of the most important features in statistical inference, because the frequently used criterion of unbiasedness is useless, since no unbiased estimator exists in general. So, other optimally criteria such as admissibility and minimaxity have to be looked for among others. In this paper we consider a subclass of the exponential families of distributi...

This paper evaluates the out-of-sample forecasting accuracy of eleven models for monthly volatility in fifteen stock markets. Volatility is defined as within-month standard deviation of continuously compounded daily returns on the stock market index of each country for the ten-year period 1988 to 1997. The first half of the sample is retained for the estimation of parameters while the second ha...

Empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function. This paper establishes new testable properties that hold when the forecaster’s loss function is unknown but testable restrictions can be imposed on the data generating process, trading off conditions on the data generating process against co...

Many performance metrics have been introduced in the literature for the evaluation of classification performance, each of them with different origins and areas of application. These metrics include accuracy, macro-accuracy, area under the ROC curve or the ROC convex hull, the mean absolute error and the Brier score or mean squared error (with its decomposition into refinement and calibration). ...

The term “empirical predictor” refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML ...