Related papers: Model Mismatch Trade-offs in LMMSE Estimation
We study least squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance. When the number of selected features $p$ is at most the sample size $n$, the estimator under consideration…
Suppose data are fitted to some parametric model but that the true model happens to be one with an additional parameter. When a parameter is to be estimated one can use likelihood estimation in the wider model or in the narrow model.…
Time-series forecasting models often encounter abrupt changes in a given period of time which generally occur due to unexpected or unknown events. Despite their scarce occurrences in the training set, abrupt changes incur loss that…
Mean-squared-error (MSE) is one of the most widely used performance metrics for the designs and analysis of multi-input-multiple-output (MIMO) communications. Weighted MSE minimization, a more general formulation of MSE minimization, plays…
A generalized state space representation of dynamical systems with random modes switching according to a white random process is presented. The new formulation includes a term, in the dynamics equation, that depends on the most recent…
This paper estimates free energy, average mutual information, and minimum mean square error (MMSE) of a linear model under two assumptions: (1) the source is generated by a Markov chain, (2) the source is generated via a hidden Markov…
This paper studies nonparametric regression with long memory (LRD) errors and predictors. First, we formulate general conditions which guarantee the standard rate of convergence for a nonparametric kernel estimator. Second, we calculate the…
We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically is in practical applications, an analytic…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
We consider a resampling scheme for parameters estimates in nonlinear regression models. We provide an estimation procedure which recycles, via random weighting, the relevant parameters estimates to construct consistent estimates of the…
Nested error regression models are commonly used to incorporate observational unit specific auxiliary variables to improve small area estimates. When the mean structure of this model is misspecified, there is generally an increase in the…
Environmental model performances need to be assessed using some statistical parameters, such as mean absolute error (MAE) and root mean square error (RMSE). The advantages and disadvantages of these parameters are still in controversial.…
The main purpose of this paper is to study the performance of two linear channel estimators for LTE Downlink systems, the Least Square Error (LSE) and the Linear Minimum Mean Square Error (LMMSE). As LTE is a MIMO-OFDM based system, a…
The minimum mean-squared error (MMSE) is one of the most popular criteria for Bayesian estimation. Conversely, the signal-to-noise ratio (SNR) is a typical performance criterion in communications, radar, and generally detection theory. In…
The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because…
The classical unbiasedness condition utilized e.g. by the best linear unbiased estimator (BLUE) is very stringent. By softening the "global" unbiasedness condition and introducing component-wise conditional unbiasedness conditions instead,…
The problem tackled in this paper is the determination of sample size for a given level and power in the context of a simple linear regression model. At a technical level, the simple linear regression model is a five-parameter model. It is…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
The problem of estimating an unknown deterministic parameter vector from sign measurements with a perturbed sensing matrix is studied in this paper. We analyze the best achievable mean square error (MSE) performance by exploring the…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…