diff --git a/lib/node_modules/@stdlib/stats/incr/nanmse/README.md b/lib/node_modules/@stdlib/stats/incr/nanmse/README.md
new file mode 100644
index 000000000000..00fc7774d970
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmse/README.md
@@ -0,0 +1,147 @@
+
+
+# incrnanmse
+
+> Compute the [mean squared error][mean-squared-error] (MSE) incrementally, ignoring `NaN` values.
+
+
+
+The [mean squared error][mean-squared-error] is defined as
+
+
+
+```math
+\mathop{\mathrm{MSE}} = \frac{1}{n} \sum_{i=0}^{n-1} (y_i - x_i)^2
+```
+
+
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var incrnanmse = require( '@stdlib/stats/incr/nanmse' );
+```
+
+#### incrnanmse()
+
+Returns an accumulator `function` which incrementally computes the [mean squared error][mean-squared-error], ignoring `NaN` values.
+
+```javascript
+var accumulator = incrnanmse();
+```
+
+#### accumulator( \[x, y] )
+
+If provided input values `x` and `y`, the accumulator function returns an updated [mean squared error][mean-squared-error]. If not provided input values `x` and `y`, the accumulator function returns the current [mean squared error][mean-squared-error].
+
+```javascript
+var accumulator = incrnanmse();
+
+var m = accumulator( 2.0, 3.0 );
+// returns 1.0
+
+m = accumulator( 1.0, NaN );
+// returns 1.0
+
+m = accumulator( -1.0, -4.0 );
+// returns 5.0
+
+m = accumulator( -3.0, 5.0 );
+// returns ~24.67
+
+m = accumulator();
+// returns ~24.67
+```
+
+
+
+
+
+
+
+## Notes
+
+- Input values are **not** type checked. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var bernoulli = require( '@stdlib/random/base/bernoulli' );
+var uniform = require( '@stdlib/random/base/uniform' );
+var incrnanmse = require( '@stdlib/stats/incr/nanmse' );
+
+var accumulator;
+var v1;
+var v2;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanmse();
+
+// For each simulated datum, update the mean squared error...
+for ( i = 0; i < 100; i++ ) {
+ v1 = ( bernoulli( 0.8 ) < 1 ) ? NaN : uniform( -50.0, 50.0 );
+ v2 = ( bernoulli( 0.8 ) < 1 ) ? NaN : uniform( -50.0, 50.0 );
+ accumulator( v1, v2 );
+}
+console.log( accumulator() );
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[mean-squared-error]: https://en.wikipedia.org/wiki/Mean_squared_error
+
+
+
+
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmse/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/incr/nanmse/benchmark/benchmark.js
new file mode 100644
index 000000000000..de45639e7222
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmse/benchmark/benchmark.js
@@ -0,0 +1,69 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var pkg = require( './../package.json' ).name;
+var incrnanmse = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var f;
+ var i;
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ f = incrnanmse();
+ if ( typeof f !== 'function' ) {
+ b.fail( 'should return a function' );
+ }
+ }
+ b.toc();
+ if ( typeof f !== 'function' ) {
+ b.fail( 'should return a function' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});
+
+bench( pkg+'::accumulator', function benchmark( b ) {
+ var acc;
+ var v;
+ var i;
+
+ acc = incrnanmse();
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ v = acc( randu()-0.5, randu()-0.5 );
+ if ( v !== v ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( v !== v ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmse/docs/img/equation_mean_squared_error.svg b/lib/node_modules/@stdlib/stats/incr/nanmse/docs/img/equation_mean_squared_error.svg
new file mode 100644
index 000000000000..ad5d623df94f
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmse/docs/img/equation_mean_squared_error.svg
@@ -0,0 +1,60 @@
+
\ No newline at end of file
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmse/docs/repl.txt b/lib/node_modules/@stdlib/stats/incr/nanmse/docs/repl.txt
new file mode 100644
index 000000000000..a99675919bf4
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmse/docs/repl.txt
@@ -0,0 +1,30 @@
+
+{{alias}}()
+ Returns an accumulator function which incrementally computes the mean
+ squared error (MSE), ignoring `NaN` values.
+
+ If provided input values, the accumulator function returns an updated mean
+ squared error. If not provided input values, the accumulator function
+ returns the current mean squared error.
+
+ Returns
+ -------
+ acc: Function
+ Accumulator function.
+
+ Examples
+ --------
+ > var accumulator = {{alias}}();
+ > var m = accumulator()
+ null
+ > m = accumulator( 2.0, 3.0 )
+ 1.0
+ > m = accumulator( 1.0, NaN )
+ 1.0
+ > m = accumulator( -5.0, 2.0 )
+ 25.0
+ > m = accumulator()
+ 25.0
+
+ See Also
+ --------
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmse/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/incr/nanmse/docs/types/index.d.ts
new file mode 100644
index 000000000000..2252f13d33fe
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmse/docs/types/index.d.ts
@@ -0,0 +1,61 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+// TypeScript Version: 4.1
+
+///
+
+/**
+* If provided input values, the accumulator function returns an updated mean squared error. If not provided input values, the accumulator function returns the current mean squared error.
+*
+* @param x - input value
+* @param y - input value
+* @returns mean squared error or null
+*/
+type accumulator = ( x?: number, y?: number ) => number | null;
+
+/**
+* Returns an accumulator function which incrementally computes the mean squared error, ignoring `NaN` values.
+*
+* @returns accumulator function
+*
+* @example
+* var accumulator = incrnanmse();
+*
+* var m = accumulator();
+* // returns null
+*
+* m = accumulator( 2.0, 3.0 );
+* // returns 1.0
+*
+*
+* m = accumulator( 1.0, NaN );
+* // returns 1.0
+*
+* m = accumulator( -5.0, 2.0 );
+* // returns 25.0
+*
+* m = accumulator();
+* // returns 25.0
+*/
+declare function incrnanmse(): accumulator;
+
+
+// EXPORTS //
+
+export = incrnanmse;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmse/docs/types/test.ts b/lib/node_modules/@stdlib/stats/incr/nanmse/docs/types/test.ts
new file mode 100644
index 000000000000..2c466e777a52
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmse/docs/types/test.ts
@@ -0,0 +1,69 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+import incrnanmse = require( './index' );
+
+
+// TESTS //
+
+// The function returns an accumulator function...
+{
+ incrnanmse(); // $ExpectType accumulator
+}
+
+// The compiler throws an error if the function is provided arguments...
+{
+ incrnanmse( '5' ); // $ExpectError
+ incrnanmse( 5 ); // $ExpectError
+ incrnanmse( true ); // $ExpectError
+ incrnanmse( false ); // $ExpectError
+ incrnanmse( null ); // $ExpectError
+ incrnanmse( undefined ); // $ExpectError
+ incrnanmse( [] ); // $ExpectError
+ incrnanmse( {} ); // $ExpectError
+ incrnanmse( ( x: number ): number => x ); // $ExpectError
+}
+
+// The function returns an accumulator function which returns an accumulated result...
+{
+ const acc = incrnanmse();
+
+ acc(); // $ExpectType number | null
+ acc( 3.14, 2.0 ); // $ExpectType number | null
+}
+
+// The compiler throws an error if the returned accumulator function is provided invalid arguments...
+{
+ const acc = incrnanmse();
+
+ acc( '5', 2.0 ); // $ExpectError
+ acc( true, 2.0 ); // $ExpectError
+ acc( false, 2.0 ); // $ExpectError
+ acc( null, 2.0 ); // $ExpectError
+ acc( [], 2.0 ); // $ExpectError
+ acc( {}, 2.0 ); // $ExpectError
+ acc( ( x: number ): number => x, 2.0 ); // $ExpectError
+
+ acc( 3.14, '5' ); // $ExpectError
+ acc( 3.14, true ); // $ExpectError
+ acc( 3.14, false ); // $ExpectError
+ acc( 3.14, null ); // $ExpectError
+ acc( 3.14, [] ); // $ExpectError
+ acc( 3.14, {} ); // $ExpectError
+ acc( 3.14, ( x: number ): number => x ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmse/examples/index.js b/lib/node_modules/@stdlib/stats/incr/nanmse/examples/index.js
new file mode 100644
index 000000000000..4ad6b5917be6
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmse/examples/index.js
@@ -0,0 +1,46 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+var randu = require( '@stdlib/random/base/randu' );
+var incrnanmse = require( './../lib' );
+
+var accumulator;
+var mse;
+var v1;
+var v2;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanmse();
+
+// For each simulated datum, update the mean squared error...
+console.log( '\nValue\tValue\tMSE\n' );
+for ( i = 0; i < 100; i++ ) {
+ if ( randu() < 0.2 ) {
+ v1 = NaN;
+ v2 = NaN;
+ } else {
+ v1 = ( randu()*100.0 ) - 50.0;
+ v2 = ( randu()*100.0 ) - 50.0;
+ }
+ mse = accumulator( v1, v2 );
+ console.log( '%d\t%d\t%d', v1.toFixed( 3 ), v2.toFixed( 3 ), ( mse === null ) ? NaN : mse.toFixed( 3 ) );
+}
+console.log( '\nFinal MSE: %d\n', accumulator() );
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmse/lib/index.js b/lib/node_modules/@stdlib/stats/incr/nanmse/lib/index.js
new file mode 100644
index 000000000000..a05cbae5d80f
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmse/lib/index.js
@@ -0,0 +1,54 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+/**
+* Compute the mean squared error incrementally, ignoring `NaN` values.
+*
+* @module @stdlib/stats/incr/nanmse
+*
+* @example
+* var incrnanmse = require( '@stdlib/stats/incr/nanmse' );
+*
+* var accumulator = incrnanmse();
+*
+* var m = accumulator();
+* // returns null
+*
+* m = accumulator( 2.0, 3.0 );
+* // returns 1.0
+*
+* m = accumulator( 1.0, NaN );
+* // returns 1.0
+*
+* m = accumulator( -5.0, 2.0 );
+* // returns 25.0
+*
+* m = accumulator();
+* // returns 25.0
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmse/lib/main.js b/lib/node_modules/@stdlib/stats/incr/nanmse/lib/main.js
new file mode 100644
index 000000000000..655b1b758b55
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmse/lib/main.js
@@ -0,0 +1,75 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var incrmse = require( '@stdlib/stats/incr/mse' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+
+
+// MAIN //
+
+/**
+* Returns an accumulator function which incrementally computes the mean squared error, ignoring `NaN` values.
+*
+* @returns {Function} accumulator function
+*
+* @example
+* var accumulator = incrnanmse();
+*
+* var m = accumulator();
+* // returns null
+*
+* m = accumulator( 2.0, 3.0 );
+* // returns 1.0
+*
+* m = accumulator( 1.0, NaN );
+* // returns 1.0
+*
+* m = accumulator( -5.0, 2.0 );
+* // returns 25.0
+*
+* m = accumulator();
+* // returns 25.0
+*/
+function incrnanmse() {
+ var mse = incrmse();
+ return accumulator;
+
+ /**
+ * If provided input values, the accumulator function returns an updated mean squared error. If not provided input values, the accumulator function returns the current mean squared error.
+ *
+ * @private
+ * @param {number} [x] - input value
+ * @param {number} [y] - input value
+ * @returns {(number|null)} mean squared error or null
+ */
+ function accumulator( x, y ) {
+ if ( arguments.length === 0 || isnan( x ) || isnan(y) ) {
+ return mse();
+ }
+ return mse( x, y );
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = incrnanmse;
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmse/package.json b/lib/node_modules/@stdlib/stats/incr/nanmse/package.json
new file mode 100644
index 000000000000..7647be05cdc8
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmse/package.json
@@ -0,0 +1,78 @@
+{
+ "name": "@stdlib/stats/incr/nanmse",
+ "version": "0.0.0",
+ "description": "Compute the mean squared error (MSE) incrementally, ignoring NaN values.",
+ "license": "Apache-2.0",
+ "author": {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ },
+ "contributors": [
+ {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ }
+ ],
+ "main": "./lib",
+ "directories": {
+ "benchmark": "./benchmark",
+ "doc": "./docs",
+ "example": "./examples",
+ "lib": "./lib",
+ "test": "./test"
+ },
+ "types": "./docs/types",
+ "scripts": {},
+ "homepage": "https://github.com/stdlib-js/stdlib",
+ "repository": {
+ "type": "git",
+ "url": "git://github.com/stdlib-js/stdlib.git"
+ },
+ "bugs": {
+ "url": "https://github.com/stdlib-js/stdlib/issues"
+ },
+ "dependencies": {},
+ "devDependencies": {},
+ "engines": {
+ "node": ">=0.10.0",
+ "npm": ">2.7.0"
+ },
+ "os": [
+ "aix",
+ "darwin",
+ "freebsd",
+ "linux",
+ "macos",
+ "openbsd",
+ "sunos",
+ "win32",
+ "windows"
+ ],
+ "keywords": [
+ "stdlib",
+ "stdmath",
+ "statistics",
+ "stats",
+ "mathematics",
+ "math",
+ "error",
+ "err",
+ "nan",
+ "msd",
+ "residuals",
+ "deviation",
+ "difference",
+ "diff",
+ "delta",
+ "incremental",
+ "accumulator",
+ "time series",
+ "timeseries",
+ "forecasting",
+ "forecast",
+ "model",
+ "selection",
+ "evaluation",
+ "prediction"
+ ]
+}
diff --git a/lib/node_modules/@stdlib/stats/incr/nanmse/test/test.js b/lib/node_modules/@stdlib/stats/incr/nanmse/test/test.js
new file mode 100644
index 000000000000..b338f81a5e14
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/incr/nanmse/test/test.js
@@ -0,0 +1,129 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var incrnanmse = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof incrnanmse, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function returns an accumulator function', function test( t ) {
+ t.equal( typeof incrnanmse(), 'function', 'returns a function' );
+ t.end();
+});
+
+tape( 'the initial accumulated value is `null`', function test( t ) {
+ var acc = incrnanmse();
+ t.equal( acc(), null, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the accumulator function incrementally computes the mean squared error', function test( t ) {
+ var expected;
+ var actual;
+ var delta;
+ var data;
+ var acc;
+ var sum;
+ var tol;
+ var N;
+ var r;
+ var x;
+ var y;
+ var i;
+ var c;
+
+ data = [
+ [ 2.0, 3.0 ],
+ [ 3.0, -1.0 ],
+ [ 2.0, 5.0 ],
+ [ 1.0, NaN ],
+ [ 4.0, -4.0 ],
+ [ NaN, 2.0 ],
+ [ 3.0, 0.0 ],
+ [ -4.0, 5.0 ]
+ ];
+ N = data.length;
+
+ acc = incrnanmse();
+
+ sum = 0;
+ c = 0;
+ for ( i = 0; i < N; i++ ) {
+ x = data[ i ][ 0 ];
+ y = data[ i ][ 1 ];
+ if ( isnan( x ) === false && isnan( y ) === false ) {
+ r = y - x;
+ sum += r * r;
+ c += 1;
+ expected = sum / c;
+ } else {
+ expected = sum / c;
+ }
+ actual = acc( x, y );
+ if ( actual === expected ) {
+ t.equal( actual, expected, 'returns expected value' );
+ } else {
+ delta = abs( expected - actual );
+ tol = 1.0 * EPS * abs( expected );
+ t.equal( delta <= tol, true, 'within tolerance. Actual: '+actual+'. Expected: '+expected+'. Delta: '+delta+'. Tol: '+tol+'.' );
+ }
+ }
+ t.end();
+});
+
+tape( 'if not provided an input value, the accumulator function returns the current mean squared error', function test( t ) {
+ var expected;
+ var actual;
+ var delta;
+ var data;
+ var acc;
+ var tol;
+ var i;
+
+ data = [
+ [ 2.0, 3.0 ],
+ [ NaN, NaN ],
+ [ 3.0, -5.0 ],
+ [ 2.0, NaN ],
+ [ 1.0, 10.0 ]
+ ];
+ acc = incrnanmse();
+ for ( i = 0; i < data.length; i++ ) {
+ acc( data[ i ][ 0 ], data[ i ][ 1 ] );
+ }
+ actual = acc();
+ expected = ( 1.0 + 64.0 + 81.0 ) / 3.0;
+ delta = abs( expected - actual );
+ tol = 1.0 * EPS * abs( expected );
+ t.equal( delta <= tol, true, 'within tolerance. Actual: '+actual+'. Expected: '+expected+'. Delta: '+delta+'. Tol: '+tol+'.' );
+ t.end();
+});